AI Chatbot Online Characters

AI Chatbot Online Characters — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

• 

  WorkingPoint

  WorkingPoint is a web-based application that provides a suite of small business management tools. It is designed to serve as a single point of access for various business operations, featuring a user-friendly interface. WorkingPoint's functionalities include double-entry bookkeeping, contact management, inventory management, invoicing, and bill and expense management. == Company == WorkingPoint, formerly Netbooks Inc, is a privately held corporation based in San Francisco, CA. The company is backed by CMEA Capital, also based in San Francisco. WorkingPoint has about ten employees and is led by CEO Tate Holt and Chairman Tom Proulx. Proulx is a co-founder of Intuit and an original author of that company’s Quicken personal finance software. The company was founded in 2007 under its original name Netbooks by co-creator Ridgely Evers. Evers set out to design a product that was more user-friendly than Intuit’s Quickbooks, which he also co-created. In mid-2009 the company officially rebranded itself and its flagship product “WorkingPoint”. The purpose of the re-branding was to disassociate the company from the product category of small laptops also known as netbooks. == Social Media Presence == WorkingPoint maintains a daily blog geared toward small business owners and managers. Each week the blog is updated with 3 WorkingPoint product feature or “how-to” posts, 2 subscriber company profiles, and 2 small business coaching posts. The company also maintains a Twitter page and a Facebook page. == Product Description (Free Version) == WorkingPoint allows businesses to invoice up to five customers (repeatedly) and provides account access for up to two individual users free of charge. Online Invoicing WorkingPoint allows users to create customized quotes and invoices online. The invoices can be used to bill customers via email or hardcopy post. WorkingPoint compiles the info from these invoices so users can track customer payments, inventory costs, shipping charges, accounts receivable and sales taxes. Users can also manage customer overpayments, provide customer loyalty discounts, and view a customer invoice history. Bill & Expense Management Users can track their bills and expenses by entering info into the WorkingPoint interface. WorkingPoint compiles this info so users can track categorized expenses, accounts paid, accounts payable, and vendor purchase history. The interface also allows users to add to their inventory while entering billing info. Double-Entry Bookeeping WorkingPoint automatically records entries under the double-entry bookkeeping system (also known as debits and credits) when the user completes invoicing and expense forms. Users can view transactions in general ledger format and perform closing entries if necessary. This functionality is designed for users who do not have an accounting background. Business Contact Management WorkingPoint provides an interface for users to manage their customer and vendor contact info. The software automatically tracks the user’s relationship with contacts, so users can track a contact’s sales and purchase history. Contacts can be imported and exported via numerous email clients including Microsoft Outlook, Yahoo! Mail, Google Gmail, and Mac Address Book. Inventory Management The software automatically adjusts inventory quantities after every purchase and sale. Users can track their current inventory quantity, average cost of inventory on-hand, cost of goods sold (COGS) and top-selling products. Users can also make manual adjustments to inventory when necessary. Financial Reporting Users can view a balance sheet, income statement, or cash flow statement pertaining to their business. The software automatically manages accruals to produce the balance sheet and income statement. Users can choose a data range from which to draw any of these reports. Financial reports can be converted to pdf format or exported (with formulas intact) to OpenOffice or Microsoft Excel. Cash Management WorkingPoint enables users to monitor cash balances on their bank accounts. The software automatically tracks cash inflows and outflows when users manage their accounts payable and accounts receivable. Business Dashboard The Business Dashboard visually and graphically displays key real-time business data. Users can customize the Dashboard to display data of their choosing. Online Company Profile Users can create an online company profile in order to have a presence on the Internet and as a basis for participation in WorkingPoint’s small business community features. Public profiles are featured in the WorkingPoint Company Directory and can be viewed externally using the URL format: https://businessname.workingpoint.com. == Product Description (Premium Version) == The premium version of WorkingPoint costs $10 per month. It includes all of the functionalities of the free version, allowing unlimited invoicing and account access. It also offers the following functions: 1099 Tax Reporting, invoice payment collection via PayPal, Email Marketing via VerticalResponse, and the Premium Reports & Accounting Package. 1099 Tax Reporting Users can identify qualifying companies and individuals for IRS Form 1099 or IRS Form 1096 reporting. WorkingPoint automatically tracks payments made to these companies and individuals. Users can then generate 1099 reports for distribution. Premium Reports & Accounting Package This includes: a Daily Operating Report providing users with sales and cash flow information, customizable accounts categorization, and cash flow statements using the indirect method of reporting. Invoice Payment Collection via PayPal Users can collect payment on their invoices via PayPal. Email Marketing via VerticalResponse The WorkingPoint premium package includes 500 email credits with the email marketing firm VerticalResponse.

  Read more →
• 

  Constellation model

  The constellation model is a probabilistic, generative model for category-level object recognition in computer vision. Like other part-based models, the constellation model attempts to represent an object class by a set of N parts under mutual geometric constraints. Because it considers the geometric relationship between different parts, the constellation model differs significantly from appearance-only, or "bag-of-words" representation models, which explicitly disregard the location of image features. The problem of defining a generative model for object recognition is difficult. The task becomes significantly complicated by factors such as background clutter, occlusion, and variations in viewpoint, illumination, and scale. Ideally, we would like the particular representation we choose to be robust to as many of these factors as possible. In category-level recognition, the problem is even more challenging because of the fundamental problem of intra-class variation. Even if two objects belong to the same visual category, their appearances may be significantly different. However, for structured objects such as cars, bicycles, and people, separate instances of objects from the same category are subject to similar geometric constraints. For this reason, particular parts of an object such as the headlights or tires of a car still have consistent appearances and relative positions. The Constellation Model takes advantage of this fact by explicitly modeling the relative location, relative scale, and appearance of these parts for a particular object category. Model parameters are estimated using an unsupervised learning algorithm, meaning that the visual concept of an object class can be extracted from an unlabeled set of training images, even if that set contains "junk" images or instances of objects from multiple categories. It can also account for the absence of model parts due to appearance variability, occlusion, clutter, or detector error. == History == The idea for a "parts and structure" model was originally introduced by Fischler and Elschlager in 1973. This model has since been built upon and extended in many directions. The Constellation Model, as introduced by Dr. Perona and his colleagues, was a probabilistic adaptation of this approach. In the late '90s, Burl et al. revisited the Fischler and Elschlager model for the purpose of face recognition. In their work, Burl et al. used manual selection of constellation parts in training images to construct a statistical model for a set of detectors and the relative locations at which they should be applied. In 2000, Weber et al. made the significant step of training the model using a more unsupervised learning process, which precluded the necessity for tedious hand-labeling of parts. Their algorithm was particularly remarkable because it performed well even on cluttered and occluded image data. Fergus et al. then improved upon this model by making the learning step fully unsupervised, having both shape and appearance learned simultaneously, and accounting explicitly for the relative scale of parts. == The method of Weber and Welling et al. == In the first step, a standard interest point detection method, such as Harris corner detection, is used to generate interest points. Image features generated from the vicinity of these points are then clustered using k-means or another appropriate algorithm. In this process of vector quantization, one can think of the centroids of these clusters as being representative of the appearance of distinctive object parts. Appropriate feature detectors are then trained using these clusters, which can be used to obtain a set of candidate parts from images. As a result of this process, each image can now be represented as a set of parts. Each part has a type, corresponding to one of the aforementioned appearance clusters, as well as a location in the image space. === Basic generative model === Weber & Welling here introduce the concept of foreground and background. Foreground parts correspond to an instance of a target object class, whereas background parts correspond to background clutter or false detections. Let T be the number of different types of parts. The positions of all parts extracted from an image can then be represented in the following "matrix," X o = ( x 11 , x 12 , ⋯ , x 1 N 1 x 21 , x 22 , ⋯ , x 2 N 2 ⋮ x T 1 , x T 2 , ⋯ , x T N T ) {\displaystyle X^{o}={\begin{pmatrix}x_{11},x_{12},{\cdots },x_{1N_{1}}\\x_{21},x_{22},{\cdots },x_{2N_{2}}\\\vdots \\x_{T1},x_{T2},{\cdots },x_{TN_{T}}\end{pmatrix}}} where N i {\displaystyle N_{i}\,} represents the number of parts of type i ∈ { 1 , … , T } {\displaystyle i\in \{1,\dots ,T\}} observed in the image. The superscript o indicates that these positions are observable, as opposed to missing. The positions of unobserved object parts can be represented by the vector x m {\displaystyle x^{m}\,} . Suppose that the object will be composed of F {\displaystyle F\,} distinct foreground parts. For notational simplicity, we assume here that F = T {\displaystyle F=T\,} , though the model can be generalized to F > T {\displaystyle F>T\,} . A hypothesis h {\displaystyle h\,} is then defined as a set of indices, with h i = j {\displaystyle h_{i}=j\,} , indicating that point x i j {\displaystyle x_{ij}\,} is a foreground point in X o {\displaystyle X^{o}\,} . The generative probabilistic model is defined through the joint probability density p ( X o , x m , h ) {\displaystyle p(X^{o},x^{m},h)\,} . === Model details === The rest of this section summarizes the details of Weber & Welling's model for a single component model. The formulas for multiple component models are extensions of those described here. To parametrize the joint probability density, Weber & Welling introduce the auxiliary variables b {\displaystyle b\,} and n {\displaystyle n\,} , where b {\displaystyle b\,} is a binary vector encoding the presence/absence of parts in detection ( b i = 1 {\displaystyle b_{i}=1\,} if h i > 0 {\displaystyle h_{i}>0\,} , otherwise b i = 0 {\displaystyle b_{i}=0\,} ), and n {\displaystyle n\,} is a vector where n i {\displaystyle n_{i}\,} denotes the number of background candidates included in the i t h {\displaystyle i^{th}} row of X o {\displaystyle X^{o}\,} . Since b {\displaystyle b\,} and n {\displaystyle n\,} are completely determined by h {\displaystyle h\,} and the size of X o {\displaystyle X^{o}\,} , we have p ( X o , x m , h ) = p ( X o , x m , h , n , b ) {\displaystyle p(X^{o},x^{m},h)=p(X^{o},x^{m},h,n,b)\,} . By decomposition, p ( X o , x m , h , n , b ) = p ( X o , x m | h , n , b ) p ( h | n , b ) p ( n ) p ( b ) {\displaystyle p(X^{o},x^{m},h,n,b)=p(X^{o},x^{m}|h,n,b)p(h|n,b)p(n)p(b)\,} The probability density over the number of background detections can be modeled by a Poisson distribution, p ( n ) = ∏ i = 1 T 1 n i ! ( M i ) n i e − M i {\displaystyle p(n)=\prod _{i=1}^{T}{\frac {1}{n_{i}!}}(M_{i})^{n_{i}}e^{-M_{i}}} where M i {\displaystyle M_{i}\,} is the average number of background detections of type i {\displaystyle i\,} per image. Depending on the number of parts F {\displaystyle F\,} , the probability p ( b ) {\displaystyle p(b)\,} can be modeled either as an explicit table of length 2 F {\displaystyle 2^{F}\,} , or, if F {\displaystyle F\,} is large, as F {\displaystyle F\,} independent probabilities, each governing the presence of an individual part. The density p ( h | n , b ) {\displaystyle p(h|n,b)\,} is modeled by p ( h | n , b ) = { 1 ∏ f = 1 F N f b f , if h ∈ H ( b , n ) 0 , for other h {\displaystyle p(h|n,b)={\begin{cases}{\frac {1}{\textstyle \prod _{f=1}^{F}N_{f}^{b_{f}}}},&{\mbox{if }}h\in H(b,n)\\0,&{\mbox{for other }}h\end{cases}}} where H ( b , n ) {\displaystyle H(b,n)\,} denotes the set of all hypotheses consistent with b {\displaystyle b\,} and n {\displaystyle n\,} , and N f {\displaystyle N_{f}\,} denotes the total number of detections of parts of type f {\displaystyle f\,} . This expresses the fact that all consistent hypotheses, of which there are ∏ f = 1 F N f b f {\displaystyle \textstyle \prod _{f=1}^{F}N_{f}^{b_{f}}} , are equally likely in the absence of information on part locations. And finally, p ( X o , x m | h , n ) = p f g ( z ) p b g ( x b g ) {\displaystyle p(X^{o},x^{m}|h,n)=p_{fg}(z)p_{bg}(x_{bg})\,} where z = ( x o x m ) {\displaystyle z=(x^{o}x^{m})\,} are the coordinates of all foreground detections, observed and missing, and x b g {\displaystyle x_{bg}\,} represents the coordinates of the background detections. Note that foreground detections are assumed to be independent of the background. p f g ( z ) {\displaystyle p_{fg}(z)\,} is modeled as a joint Gaussian with mean μ {\displaystyle \mu \,} and covariance Σ {\displaystyle \Sigma \,} . === Classification === The ultimate objective of this model is to classify images into classes "object present" (class C 1 {\displaystyle C_{1}\,} ) and "object absent" (class C 0 {\displaystyle C_{0}\,} ) given t

  Read more →
• 

  Q-learning

  Q-learning is a reinforcement learning algorithm that trains an agent to assign values to its possible actions based on its current state, without requiring a model of the environment (model-free). It can handle problems with stochastic transitions and rewards without requiring adaptations. For example, in a grid maze, an agent learns to reach an exit worth 10 points. At a junction, Q-learning might assign a higher value to moving right than left if right gets to the exit faster, improving this choice by trying both directions over time. For any finite Markov decision process, Q-learning finds an optimal policy in the sense of maximizing the expected value of the total reward over any and all successive steps, starting from the current state. Q-learning can identify an optimal action-selection policy for any given finite Markov decision process, given infinite exploration time and a partly random policy. "Q" refers to the function that the algorithm computes: the expected reward—that is, the quality—of an action taken in a given state. == Reinforcement learning == Reinforcement learning involves an agent, a set of states S {\displaystyle {\mathcal {S}}} , and a set A {\displaystyle {\mathcal {A}}} of actions per state. By performing an action a ∈ A {\displaystyle a\in {\mathcal {A}}} , the agent transitions from state to state. Executing an action in a specific state provides the agent with a reward (a numerical score). The goal of the agent is to maximize its total reward. It does this by adding the maximum reward attainable from future states to the reward for achieving its current state, effectively influencing the current action by the potential future reward. This potential reward is a weighted sum of expected values of the rewards of all future steps starting from the current state. As an example, consider the process of boarding a train, in which the reward is measured by the negative of the total time spent boarding (alternatively, the cost of boarding the train is equal to the boarding time). One strategy is to enter the train door as soon as they open, minimizing the initial wait time for yourself. If the train is crowded, however, then you will have a slow entry after the initial action of entering the door as people are fighting you to depart the train as you attempt to board. The total boarding time, or cost, is then: 0 seconds wait time + 15 seconds fight time On the next day, by random chance (exploration), you decide to wait and let other people depart first. This initially results in a longer wait time. However, less time is spent fighting the departing passengers. Overall, this path has a higher reward than that of the previous day, since the total boarding time is now: 5 second wait time + 0 second fight time Through exploration, despite the initial (patient) action resulting in a larger cost (or negative reward) than in the forceful strategy, the overall cost is lower, thus revealing a more rewarding strategy. == Algorithm == After Δ t {\displaystyle \Delta t} steps into the future the agent will decide some next step. The weight for this step is calculated as γ Δ t {\displaystyle \gamma ^{\Delta t}} , where γ {\displaystyle \gamma } (the discount factor) is a number between 0 and 1 ( 0 ≤ γ ≤ 1 {\displaystyle 0\leq \gamma \leq 1} ). Assuming γ < 1 {\displaystyle \gamma <1} , it has the effect of valuing rewards received earlier higher than those received later (reflecting the value of a "good start"). γ {\displaystyle \gamma } may also be interpreted as the probability to succeed (or survive) at every step Δ t {\displaystyle \Delta t} . The algorithm, therefore, has a function that calculates the quality of a state–action combination: Q : S × A → R {\displaystyle Q:{\mathcal {S}}\times {\mathcal {A}}\to \mathbb {R} } . Before learning begins, ⁠ Q {\displaystyle Q} ⁠ is initialized to a possibly arbitrary fixed value (chosen by the programmer). Then, at each time t {\displaystyle t} the agent selects an action A t {\displaystyle A_{t}} , observes a reward R t + 1 {\displaystyle R_{t+1}} , enters a new state S t + 1 {\displaystyle S_{t+1}} (that may depend on both the previous state S t {\displaystyle S_{t}} and the selected action), and Q {\displaystyle Q} is updated. The core of the algorithm is a Bellman equation as a simple value iteration update, using the weighted average of the current value and the new information: Q n e w ( S t , A t ) ← ( 1 − α ⏟ learning rate ) ⋅ Q ( S t , A t ) ⏟ current value + α ⏟ learning rate ⋅ ( R t + 1 ⏟ reward + γ ⏟ discount factor ⋅ max a Q ( S t + 1 , a ) ⏟ estimate of optimal future value ⏟ new value (temporal difference target) ) {\displaystyle Q^{new}(S_{t},A_{t})\leftarrow (1-\underbrace {\alpha } _{\text{learning rate}})\cdot \underbrace {Q(S_{t},A_{t})} _{\text{current value}}+\underbrace {\alpha } _{\text{learning rate}}\cdot {\bigg (}\underbrace {\underbrace {R_{t+1}} _{\text{reward}}+\underbrace {\gamma } _{\text{discount factor}}\cdot \underbrace {\max _{a}Q(S_{t+1},a)} _{\text{estimate of optimal future value}}} _{\text{new value (temporal difference target)}}{\bigg )}} where R t + 1 {\displaystyle R_{t+1}} is the reward received when moving from the state S t {\displaystyle S_{t}} to the state S t + 1 {\displaystyle S_{t+1}} , and α {\displaystyle \alpha } is the learning rate ( 0 < α ≤ 1 ) {\displaystyle (0<\alpha \leq 1)} . Note that Q n e w ( S t , A t ) {\displaystyle Q^{new}(S_{t},A_{t})} is the sum of three terms: ( 1 − α ) Q ( S t , A t ) {\displaystyle (1-\alpha )Q(S_{t},A_{t})} : the current value (weighted by one minus the learning rate) α R t + 1 {\displaystyle \alpha \,R_{t+1}} : the reward R t + 1 {\displaystyle R_{t+1}} to obtain if action A t {\displaystyle A_{t}} is taken when in state S t {\displaystyle S_{t}} (weighted by learning rate) α γ max a Q ( S t + 1 , a ) {\displaystyle \alpha \gamma \max _{a}Q(S_{t+1},a)} : the maximum reward that can be obtained from state S t + 1 {\displaystyle S_{t+1}} (weighted by learning rate and discount factor) An episode of the algorithm ends when state S t + 1 {\displaystyle S_{t+1}} is a final or terminal state. However, Q-learning can also learn in non-episodic tasks (as a result of the property of convergent infinite series). If the discount factor is lower than 1, the action values are finite even if the problem can contain infinite loops or paths. For all final states s f {\displaystyle s_{f}} , Q ( s f , a ) {\displaystyle Q(s_{f},a)} is never updated, but is set to the reward value r {\displaystyle r} observed for state s f {\displaystyle s_{f}} . In most cases, Q ( s f , a ) {\displaystyle Q(s_{f},a)} can be taken to equal zero. == Influence of variables == === Learning rate === The learning rate or step size determines to what extent newly acquired information overrides old information. A factor of 0 makes the agent learn nothing (exclusively exploiting prior knowledge), while a factor of 1 makes the agent consider only the most recent information (ignoring prior knowledge to explore possibilities). In fully deterministic environments, a learning rate of α t = 1 {\displaystyle \alpha _{t}=1} is optimal. When the problem is stochastic, the algorithm converges under some technical conditions on the learning rate that require it to decrease to zero. In practice, often a constant learning rate is used, such as α t = 0.1 {\displaystyle \alpha _{t}=0.1} for all t {\displaystyle t} . === Discount factor === The discount factor ⁠ γ {\displaystyle \gamma } ⁠ determines the importance of future rewards. A factor of 0 will make the agent "myopic" (or short-sighted) by only considering current rewards, i.e. r t {\displaystyle r_{t}} (in the update rule above), while a factor approaching 1 will make it strive for a long-term high reward. If the discount factor meets or exceeds 1, the action values may diverge. For ⁠ γ = 1 {\displaystyle \gamma =1} ⁠, without a terminal state, or if the agent never reaches one, all environment histories become infinitely long, and utilities with additive, undiscounted rewards generally become infinite. Even with a discount factor only slightly lower than 1, Q-function learning leads to propagation of errors and instabilities when the value function is approximated with an artificial neural network. In that case, starting with a lower discount factor and increasing it towards its final value accelerates learning. === Initial conditions (Q0) === Since Q-learning is an iterative algorithm, it implicitly assumes an initial condition before the first update occurs. High initial values, also known as "optimistic initial conditions", can encourage exploration: no matter what action is selected, the update rule will cause it to have lower values than the other alternative, thus increasing their choice probability. The first reward r {\displaystyle r} can be used to reset the initial conditions. According to this idea, the first time an action is taken the reward is used to set the value

  Read more →
• 

  Randomized weighted majority algorithm

  The randomized weighted majority algorithm is an algorithm in machine learning theory for aggregating expert predictions to a series of decision problems. It is a simple and effective method based on weighted voting which improves on the mistake bound of the deterministic weighted majority algorithm. In fact, in the limit, its prediction rate can be arbitrarily close to that of the best-predicting expert. == Example == Imagine that every morning before the stock market opens, we get a prediction from each of our "experts" about whether the stock market will go up or down. Our goal is to somehow combine this set of predictions into a single prediction that we then use to make a buy or sell decision for the day. The principal challenge is that we do not know which experts will give better or worse predictions. The RWMA gives us a way to do this combination such that our prediction record will be nearly as good as that of the single expert which, in hindsight, gave the most accurate predictions. == Motivation == In machine learning, the weighted majority algorithm (WMA) is a deterministic meta-learning algorithm for aggregating expert predictions. In pseudocode, the WMA is as follows: initialize all experts to weight 1 for each round: add each expert's weight to the option they predicted predict the option with the largest weighted sum multiply the weights of all experts who predicted wrongly by 1 2 {\displaystyle {\frac {1}{2}}} Suppose there are n {\displaystyle n} experts and the best expert makes m {\displaystyle m} mistakes. Then, the weighted majority algorithm (WMA) makes at most 2.4 ( log 2 ⁡ n + m ) {\displaystyle 2.4(\log _{2}n+m)} mistakes. This bound is highly problematic in the case of highly error-prone experts. Suppose, for example, the best expert makes a mistake 20% of the time; that is, in N = 100 {\displaystyle N=100} rounds using n = 10 {\displaystyle n=10} experts, the best expert makes m = 20 {\displaystyle m=20} mistakes. Then, the weighted majority algorithm only guarantees an upper bound of 2.4 ( log 2 ⁡ 10 + 20 ) ≈ 56 {\displaystyle 2.4(\log _{2}10+20)\approx 56} mistakes. As this is a known limitation of the weighted majority algorithm, various strategies have been explored in order to improve the dependence on m {\displaystyle m} . In particular, we can do better by introducing randomization. Drawing inspiration from the Multiplicative Weights Update Method algorithm, we will probabilistically make predictions based on how the experts have performed in the past. Similarly to the WMA, every time an expert makes a wrong prediction, we will decrement their weight. Mirroring the MWUM, we will then use the weights to make a probability distribution over the actions and draw our action from this distribution (instead of deterministically picking the majority vote as the WMA does). == Randomized weighted majority algorithm (RWMA) == The randomized weighted majority algorithm is an attempt to improve the dependence of the mistake bound of the WMA on m {\displaystyle m} . Instead of predicting based on majority vote, the weights, are used as probabilities for choosing the experts in each round and are updated over time (hence the name randomized weighted majority). Precisely, if w i {\displaystyle w_{i}} is the weight of expert i {\displaystyle i} , let W = ∑ i w i {\displaystyle W=\sum _{i}w_{i}} . We will follow expert i {\displaystyle i} with probability w i W {\displaystyle {\frac {w_{i}}{W}}} . This results in the following algorithm: initialize all experts to weight 1. for each round: add all experts' weights together to obtain the total weight W {\displaystyle W} choose expert i {\displaystyle i} randomly with probability w i W {\displaystyle {\frac {w_{i}}{W}}} predict as the chosen expert predicts multiply the weights of all experts who predicted wrongly by β {\displaystyle \beta } The goal is to bound the worst-case expected number of mistakes, assuming that the adversary has to select one of the answers as correct before we make our coin toss. This is a reasonable assumption in, for instance, the stock market example provided above: the variance of a stock price should not depend on the opinions of experts that influence private buy or sell decisions, so we can treat the price change as if it was decided before the experts gave their recommendations for the day. The randomized algorithm is better in the worst case than the deterministic algorithm (weighted majority algorithm): in the latter, the worst case was when the weights were split 50/50. But in the randomized version, since the weights are used as probabilities, there would still be a 50/50 chance of getting it right. In addition, generalizing to multiplying the weights of the incorrect experts by β < 1 {\displaystyle \beta <1} instead of strictly 1 2 {\displaystyle {\frac {1}{2}}} allows us to trade off between dependence on m {\displaystyle m} and log 2 ⁡ n {\displaystyle \log _{2}n} . This trade-off will be quantified in the analysis section. == Analysis == Let W t {\displaystyle W_{t}} denote the total weight of all experts at round t {\displaystyle t} . Also let F t {\displaystyle F_{t}} denote the fraction of weight placed on experts which predict the wrong answer at round t {\displaystyle t} . Finally, let N {\displaystyle N} be the total number of rounds in the process. By definition, F t {\displaystyle F_{t}} is the probability that the algorithm makes a mistake on round t {\displaystyle t} . It follows from the linearity of expectation that if M {\displaystyle M} denotes the total number of mistakes made during the entire process, E [ M ] = ∑ t = 1 N F t {\displaystyle E[M]=\sum _{t=1}^{N}F_{t}} . After round t {\displaystyle t} , the total weight is decreased by ( 1 − β ) F t W t {\displaystyle \ (1-\beta )F_{t}W_{t}} , since all weights corresponding to a wrong answer are multiplied by β < 1 {\displaystyle \ \beta <1} . It then follows that W t + 1 = W t ( 1 − ( 1 − β ) F t ) {\displaystyle W_{t+1}=W_{t}(1-(1-\beta )F_{t})} . By telescoping, since W 1 = n {\displaystyle W_{1}=n} , it follows that the total weight after the process concludes is On the other hand, suppose that m {\displaystyle \ m} is the number of mistakes made by the best-performing expert. At the end, this expert has weight β m {\displaystyle \ \beta ^{m}} . It follows, then, that the total weight is at least this much; in other words, W ≥ β m {\displaystyle \ W\geq \beta ^{m}} . This inequality and the above result imply Taking the natural logarithm of both sides yields Now, the Taylor series of the natural logarithm is In particular, it follows that ln ⁡ ( 1 − ( 1 − β ) F t ) < − ( 1 − β ) F t {\displaystyle \ \ln(1-(1-\beta )F_{t})<-(1-\beta )F_{t}} . Thus, Recalling that E [ M ] = ∑ t = 1 N F t {\displaystyle E[M]=\sum _{t=1}^{N}F_{t}} and rearranging, it follows that Now, as β → 1 {\displaystyle \beta \to 1} from below, the first constant tends to 1 {\displaystyle 1} ; however, the second constant tends to + ∞ {\displaystyle +\infty } . To quantify this tradeoff, define ε = 1 − β {\displaystyle \varepsilon =1-\beta } to be the penalty associated with getting a prediction wrong. Then, again applying the Taylor series of the natural logarithm, It then follows that the mistake bound, for small ε {\displaystyle \varepsilon } , can be written in the form ( 1 + ϵ 2 + O ( ε 2 ) ) m + ϵ − 1 ln ⁡ ( n ) {\displaystyle \ \left(1+{\frac {\epsilon }{2}}+O(\varepsilon ^{2})\right)m+\epsilon ^{-1}\ln(n)} . In English, the less that we penalize experts for their mistakes, the more that additional experts will lead to initial mistakes but the closer we get to capturing the predictive accuracy of the best expert as time goes on. In particular, given a sufficiently low value of ε {\displaystyle \varepsilon } and enough rounds, the randomized weighted majority algorithm can get arbitrarily close to the correct prediction rate of the best expert. In particular, as long as m {\displaystyle m} is sufficiently large compared to ln ⁡ ( n ) {\displaystyle \ln(n)} (so that their ratio is sufficiently small), we can assign we can obtain an upper bound on the number of mistakes equal to This implies that the "regret bound" on the algorithm (that is, how much worse it performs than the best expert) is sublinear, at O ( m ln ⁡ ( n ) ) {\displaystyle O({\sqrt {m\ln(n)}})} . == Revisiting the motivation == Recall that the motivation for the randomized weighted majority algorithm was given by an example where the best expert makes a mistake 20% of the time. Precisely, in N = 100 {\displaystyle N=100} rounds, with n = 10 {\displaystyle n=10} experts, where the best expert makes m = 20 {\displaystyle m=20} mistakes, the deterministic weighted majority algorithm only guarantees an upper bound of 2.4 ( log 2 ⁡ 10 + 20 ) ≈ 56 {\displaystyle 2.4(\log _{2}10+20)\approx 56} . By the analysis above, it follows that minimizing the number of worst-case expected mistakes is equivalent to minimizing the fun

  Read more →
• 

  Apertus (LLM)

  Apertus is a public large language model, developed by the Swiss AI Initiative (a collaboration between EPFL, ETH Zurich, and the Swiss National Supercomputing Centre). It was released on September 2, 2025, under the free and open-source Apache 2.0 license. Designed initially for business and research use cases around the world, Apertus was trained on over 1800 languages, and comes in 8 billion or 70 billion parameter versions and is available on Hugging Face for download. The model was developed aiming to adhere to European copyright law, and is one of the first examples of AI as a public good in the vein of AI Sovereignty. It is also the first large model to comply with the European Union's Artificial Intelligence Act. At its launch, the model creators emphasized multilinguality, transparency, and auditability as priorities in contrast to commercial frontier model. While international reception was largely positive, the first iteration was significantly behind the capabilities of frontier models and needs adaptation for many use cases with chatbots being a secondary but not a primary use case. As of late 2025, it was considered the largest and most capable fully open model. The capability of future models will depend in part on how much more funding can be secured.

  Read more →
• 

  Perceptron

  In machine learning, the perceptron is an algorithm for supervised learning of binary classifiers. A binary classifier is a function that can decide whether or not an input, represented by a vector of numbers, belongs to some specific class. It is a type of linear classifier, i.e. a classification algorithm that makes its predictions based on a linear predictor function combining a set of weights with the feature vector. == History == The artificial neuron and artificial neural network were invented in 1943 by Warren McCulloch and Walter Pitts in their seminal paper "A Logical Calculus of the Ideas Immanent in Nervous Activity". In 1957, Frank Rosenblatt was at the Cornell Aeronautical Laboratory. He simulated the perceptron on an IBM 704. Later, he obtained funding by the Information Systems Branch of the United States Office of Naval Research and the Rome Air Development Center, to build a custom-made computer, the Mark I Perceptron. It was first publicly demonstrated on 23 June 1960. The machine was "part of a previously secret four-year NPIC [the US' National Photographic Interpretation Center] effort from 1963 through 1966 to develop this algorithm into a useful tool for photo-interpreters". Rosenblatt described the details of the perceptron in a 1958 paper. His organization of a perceptron is constructed of three kinds of cells ("units"): S, A, R, which stand for "sensory", "association" and "response". He presented at the first international symposium on AI, Mechanisation of Thought Processes, which took place in 1958 November. Rosenblatt's project was funded under Contract Nonr-401(40) "Cognitive Systems Research Program", which lasted from 1959 to 1970, and Contract Nonr-2381(00) "Project PARA" ("PARA" means "Perceiving and Recognition Automata"), which lasted from 1957 to 1963. In 1959, the Institute for Defense Analysis awarded his group a $10,000 contract. By September 1961, the ONR awarded further $153,000 worth of contracts, with $108,000 committed for 1962. The ONR research manager, Marvin Denicoff, stated that ONR, instead of ARPA, funded the Perceptron project, because the project was unlikely to produce technological results in the near or medium term. Funding from ARPA go up to the order of millions dollars, while from ONR are on the order of 10,000 dollars. Meanwhile, the head of IPTO at ARPA, J.C.R. Licklider, was interested in 'self-organizing', 'adaptive' and other biologically-inspired methods in the 1950s; but by the mid-1960s he was openly critical of these, including the perceptron. Instead he strongly favored the logical AI approach of Simon and Newell. === Mark I Perceptron machine === The perceptron was intended to be a machine, rather than a program, and while its first implementation was in software for the IBM 704, it was subsequently implemented in custom-built hardware as the Mark I Perceptron with the project name "Project PARA", designed for image recognition. The machine is currently in Smithsonian National Museum of American History. The Mark I Perceptron had three layers. One version was implemented as follows: An array of 400 photocells arranged in a 20x20 grid, named "sensory units" (S-units), or "input retina". Each S-unit can connect to up to 40 A-units. A hidden layer of 512 perceptrons, named "association units" (A-units). An output layer of eight perceptrons, named "response units" (R-units). Rosenblatt called this three-layered perceptron network the alpha-perceptron, to distinguish it from other perceptron models he experimented with. The S-units are connected to the A-units randomly (according to a table of random numbers) via a plugboard (see photo), to "eliminate any particular intentional bias in the perceptron". The connection weights are fixed, not learned. Rosenblatt was adamant about the random connections, as he believed the retina was randomly connected to the visual cortex, and he wanted his perceptron machine to resemble human visual perception. The A-units are connected to the R-units, with adjustable weights encoded in potentiometers, and weight updates during learning were performed by electric motors.The hardware details are in an operators' manual. In a 1958 press conference organized by the US Navy, Rosenblatt made statements about the perceptron that caused a heated controversy among the fledgling AI community; based on Rosenblatt's statements, The New York Times reported the perceptron to be "the embryo of an electronic computer that [the Navy] expects will be able to walk, talk, see, write, reproduce itself and be conscious of its existence." The Photo Division of Central Intelligence Agency, from 1960 to 1964, studied the use of Mark I Perceptron machine for recognizing militarily interesting silhouetted targets (such as planes and ships) in aerial photos. === Principles of Neurodynamics (1962) === Rosenblatt described his experiments with many variants of the Perceptron machine in a book Principles of Neurodynamics (1962). The book is a published version of the 1961 report. Among the variants are: "cross-coupling" (connections between units within the same layer) with possibly closed loops, "back-coupling" (connections from units in a later layer to units in a previous layer), four-layer perceptrons where the last two layers have adjustable weights (and thus a proper multilayer perceptron), incorporating time-delays to perceptron units, to allow for processing sequential data, analyzing audio (instead of images). The machine was shipped from Cornell to Smithsonian in 1967, under a government transfer administered by the Office of Naval Research. === Perceptrons (1969) === Although the perceptron initially seemed promising, it was quickly proved that perceptrons could not be trained to recognise many classes of patterns. This caused the field of neural network research to stagnate for many years, before it was recognised that a feedforward neural network with two or more layers (also called a multilayer perceptron) had greater processing power than perceptrons with one layer (also called a single-layer perceptron). Single-layer perceptrons are only capable of learning linearly separable patterns. For a classification task with some step activation function, a single node will have a single line dividing the data points forming the patterns. More nodes can create more dividing lines, but those lines must somehow be combined to form more complex classifications. A second layer of perceptrons, or even linear nodes, are sufficient to solve many otherwise non-separable problems. In 1969, a famous book entitled Perceptrons by Marvin Minsky and Seymour Papert showed that it was impossible for these classes of network to learn an XOR function. It is often incorrectly believed that they also conjectured that a similar result would hold for a multi-layer perceptron network. However, this is not true, as both Minsky and Papert already knew that multi-layer perceptrons were capable of producing an XOR function. (See the page on Perceptrons (book) for more information.) Nevertheless, the often-miscited Minsky and Papert text caused a significant decline in interest and funding of neural network research. It took ten more years until neural network research experienced a resurgence in the 1980s. This text was reprinted in 1987 as "Perceptrons - Expanded Edition" where some errors in the original text are shown and corrected. === Subsequent work === Rosenblatt continued working on perceptrons despite diminishing funding. The last attempt was Tobermory, built between 1961 and 1967, built for speech recognition. It occupied an entire room. It had 4 layers with 12,000 weights implemented by toroidal magnetic cores. By the time of its completion, simulation on digital computers had become faster than purpose-built perceptron machines. He died in a boating accident in 1971. A simulation program for neural networks was written for IBM 7090/7094, and was used to study various pattern recognition applications, such as character recognition, particle tracks in bubble-chamber photographs; phoneme, isolated word, and continuous speech recognition; speaker verification; and center-of-attention mechanisms for image processing. The kernel perceptron algorithm was already introduced in 1964 by Aizerman et al. Margin bounds guarantees were given for the Perceptron algorithm in the general non-separable case first by Freund and Schapire (1998), and more recently by Mohri and Rostamizadeh (2013) who extend previous results and give new and more favorable L1 bounds. The perceptron is a simplified model of a biological neuron. While the complexity of biological neuron models is often required to fully understand neural behavior, research suggests a perceptron-like linear model can produce some behavior seen in real neurons. The solution spaces of decision boundaries for all binary functions and learning behaviors are studied in. == Definition == In the modern sense, the perceptron is an algori

  Read more →
• 

  K-nearest neighbors algorithm

  In statistics, the k-nearest neighbors algorithm (k-NN) is a non-parametric supervised learning method. It was first developed by Evelyn Fix and Joseph Hodges in 1951, and later expanded by Thomas Cover. In classification, a new example is assigned a label based on the labels of its k nearest training examples; in regression, the prediction is computed from the values of those neighbors. Most often, it is used for classification, as a k-NN classifier, the output of which is a class membership. An object is classified by a plurality vote of its neighbors, with the object being assigned to the class most common among its k nearest neighbors (k is a positive integer, typically small). If k = 1, then the object is simply assigned to the class of that single nearest neighbor. The k-NN algorithm can also be generalized for regression. In k-NN regression, also known as nearest neighbor smoothing, the output is the property value for the object. This value is the average of the values of k nearest neighbors. If k = 1, then the output is simply assigned to the value of that single nearest neighbor, also known as nearest neighbor interpolation. For both classification and regression, a useful technique can be to assign weights to the contributions of the neighbors, so that nearer neighbors contribute more to the average than distant ones. For example, a common weighting scheme consists of giving each neighbor a weight of 1/d, where d is the distance to the neighbor. The input consists of the k closest training examples in a data set. The neighbors are taken from a set of objects for which the class (for k-NN classification) or the object property value (for k-NN regression) is known. This can be thought of as the training set for the algorithm, though no explicit training step is required. A peculiarity (sometimes even a disadvantage) of the k-NN algorithm is its sensitivity to the local structure of the data. In k-NN classification the function is only approximated locally and all computation is deferred until function evaluation. Since this algorithm relies on distance, if the features represent different physical units or come in vastly different scales, then feature-wise normalizing of the training data can greatly improve its accuracy. == Statistical setting == Suppose we have pairs ( X 1 , Y 1 ) , ( X 2 , Y 2 ) , … , ( X n , Y n ) {\displaystyle (X_{1},Y_{1}),(X_{2},Y_{2}),\dots ,(X_{n},Y_{n})} taking values in R d × { 1 , 2 } {\displaystyle \mathbb {R} ^{d}\times \{1,2\}} , where Y is the class label of X, so that X | Y = r ∼ P r {\displaystyle X|Y=r\sim P_{r}} for r = 1 , 2 {\displaystyle r=1,2} (and probability distributions P r {\displaystyle P_{r}} ). Given some norm ‖ ⋅ ‖ {\displaystyle \|\cdot \|} on R d {\displaystyle \mathbb {R} ^{d}} and a point x ∈ R d {\displaystyle x\in \mathbb {R} ^{d}} , let ( X ( 1 ) , Y ( 1 ) ) , … , ( X ( n ) , Y ( n ) ) {\displaystyle (X_{(1)},Y_{(1)}),\dots ,(X_{(n)},Y_{(n)})} be a reordering of the training data such that ‖ X ( 1 ) − x ‖ ≤ ⋯ ≤ ‖ X ( n ) − x ‖ {\displaystyle \|X_{(1)}-x\|\leq \dots \leq \|X_{(n)}-x\|} . == Algorithm == The training examples are vectors in a multidimensional feature space, each with a class label. The training phase of the algorithm consists only of storing the feature vectors and class labels of the training samples. In the classification phase, k is a user-defined constant, and an unlabeled vector (a query or test point) is classified by assigning the label which is most frequent among the k training samples nearest to that query point. A commonly used distance metric for continuous variables is Euclidean distance. For discrete variables, such as for text classification, another metric can be used, such as the overlap metric (or Hamming distance). In the context of gene expression microarray data, for example, k-NN has been employed with correlation coefficients, such as Pearson and Spearman, as a metric. Often, the classification accuracy of k-NN can be improved significantly if the distance metric is learned with specialized algorithms such as large margin nearest neighbor or neighborhood components analysis. A drawback of the basic "majority voting" classification occurs when the class distribution is skewed. That is, examples of a more frequent class tend to dominate the prediction of the new example, because they tend to be common among the k nearest neighbors due to their large number. One way to overcome this problem is to weight the classification, taking into account the distance from the test point to each of its k nearest neighbors. The class (or value, in regression problems) of each of the k nearest points is multiplied by a weight proportional to the inverse of the distance from that point to the test point. Another way to overcome skew is by abstraction in data representation. For example, in a self-organizing map (SOM), each node is a representative (a center) of a cluster of similar points, regardless of their density in the original training data. k-NN can then be applied to the SOM. == Parameter selection == The best choice of k depends upon the data; generally, larger values of k reduces effect of the noise on the classification, but make boundaries between classes less distinct. A good k can be selected by various heuristic techniques (see hyperparameter optimization). The special case where the class is predicted to be the class of the closest training sample (i.e. when k = 1) is called the nearest neighbor algorithm. The accuracy of the k-NN algorithm can be severely degraded by the presence of noisy or irrelevant features, or if the feature scales are not consistent with their importance. Much research effort has been put into selecting or scaling features to improve classification. A particularly popular approach is the use of evolutionary algorithms to optimize feature scaling. Another popular approach is to scale features by the mutual information of the training data with the training classes. In binary (two class) classification problems, it is helpful to choose k to be an odd number as this avoids tied votes. One popular way of choosing the empirically optimal k in this setting is via bootstrap method. == The 1-nearest neighbor classifier == The most intuitive nearest neighbour type classifier is the one nearest neighbour classifier that assigns a point x to the class of its closest neighbour in the feature space, that is C n 1 n n ( x ) = Y ( 1 ) {\displaystyle C_{n}^{1nn}(x)=Y_{(1)}} . As the size of training data set approaches infinity, the one nearest neighbour classifier guarantees an error rate of no worse than twice the Bayes error rate (the minimum achievable error rate given the distribution of the data). == The weighted nearest neighbour classifier == The k-nearest neighbour classifier can be viewed as assigning the k nearest neighbours a weight 1 / k {\displaystyle 1/k} and all others 0 weight. This can be generalised to weighted nearest neighbour classifiers. That is, where the ith nearest neighbour is assigned a weight w n i {\displaystyle w_{ni}} , with ∑ i = 1 n w n i = 1 {\textstyle \sum _{i=1}^{n}w_{ni}=1} . An analogous result on the strong consistency of weighted nearest neighbour classifiers also holds. Let C n w n n {\displaystyle C_{n}^{wnn}} denote the weighted nearest classifier with weights { w n i } i = 1 n {\displaystyle \{w_{ni}\}_{i=1}^{n}} . Subject to regularity conditions, which in asymptotic theory are conditional variables which require assumptions to differentiate among parameters with some criteria. On the class distributions the excess risk has the following asymptotic expansion R R ( C n w n n ) − R R ( C Bayes ) = ( B 1 s n 2 + B 2 t n 2 ) { 1 + o ( 1 ) } , {\displaystyle {\mathcal {R}}_{\mathcal {R}}(C_{n}^{wnn})-{\mathcal {R}}_{\mathcal {R}}(C^{\text{Bayes}})=\left(B_{1}s_{n}^{2}+B_{2}t_{n}^{2}\right)\{1+o(1)\},} for constants B 1 {\displaystyle B_{1}} and B 2 {\displaystyle B_{2}} where s n 2 = ∑ i = 1 n w n i 2 {\displaystyle s_{n}^{2}=\sum _{i=1}^{n}w_{ni}^{2}} and t n = n − 2 / d ∑ i = 1 n w n i { i 1 + 2 / d − ( i − 1 ) 1 + 2 / d } {\displaystyle t_{n}=n^{-2/d}\sum _{i=1}^{n}w_{ni}\left\{i^{1+2/d}-(i-1)^{1+2/d}\right\}} . The optimal weighting scheme { w n i ∗ } i = 1 n {\displaystyle \{w_{ni}^{}\}_{i=1}^{n}} , that balances the two terms in the display above, is given as follows: set k ∗ = ⌊ B n 4 d + 4 ⌋ {\displaystyle k^{}=\lfloor Bn^{\frac {4}{d+4}}\rfloor } , w n i ∗ = 1 k ∗ [ 1 + d 2 − d 2 k ∗ 2 / d { i 1 + 2 / d − ( i − 1 ) 1 + 2 / d } ] {\displaystyle w_{ni}^{}={\frac {1}{k^{}}}\left[1+{\frac {d}{2}}-{\frac {d}{2{k^{}}^{2/d}}}\{i^{1+2/d}-(i-1)^{1+2/d}\}\right]} for i = 1 , 2 , … , k ∗ {\displaystyle i=1,2,\dots ,k^{}} and w n i ∗ = 0 {\displaystyle w_{ni}^{}=0} for i = k ∗ + 1 , … , n {\displaystyle i=k^{}+1,\dots ,n} . With optimal weights the dominant term in the asymptotic expansion of the excess risk is O ( n − 4 d + 4 ) {\displaystyle {\mathcal {O}}(n^{-{\frac {4}{d+4}}})}

  Read more →
• 

  Kubeflow

  Kubeflow is an open-source platform for machine learning and MLOps on Kubernetes introduced by Google. The different stages in a typical machine learning lifecycle are represented with different software components in Kubeflow, including model development (Kubeflow Notebooks), model training (Kubeflow Pipelines, Kubeflow Training Operator), model serving (KServe), and automated machine learning (Katib). Each component of Kubeflow can be deployed separately, and it is not a requirement to deploy every component. == History == The Kubeflow project was first announced at KubeCon + CloudNativeCon North America 2017 by Google engineers David Aronchick, Jeremy Lewi, and Vishnu Kannan to address a perceived lack of flexible options for building production-ready machine learning systems. The project has also stated it began as a way for Google to open-source how they ran TensorFlow internally. The first release of Kubeflow (Kubeflow 0.1) was announced at KubeCon + CloudNativeCon Europe 2018. Kubeflow 1.0 was released in March 2020 via a public blog post announcing that many Kubeflow components were graduating to a "stable status", indicating they were now ready for production usage. In October 2022, Google announced that the Kubeflow project had applied to join the Cloud Native Computing Foundation. In July 2023, the foundation voted to accept Kubeflow as an incubating stage project. == Components == === Kubeflow Notebooks for model development === Machine learning models are developed in the notebooks component called Kubeflow Notebooks. The component runs web-based development environments inside a Kubernetes cluster, with native support for Jupyter Notebook, Visual Studio Code, and RStudio. === Kubeflow Pipelines for model training === Once developed, models are trained in the Kubeflow Pipelines component. The component acts as a platform for building and deploying portable, scalable machine learning workflows based on Docker containers. Google Cloud Platform has adopted the Kubeflow Pipelines DSL within its Vertex AI Pipelines product. === Kubeflow Training Operator for model training === For certain machine learning models and libraries, the Kubeflow Training Operator component provides Kubernetes custom resources support. The component runs distributed or non-distributed TensorFlow, PyTorch, Apache MXNet, XGBoost, and MPI training jobs on Kubernetes. === KServe for model serving === The KServe component (previously named KFServing) provides Kubernetes custom resources for serving machine learning models on arbitrary frameworks including TensorFlow, XGBoost, scikit-learn, PyTorch, and ONNX. KServe was developed collaboratively by Google, IBM, Bloomberg, NVIDIA, and Seldon. Publicly disclosed adopters of KServe include Bloomberg, Gojek, the Wikimedia Foundation, and others. === Katib for automated machine learning === Lastly, Kubeflow includes a component for automated training and development of machine learning models, the Katib component. It is described as a Kubernetes-native project and features hyperparameter tuning, early stopping, and neural architecture search. == Release timeline ==

  Read more →
• 

  List of Java software and tools

  This is a list of software and programming tools for the Java programming language, which includes frameworks, libraries, IDEs, build tools, application servers, and related projects. == Java frameworks == == Libraries == Apache Ant – build automation tool Apache Batik – SVG processing Apache Cayenne – object-relational mapping Apache Xerces – collection of software libraries for parsing, validating, serializing and manipulating XML. Applet – applet API Ardor3D – 3D graphics engine Bonita BPM – workflow engine Cassowary – constraint solving Checkstyle – static code analysis GNU Classpath – standard library implementation Colt – scientific computing and technical computing Commons Daemon – manages applications as daemons DESMO-J – discrete event simulation Diagrams.net – diagramming Disruptor – high-performance messaging Dom4j – XML processing Dynamic Languages Toolkit – support for dynamic programming languages on the JVM Echo – GUI Flying Saucer – XHTML/CSS rendering Formatting Objects Processor – XSL-FO to PDF H2 Database Engine – relational database IAIK-JCE – cryptography Internet Foundation Classes – legacy GUI JavaBeans – reusable component architecture for enabling encapsulation, events, and properties for software components JavaCC – open-source parser generator and lexical analyzer Java Class Library – standard library of Java and other JVM languages Java Native Access – provides Java programs easy access to native shared libraries without using the Java Native Interface Javolution – real-time computing Jblas – linear algebra JDBCFacade – simplifies JDBC use JExcel – Excel API JFugue – music programming JMusic – music programming Joget Workflow – workflow engine JOOQ Object Oriented Querying – fluent API for SQL JPOS – financial messaging JUNG – open-source graph modeling and visualization LanguageWare – language processing LibGDX – game development Modular Audio Recognition Framework – collection of voice, sound, speech, text and natural language processing algorithms. ASM – bytecode manipulation Open Inventor – 3D graphics OpenPDF – PDF Parallel Colt – parallel computing Parboiled – parser PlayN – game development QOCA – constraint solving QtJambi – Qt bindings SLF4J – logging StableUpdate – update management SWT – GUI SuanShu – numerical computing SwingLabs – GUI extensions UBY – natural language processing Undecimber – calendar XDoclet – attribute-oriented programming XINS – XML network services XStream – object serialization == Machine learning and AI == Apache Mahout – scalable machine learning library focused on clustering, classification, and collaborative filtering Apache MXNet – deep learning framework with Java API support Apache OpenNLP – machine learning based toolkit for natural language processing of text Deeplearning4j – distributed deep learning library Deep Java Library – open-source deep learning framework developed by Amazon Web Services Encog – framework for neural networks, genetic algorithms, Hidden Markov model, and Bayesian networks. LIBSVM – Support Vector Machine implementation Mallet – machine learning toolkit for classification, clustering, and topic modeling. MLlib – distributed machine-learning framework on top of Apache Spark Core Neuroph – lightweight neural network framework Weka – collection of machine learning algorithms for data mining Yooreeka – machine learning == Data mining == Java Data Mining (JDM) – standard Java API for data mining Massive Online Analysis (MOA) – data stream mining with concept drift == Math and scientific libraries == Apache Commons Math – general-purpose mathematics library including statistics, linear algebra, and optimization. Colt – high-performance scientific computing, including linear algebra and random numbers. Efficient Java Matrix Library (EJML) – dense and sparse matrix computations and linear algebra Easy Java Simulations – Open Source Physics project designed to create discrete computer simulations Exp4j – evaluates mathematical expressions at runtime GroovyLab – numerical computational environment Hipparchus – fork of Apache Commons Math with updated algorithms for statistics, linear algebra, and optimization. JAMA – numerical linear algebra library Jblas: Linear Algebra for Java (Jblas) – linear algebra library using native BLAS/LAPACK bindings Java Astrodynamics Toolkit – numerical library of software components for use in spaceflight applications for Java or MATLAB Matrix Toolkit Java (MTJ) – linear algebra library with BLAS and LAPACK support OjAlgo – optimization, linear algebra, and financial calculations. OptimJ – extension for mathematical optimization and constraint programming Parallel Colt – A parallel extension of Colt SuanShu – numerical analysis, linear algebra, statistics, and optimization. == Integrated development environments == See also: Java IDEs on Wikibooks Android Studio – IDE for Google's Android operating system BlueJ – educational IDE for teaching Java DrJava – lightweight Java IDE for beginners Eclipse IDE – open-source IDE with extensive plugin ecosystem Greenfoot – educational IDE IntelliJ IDEA – commercial and community editions from JetBrains JDeveloper – freeware IDE supplied by Oracle Corporation jGRASP – software visualizations MyEclipse – Java EE IDE NetBeans IDE – Apache NetBeans Visual Studio Code – general-purpose editor with Java extensions === Online IDEs === Eclipse Che GitHub Codespaces JDoodle Replit == Text editors with Java support == == Build tools and package managers == Apache Ant – automating software build Apache Ivy – subproject of Apache Ant Apache Maven – build automation and dependency management Boot – build automation for Clojure CMake – build tool with limited support for java Gradle – modern build automation tool Go continuous delivery (GoCD) – continuous delivery and build automation server Jenkins – automation server continuous delivery JitPack – package repository for Git projects Leiningen – build automation for Clojure Simple build tool (sbt) – open-source build tool Spring Roo – rapid application development of Java-based enterprise software WaveMaker – low-code development platform == Java runtimes, compilers and virtual machines == Android Runtime – runtime environment javac – Java programming language compiler Java Virtual Machine (JVM) – virtual machine that executes Java bytecode JD Decompiler JEB decompiler – disassembler and decompiler software for Android applications GraalVM – Just-in-time compilation HotSpot – JVM implementation included in OpenJDK == JVM languages and dialects == Clojure – Lisp dialect Groovy JRuby – Ruby implementation Jython – Python implementation Kotlin – popular for Android app development Renjin – R implementation Scala == Application servers and containers == Apache Geronimo – open source application server Apache MINA – event-driven asynchronous network application framework Apache Tomcat – web container and web server Apache TomEE – Apache Tomcat with Java EE features Borland Enterprise Server – discontinued application server by Borland ColdFusion – commercial application server by Adobe Systems GlassFish – application server for Jakarta EE IBM WebSphere Application Server – enterprise application server by IBM IBM WebSphere Application Server Community Edition – open source edition of WebSphere (discontinued) JBoss Enterprise Application Platform – Red Hat's supported distribution of JBoss/WildFly JEUS – commercial Java EE application server from TmaxSoft Jetty – HTTP server and web container Lucee (formerly Railo) – open source CFML application server Netty – non-blocking I/O client–server framework for network applications Oracle Containers for J2EE – discontinued application server by Oracle Oracle WebLogic Server – enterprise application server by Oracle Orion Application Server – early commercial Java EE server by IronFlare Payara Server – fork of GlassFish for production use Resin – Java application server by Caucho (open source and professional editions) SAP NetWeaver Application Server – enterprise application server by SAP WildFly – application server == Debugging and profiling tools == jdb – Java debugger bundled with the JDK JConsole – JMX-compliant monitoring tool JDK Flight Recorder – method profiling, allocation profiling, and garbage collection related events. JProfiler – commercial Java profiler VisualVM – visual tool integrating commandline JDK tools for profiling and monitoring == Testing and quality assurance == Apache JMeter – load testing tool JaCoCo – Java code coverage library JArchitect – analyzes code quality, architecture, and dependencies. Jtest – software testing and static analysis JUnit – unit testing framework Mockito – open-source testing framework for Java PMD – static program analysis source code analyzer Selenium – browser automation for web app testing Spock – test framework SpotBugs (formerly FindBugs) – static analysis tool TestNG – testing framework inspired by JUnit and NUnit == Other == Apache XMLBeans –

  Read more →
• 

  Mating pool

  Mating pool is a concept used in evolutionary algorithms and means a population of parents for the next population. The mating pool is formed by candidate solutions that the selection operators deem to have the highest fitness in the current population. Solutions that are included in the mating pool are referred to as parents. Individual solutions can be repeatedly included in the mating pool, with individuals of higher fitness values having a higher chance of being included multiple times. Crossover operators are then applied to the parents, resulting in recombination of genes recognized as superior. Lastly, random changes in the genes are introduced through mutation operators, increasing the genetic variation in the gene pool. Those two operators improve the chance of creating new, superior solutions. A new generation of solutions is thereby created, the children, who will constitute the next population. Depending on the selection method, the total number of parents in the mating pool can be different to the size of the initial population, resulting in a new population that’s smaller. To continue the algorithm with an equally sized population, random individuals from the old populations can be chosen and added to the new population. At this point, the fitness value of the new solutions is evaluated. If the termination conditions are fulfilled, processes come to an end. Otherwise, they are repeated. The repetition of the steps result in candidate solutions that evolve towards the most optimal solution over time. The genes will become increasingly uniform towards the most optimal gene, a process called convergence. If 95% of the population share the same version of a gene, the gene has converged. When all the individual fitness values have reached the value of the best individual, i.e. all the genes have converged, population convergence is achieved. == Mating pool creation == Several methods can be applied to create a mating pool. All of these processes involve the selective breeding of a particular number of individuals within a population. There are multiple criteria that can be employed to determine which individuals make it into the mating pool and which are left behind. The selection methods can be split into three general types: fitness proportionate selection, ordinal based selection and threshold based selection. === Fitness proportionate selection === In the case of fitness proportionate selection, random individuals are selected to enter the pool. However, the ones with a higher level of fitness are more likely to be picked and therefore have a greater chance of passing on their features to the next generation. One of the techniques used in this type of parental selection is the roulette wheel selection. This approach divides a hypothetical circular wheel into different slots, the size of which is equal to the fitness values of each potential candidate. Afterwards, the wheel is rotated and a fixed point determines which individual gets picked. The greater the fitness value of an individual, the higher the probability of being chosen as a parent by the random spin of the wheel. Alternatively, stochastic universal sampling can be implemented. This selection method is also based on the rotation of a spinning wheel. However, in this case there is more than one fixed point and as a result all of the mating pool members will be selected simultaneously. === Ordinal based selection === The ordinal based selection methods include the tournament and ranking selection. Tournament selection involves the random selection of individuals of a population and the subsequent comparison of their fitness levels. The winners of these “tournaments” are the ones with the highest values and will be put into the mating pool as parents. In ranking selection all the individuals are sorted based on their fitness values. Then, the selection of the parents is made according to the rank of the candidates. Every individual has a chance of being chosen, but higher ranked ones are favored === Threshold based selection === The last type of selection method is referred to as the threshold based method. This includes the truncation selection method, which sorts individuals based on their phenotypic values on a specific trait and later selects the proportion of them that are within a certain threshold as parents.

  Read more →
• 

  Promoter based genetic algorithm

  The promoter based genetic algorithm (PBGA) is a genetic algorithm for neuroevolution developed by F. Bellas and R.J. Duro in the Integrated Group for Engineering Research (GII) at the University of Coruña, in Spain. It evolves variable size feedforward artificial neural networks (ANN) that are encoded into sequences of genes for constructing a basic ANN unit. Each of these blocks is preceded by a gene promoter acting as an on/off switch that determines if that particular unit will be expressed or not. == PBGA basics == The basic unit in the PBGA is a neuron with all of its inbound connections as represented in the following figure: The genotype of a basic unit is a set of real valued weights followed by the parameters of the neuron and proceeded by an integer valued field that determines the promoter gene value and, consequently, the expression of the unit. By concatenating units of this type we can construct the whole network. With this encoding it is imposed that the information that is not expressed is still carried by the genotype in evolution but it is shielded from direct selective pressure, maintaining this way the diversity in the population, which has been a design premise for this algorithm. Therefore, a clear difference is established between the search space and the solution space, permitting information learned and encoded into the genotypic representation to be preserved by disabling promoter genes. == Results == The PBGA was originally presented within the field of autonomous robotics, in particular in the real time learning of environment models of the robot. It has been used inside the Multilevel Darwinist Brain (MDB) cognitive mechanism developed in the GII for real robots on-line learning. In another paper it is shown how the application of the PBGA together with an external memory that stores the successful obtained world models, is an optimal strategy for adaptation in dynamic environments. Recently, the PBGA has provided results that outperform other neuroevolutionary algorithms in non-stationary problems, where the fitness function varies in time.

  Read more →
• 

  Cultural algorithm

  Cultural algorithms (CA) are a branch of evolutionary computation where there is a knowledge component that is called the belief space in addition to the population component. In this sense, cultural algorithms can be seen as an extension to a conventional genetic algorithm. Cultural algorithms were introduced by Reynolds (see references). == Belief space == The belief space of a cultural algorithm is divided into distinct categories. These categories represent different domains of knowledge that the population has of the search space. The belief space is updated after each iteration by the best individuals of the population. The best individuals can be selected using a fitness function that assesses the performance of each individual in population much like in genetic algorithms. === List of belief space categories === Normative knowledge A collection of desirable value ranges for the individuals in the population component e.g. acceptable behavior for the agents in population. Domain specific knowledge Information about the domain of the cultural algorithm problem is applied to. Situational knowledge Specific examples of important events - e.g. successful/unsuccessful solutions Temporal knowledge History of the search space - e.g. the temporal patterns of the search process Spatial knowledge Information about the topography of the search space == Population == The population component of the cultural algorithm is approximately the same as that of the genetic algorithm. == Communication protocol == Cultural algorithms require an interface between the population and belief space. The best individuals of the population can update the belief space via the update function. Also, the knowledge categories of the belief space can affect the population component via the influence function. The influence function can affect population by altering the genome or the actions of the individuals. == Pseudocode for cultural algorithms == Initialize population space (choose initial population) Initialize belief space (e.g. set domain specific knowledge and normative value-ranges) Repeat until termination condition is met Perform actions of the individuals in population space Evaluate each individual by using the fitness function Select the parents to reproduce a new generation of offspring Let the belief space alter the genome of the offspring by using the influence function Update the belief space by using the accept function (this is done by letting the best individuals to affect the belief space) == Applications == Various optimization problems Social simulation Real-parameter optimization

  Read more →
• 

  Neural style transfer

  Neural style transfer (NST) software algorithms are able to manipulate digital images, or videos, in order to adopt the appearance or visual style of another image. NST algorithms are characterized by their use of deep neural networks for the sake of image transformation. Common uses for NST are the creation of artificial artwork from photographs, for example by transferring the appearance of famous paintings to user-supplied photographs. Several notable mobile apps use NST techniques for this purpose, including DeepArt and Prisma. This method has been used by artists and designers around the globe to develop new artwork based on existent style(s). == History == NST is an example of image stylization, a problem studied for over two decades within the field of non-photorealistic rendering. The first two example-based style transfer algorithms were image analogies and image quilting. Both of these methods were based on patch-based texture synthesis algorithms. Given a training pair of images–a photo and an artwork depicting that photo–a transformation could be learned and then applied to create new artwork from a new photo, by analogy. If no training photo was available, it would need to be produced by processing the input artwork; image quilting did not require this processing step, though it was demonstrated on only one style. NST was first published in the paper "A Neural Algorithm of Artistic Style" by Leon Gatys et al., originally released to ArXiv 2015, and subsequently accepted by the peer-reviewed CVPR conference in 2016. The original paper used a VGG-19 architecture that has been pre-trained to perform object recognition using the ImageNet dataset. In 2017, Google AI introduced a method that allows a single deep convolutional style transfer network to learn multiple styles at the same time. This algorithm permits style interpolation in real-time, even when done on video media. == Mathematics == This section closely follows the original paper. === Overview === The idea of Neural Style Transfer (NST) is to take two images—a content image p → {\displaystyle {\vec {p}}} and a style image a → {\displaystyle {\vec {a}}} —and generate a third image x → {\displaystyle {\vec {x}}} that minimizes a weighted combination of two loss functions: a content loss L content ( p → , x → ) {\displaystyle {\mathcal {L}}_{\text{content }}({\vec {p}},{\vec {x}})} and a style loss L style ( a → , x → ) {\displaystyle {\mathcal {L}}_{\text{style }}({\vec {a}},{\vec {x}})} . The total loss is a linear sum of the two: L NST ( p → , a → , x → ) = α L content ( p → , x → ) + β L style ( a → , x → ) {\displaystyle {\mathcal {L}}_{\text{NST}}({\vec {p}},{\vec {a}},{\vec {x}})=\alpha {\mathcal {L}}_{\text{content}}({\vec {p}},{\vec {x}})+\beta {\mathcal {L}}_{\text{style}}({\vec {a}},{\vec {x}})} By jointly minimizing the content and style losses, NST generates an image that blends the content of the content image with the style of the style image. Both the content loss and the style loss measures the similarity of two images. The content similarity is the weighted sum of squared-differences between the neural activations of a single convolutional neural network (CNN) on two images. The style similarity is the weighted sum of Gram matrices within each layer (see below for details). The original paper used a VGG-19 CNN, but the method works for any CNN. === Symbols === Let x → {\textstyle {\vec {x}}} be an image input to a CNN. Let F l ∈ R N l × M l {\textstyle F^{l}\in \mathbb {R} ^{N_{l}\times M_{l}}} be the matrix of filter responses in layer l {\textstyle l} to the image x → {\textstyle {\vec {x}}} , where: N l {\textstyle N_{l}} is the number of filters in layer l {\textstyle l} ; M l {\textstyle M_{l}} is the height times the width (i.e. number of pixels) of each filter in layer l {\textstyle l} ; F i j l ( x → ) {\textstyle F_{ij}^{l}({\vec {x}})} is the activation of the i th {\textstyle i^{\text{th}}} filter at position j {\textstyle j} in layer l {\textstyle l} . A given input image x → {\textstyle {\vec {x}}} is encoded in each layer of the CNN by the filter responses to that image, with higher layers encoding more global features, but losing details on local features. === Content loss === Let p → {\textstyle {\vec {p}}} be an original image. Let x → {\textstyle {\vec {x}}} be an image that is generated to match the content of p → {\textstyle {\vec {p}}} . Let P l {\textstyle P^{l}} be the matrix of filter responses in layer l {\textstyle l} to the image p → {\textstyle {\vec {p}}} . The content loss is defined as the squared-error loss between the feature representations of the generated image and the content image at a chosen layer l {\displaystyle l} of a CNN: L content ( p → , x → , l ) = 1 2 ∑ i , j ( A i j l ( x → ) − A i j l ( p → ) ) 2 {\displaystyle {\mathcal {L}}_{\text{content }}({\vec {p}},{\vec {x}},l)={\frac {1}{2}}\sum _{i,j}\left(A_{ij}^{l}({\vec {x}})-A_{ij}^{l}({\vec {p}})\right)^{2}} where A i j l ( x → ) {\displaystyle A_{ij}^{l}({\vec {x}})} and A i j l ( p → ) {\displaystyle A_{ij}^{l}({\vec {p}})} are the activations of the i th {\displaystyle i^{\text{th}}} filter at position j {\displaystyle j} in layer l {\displaystyle l} for the generated and content images, respectively. Minimizing this loss encourages the generated image to have similar content to the content image, as captured by the feature activations in the chosen layer. The total content loss is a linear sum of the content losses of each layer: L content ( p → , x → ) = ∑ l v l L content ( p → , x → , l ) {\displaystyle {\mathcal {L}}_{\text{content }}({\vec {p}},{\vec {x}})=\sum _{l}v_{l}{\mathcal {L}}_{\text{content }}({\vec {p}},{\vec {x}},l)} , where the v l {\displaystyle v_{l}} are positive real numbers chosen as hyperparameters. === Style loss === The style loss is based on the Gram matrices of the generated and style images, which capture the correlations between different filter responses at different layers of the CNN: L style ( a → , x → ) = ∑ l = 0 L w l E l , {\displaystyle {\mathcal {L}}_{\text{style }}({\vec {a}},{\vec {x}})=\sum _{l=0}^{L}w_{l}E_{l},} where E l = 1 4 N l 2 M l 2 ∑ i , j ( G i j l ( x → ) − G i j l ( a → ) ) 2 . {\displaystyle E_{l}={\frac {1}{4N_{l}^{2}M_{l}^{2}}}\sum _{i,j}\left(G_{ij}^{l}({\vec {x}})-G_{ij}^{l}({\vec {a}})\right)^{2}.} Here, G i j l ( x → ) {\displaystyle G_{ij}^{l}({\vec {x}})} and G i j l ( a → ) {\displaystyle G_{ij}^{l}({\vec {a}})} are the entries of the Gram matrices for the generated and style images at layer l {\displaystyle l} . Explicitly, G i j l ( x → ) = ∑ k F i k l ( x → ) F j k l ( x → ) {\displaystyle G_{ij}^{l}({\vec {x}})=\sum _{k}F_{ik}^{l}({\vec {x}})F_{jk}^{l}({\vec {x}})} Minimizing this loss encourages the generated image to have similar style characteristics to the style image, as captured by the correlations between feature responses in each layer. The idea is that activation pattern correlations between filters in a single layer captures the "style" on the order of the receptive fields at that layer. Similarly to the previous case, the w l {\displaystyle w_{l}} are positive real numbers chosen as hyperparameters. === Hyperparameters === In the original paper, they used a particular choice of hyperparameters. The style loss is computed by w l = 0.2 {\displaystyle w_{l}=0.2} for the outputs of layers conv1_1, conv2_1, conv3_1, conv4_1, conv5_1 in the VGG-19 network, and zero otherwise. The content loss is computed by w l = 1 {\displaystyle w_{l}=1} for conv4_2, and zero otherwise. The ratio α / β ∈ [ 5 , 50 ] × 10 − 4 {\displaystyle \alpha /\beta \in [5,50]\times 10^{-4}} . === Training === Image x → {\displaystyle {\vec {x}}} is initially approximated by adding a small amount of white noise to input image p → {\displaystyle {\vec {p}}} and feeding it through the CNN. Then we successively backpropagate this loss through the network with the CNN weights fixed in order to update the pixels of x → {\displaystyle {\vec {x}}} . After several thousand epochs of training, an x → {\displaystyle {\vec {x}}} (hopefully) emerges that matches the style of a → {\displaystyle {\vec {a}}} and the content of p → {\displaystyle {\vec {p}}} . As of 2017, when implemented on a GPU, it takes a few minutes to converge. == Extensions == In some practical implementations, it is noted that the resulting image has too much high-frequency artifact, which can be suppressed by adding the total variation to the total loss. Compared to VGGNet, AlexNet does not work well for neural style transfer. NST has also been extended to videos. Subsequent work improved the speed of NST for images by using special-purpose normalizations. In a paper by Fei-Fei Li et al. adopted a different regularized loss metric and accelerated method for training to produce results in real-time (three orders of magnitude faster than Gatys). Their idea was to use not the pixel-based loss defined above but rather a 'perceptual loss' measuring t

  Read more →
• 

  Chromosome (evolutionary algorithm)

  A chromosome or genotype in evolutionary algorithms (EA) is a set of parameters which define a proposed solution of the problem that the evolutionary algorithm is trying to solve. The set of all solutions, also called individuals according to the biological model, is known as the population. The genome of an individual consists of one, more rarely of several, chromosomes and corresponds to the genetic representation of the task to be solved. A chromosome is composed of a set of genes, where a gene consists of one or more semantically connected parameters, which are often also called decision variables. They determine one or more phenotypic characteristics of the individual or at least have an influence on them. In the basic form of genetic algorithms, the chromosome is represented as a binary string, while in later variants and in EAs in general, a wide variety of other data structures are used. == Chromosome design == When creating the genetic representation of a task, it is determined which decision variables and other degrees of freedom of the task should be improved by the EA and possible additional heuristics and how the genotype-phenotype mapping should look like. The design of a chromosome translates these considerations into concrete data structures for which an EA then has to be selected, configured, extended, or, in the worst case, created. Finding a suitable representation of the problem domain for a chromosome is an important consideration, as a good representation will make the search easier by limiting the search space; similarly, a poorer representation will allow a larger search space. In this context, suitable mutation and crossover operators must also be found or newly defined to fit the chosen chromosome design. An important requirement for these operators is that they not only allow all points in the search space to be reached in principle, but also make this as easy as possible. The following requirements must be met by a well-suited chromosome: It must allow the accessibility of all admissible points in the search space. Design of the chromosome in such a way that it covers only the search space and no additional areas. so that there is no redundancy or only as little redundancy as possible. Observance of strong causality: small changes in the chromosome should only lead to small changes in the phenotype. This is also called locality of the relationship between search and problem space. Designing the chromosome in such a way that it excludes prohibited regions in the search space completely or as much as possible. While the first requirement is indispensable, depending on the application and the EA used, one usually only has to be satisfied with fulfilling the remaining requirements as far as possible. The evolutionary search is supported and possibly considerably accelerated by a fulfillment as complete as possible. == Examples of chromosomes == === Chromosomes for binary codings === In their classical form, GAs use bit strings and map the decision variables to be optimized onto them. An example for one Boolean and three integer decision variables with the value ranges 0 ≤ D 1 ≤ 60 {\displaystyle 0\leq D_{1}\leq 60} , 28 ≤ D 2 ≤ 30 {\displaystyle 28\leq D_{2}\leq 30} and − 12 ≤ D 3 ≤ 14 {\displaystyle -12\leq D_{3}\leq 14} may illustrate this: Note that the negative number here is given in two's complement. This straight forward representation uses five bits to represent the three values of D 2 {\displaystyle D_{2}} , although two bits would suffice. This is a significant redundancy. An improved alternative, where 28 is to be added for the genotype-phenotype mapping, could look like this: with D 2 = 28 + D 2 ′ = 29 {\displaystyle D_{2}=28+D'_{2}=29} . === Chromosomes with real-valued or integer genes === For the processing of tasks with real-valued or mixed-integer decision variables, EAs such as the evolution strategy or the real-coded GAs are suited. In the case of mixed-integer values, rounding is often used, but this represents some violation of the redundancy requirement. If the necessary precisions of the real values can be reasonably narrowed down, this violation can be remedied by using integer-coded GAs. For this purpose, the valid digits of real values are mapped to integers by multiplication with a suitable factor. For example, 12.380 becomes the integer 12380 by multiplying by 1000. This must of course be taken into account in genotype-phenotype mapping for evaluation and result presentation. A common form is a chromosome consisting of a list or an array of integer or real values. === Chromosomes for permutations === Combinatorial problems are mainly concerned with finding an optimal sequence of a set of elementary items. As an example, consider the problem of the traveling salesman who wants to visit a given number of cities exactly once on the shortest possible tour. The simplest and most obvious mapping onto a chromosome is to number the cities consecutively, to interpret a resulting sequence as permutation and to store it directly in a chromosome, where one gene corresponds to the ordinal number of a city. Then, however, the variation operators may only change the gene order and not remove or duplicate any genes. The chromosome thus contains the path of a possible tour to the cities. As an example the sequence 3 , 5 , 7 , 1 , 4 , 2 , 9 , 6 , 8 {\displaystyle 3,5,7,1,4,2,9,6,8} of nine cities may serve, to which the following chromosome corresponds: In addition to this encoding frequently called path representation, there are several other ways of representing a permutation, for example the ordinal representation or the matrix representation. === Chromosomes for co-evolution === When a genetic representation contains, in addition to the decision variables, additional information that influences evolution and/or the mapping of the genotype to the phenotype and is itself subject to evolution, this is referred to as co-evolution. A typical example is the evolution strategy (ES), which includes one or more mutation step sizes as strategy parameters in each chromosome. Another example is an additional gene to control a selection heuristic for resource allocation in a scheduling tasks. This approach is based on the assumption that good solutions are based on an appropriate selection of strategy parameters or on control gene(s) that influences genotype-phenotype mapping. The success of the ES gives evidence to this assumption. === Chromosomes for complex representations === The chromosomes presented above are well suited for processing tasks of continuous, mixed-integer, pure-integer or combinatorial optimization. For a combination of these optimization areas, on the other hand, it becomes increasingly difficult to map them to simple strings of values, depending on the task. The following extension of the gene concept is proposed by the EA GLEAM (General Learning Evolutionary Algorithm and Method) for this purpose: A gene is considered to be the description of an element or elementary trait of the phenotype, which may have multiple parameters. For this purpose, gene types are defined that contain as many parameters of the appropriate data type as are required to describe the particular element of the phenotype. A chromosome now consists of genes as data objects of the gene types, whereby, depending on the application, each gene type occurs exactly once as a gene or can be contained in the chromosome any number of times. The latter leads to chromosomes of dynamic length, as they are required for some problems. The gene type definitions also contain information on the permissible value ranges of the gene parameters, which are observed during chromosome generation and by corresponding mutations, so they cannot lead to lethal mutations. For tasks with a combinatorial part, there are suitable genetic operators that can move or reposition genes as a whole, i.e. with their parameters. A scheduling task is used as an illustration, in which workflows are to be scheduled that require different numbers of heterogeneous resources. A workflow specifies which work steps can be processed in parallel and which have to be executed one after the other. In this context, heterogeneous resources mean different processing times at different costs in addition to different processing capabilities. Each scheduling operation therefore requires one or more parameters that determine the resource selection, where the value ranges of the parameters depend on the number of alternative resources available for each work step. A suitable chromosome provides one gene type per work step and in this case one corresponding gene, which has one parameter for each required resource. The order of genes determines the order of scheduling operations and, therefore, the precedence in case of allocation conflicts. The exemplary gene type definition of work step 15 with two resources, for which there are four and seven alternatives respectively

  Read more →
• 

  Medoid

  Medoids are representative objects of a data set or a cluster within a data set whose sum of dissimilarities to all the objects in the cluster is minimal. Medoids are similar in concept to means or centroids, but medoids are always restricted to be members of the data set. Medoids are most commonly used on data when a mean or centroid cannot be defined, such as graphs. They are also used in contexts where the centroid is not representative of the dataset like in images, 3-D trajectories and gene expression (where while the data is sparse the medoid need not be). These are also of interest while wanting to find a representative using some distance other than squared euclidean distance (for instance in movie-ratings). For some data sets there may be more than one medoid, as with medians. A common application of the medoid is the k-medoids clustering algorithm, which is similar to the k-means algorithm but works when a mean or centroid is not definable. This algorithm basically works as follows. First, a set of medoids is chosen at random. Second, the distances to the other points are computed. Third, data are clustered according to the medoid they are most similar to. Fourth, the medoid set is optimized via an iterative process. Note that a medoid is not equivalent to a median, a geometric median, or centroid. A median is only defined on 1-dimensional data, and it only minimizes dissimilarity to other points for metrics induced by a norm (such as the Manhattan distance or Euclidean distance). A geometric median is defined in any dimension, but unlike a medoid, it is not necessarily a point from within the original dataset. == Definition == Let X := { x 1 , x 2 , … , x n } {\textstyle {\mathcal {X}}:=\{x_{1},x_{2},\dots ,x_{n}\}} be a set of n {\textstyle n} points in a space with a distance function d. Medoid is defined as x medoid = arg ⁡ min y ∈ X ∑ i = 1 n d ( y , x i ) . {\displaystyle x_{\text{medoid}}=\arg \min _{y\in {\mathcal {X}}}\sum _{i=1}^{n}d(y,x_{i}).} == Clustering with medoids == Medoids are a popular replacement for the cluster mean when the distance function is not (squared) Euclidean distance, or not even a metric (as the medoid does not require the triangle inequality). When partitioning the data set into clusters, the medoid of each cluster can be used as a representative of each cluster. Clustering algorithms based on the idea of medoids include: Partitioning Around Medoids (PAM), the standard k-medoids algorithm Hierarchical Clustering Around Medoids (HACAM), which uses medoids in hierarchical clustering == Algorithms to compute the medoid of a set == From the definition above, it is clear that the medoid of a set X {\displaystyle {\mathcal {X}}} can be computed after computing all pairwise distances between points in the ensemble. This would take O ( n 2 ) {\textstyle O(n^{2})} distance evaluations (with n = | X | {\displaystyle n=|{\mathcal {X}}|} ). In the worst case, one can not compute the medoid with fewer distance evaluations. However, there are many approaches that allow us to compute medoids either exactly or approximately in sub-quadratic time under different statistical models. If the points lie on the real line, computing the medoid reduces to computing the median which can be done in O ( n ) {\textstyle O(n)} by Quick-select algorithm of Hoare. However, in higher dimensional real spaces, no linear-time algorithm is known. RAND is an algorithm that estimates the average distance of each point to all the other points by sampling a random subset of other points. It takes a total of O ( n log ⁡ n ϵ 2 ) {\textstyle O\left({\frac {n\log n}{\epsilon ^{2}}}\right)} distance computations to approximate the medoid within a factor of ( 1 + ϵ Δ ) {\textstyle (1+\epsilon \Delta )} with high probability, where Δ {\textstyle \Delta } is the maximum distance between two points in the ensemble. Note that RAND is an approximation algorithm, and moreover Δ {\textstyle \Delta } may not be known apriori. RAND was leveraged by TOPRANK which uses the estimates obtained by RAND to focus on a small subset of candidate points, evaluates the average distance of these points exactly, and picks the minimum of those. TOPRANK needs O ( n 5 3 log 4 3 ⁡ n ) {\textstyle O(n^{\frac {5}{3}}\log ^{\frac {4}{3}}n)} distance computations to find the exact medoid with high probability under a distributional assumption on the average distances. trimed presents an algorithm to find the medoid with O ( n 3 2 2 Θ ( d ) ) {\textstyle O(n^{\frac {3}{2}}2^{\Theta (d)})} distance evaluations under a distributional assumption on the points. The algorithm uses the triangle inequality to cut down the search space. Meddit leverages a connection of the medoid computation with multi-armed bandits and uses an upper-Confidence-bound type of algorithm to get an algorithm which takes O ( n log ⁡ n ) {\textstyle O(n\log n)} distance evaluations under statistical assumptions on the points. Correlated Sequential Halving also leverages multi-armed bandit techniques, improving upon Meddit. By exploiting the correlation structure in the problem, the algorithm is able to provably yield drastic improvement (usually around 1-2 orders of magnitude) in both number of distance computations needed and wall clock time. == Implementations == An implementation of RAND, TOPRANK, and trimed can be found here. An implementation of Meddit can be found here and here. An implementation of Correlated Sequential Halving can be found here. == Medoids in text and natural language processing (NLP) == Medoids can be applied to various text and NLP tasks to improve the efficiency and accuracy of analyses. By clustering text data based on similarity, medoids can help identify representative examples within the dataset, leading to better understanding and interpretation of the data. === Text clustering === Text clustering is the process of grouping similar text or documents together based on their content. Medoid-based clustering algorithms can be employed to partition large amounts of text into clusters, with each cluster represented by a medoid document. This technique helps in organizing, summarizing, and retrieving information from large collections of documents, such as in search engines, social media analytics and recommendation systems. === Text summarization === Text summarization aims to produce a concise and coherent summary of a larger text by extracting the most important and relevant information. Medoid-based clustering can be used to identify the most representative sentences in a document or a group of documents, which can then be combined to create a summary. This approach is especially useful for extractive summarization tasks, where the goal is to generate a summary by selecting the most relevant sentences from the original text. === Sentiment analysis === Sentiment analysis involves determining the sentiment or emotion expressed in a piece of text, such as positive, negative, or neutral. Medoid-based clustering can be applied to group text data based on similar sentiment patterns. By analyzing the medoid of each cluster, researchers can gain insights into the predominant sentiment of the cluster, helping in tasks such as opinion mining, customer feedback analysis, and social media monitoring. === Topic modeling === Topic modeling is a technique used to discover abstract topics that occur in a collection of documents. Medoid-based clustering can be applied to group documents with similar themes or topics. By analyzing the medoids of these clusters, researchers can gain an understanding of the underlying topics in the text corpus, facilitating tasks such as document categorization, trend analysis, and content recommendation. === Techniques for measuring text similarity in medoid-based clustering === When applying medoid-based clustering to text data, it is essential to choose an appropriate similarity measure to compare documents effectively. Each technique has its advantages and limitations, and the choice of the similarity measure should be based on the specific requirements and characteristics of the text data being analyzed. The following are common techniques for measuring text similarity in medoid-based clustering: ==== Cosine similarity ==== Cosine similarity is a widely used measure to compare the similarity between two pieces of text. It calculates the cosine of the angle between two document vectors in a high-dimensional space. Cosine similarity ranges between -1 and 1, where a value closer to 1 indicates higher similarity, and a value closer to -1 indicates lower similarity. By visualizing two lines originating from the origin and extending to the respective points of interest, and then measuring the angle between these lines, one can determine the similarity between the associated points. Cosine similarity is less affected by document length, so it may be better at producing medoids that are representative of the content of a cluster instead of the lengt

  Read more →