AI Assistant Intellij

AI Assistant Intellij — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

Clef (app)

Clef was a San Francisco-based technology company, known for developing a mobile app that created a two-factor authentication for websites. It allowed users to access sites with a single login password management service which stores encrypted passwords in private accounts. It had a standard verification method that requires access to data on the mobile phone to confirm the user's identity. The application required a Wi-Fi or mobile network, and the user could log in by scanning the computer screen with their phone. == History == Clef was founded in 2013 by Mark Hudnall, B. Byrne and Jesse Pollak. It raised $1.6 million in seed funding in November 2014. Clef integrated with many websites and applications, including WordPress. On March 17, 2017, Clef announced they would no longer support the plugin after June 6, 2017; Clef was acquired by Authy, another 2FA service, which later got acquired by Twilio.
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Information gain (decision tree)

In the context of decision trees in information theory and machine learning, information gain refers to the conditional expected value of the Kullback–Leibler divergence of the univariate probability distribution of one variable from the conditional distribution of this variable given the other one. (In broader contexts, information gain can also be used as a synonym for either Kullback–Leibler divergence or mutual information, but the focus of this article is on the more narrow meaning below.) Explicitly, the information gain of a random variable X {\displaystyle X} obtained from an observation of a random variable A {\displaystyle A} taking value a {\displaystyle a} is defined as: I G ( X , a ) = D KL ( P X ∣ a ∥ P X ) {\displaystyle {\mathit {IG}}(X,a)=D_{\text{KL}}{\bigl (}P_{X\mid a}\parallel P_{X}{\bigr )}} In other words, it is the Kullback–Leibler divergence of P X ( x ) {\displaystyle P_{X}(x)} (the prior distribution for X {\displaystyle X} ) from P X ∣ a ( x ) {\displaystyle P_{X\mid a}(x)} (the posterior distribution for X {\displaystyle X} given A = a {\displaystyle A=a} ). The expected value of the information gain is the mutual information I ( X ; A ) {\displaystyle I(X;A)} : E A ⁡ [ I G ( X , A ) ] = I ( X ; A ) {\displaystyle \operatorname {E} _{A}[{\mathit {IG}}(X,A)]=I(X;A)} i.e. the reduction in the entropy of X {\displaystyle X} achieved by learning the state of the random variable A {\displaystyle A} . In machine learning, this concept can be used to define a preferred sequence of attributes to investigate to most rapidly narrow down the state of X. Such a sequence (which depends on the outcome of the investigation of previous attributes at each stage) is called a decision tree, and when applied in the area of machine learning is known as decision tree learning. Usually an attribute with high mutual information should be preferred to other attributes. == General definition == In general terms, the expected information gain is the reduction in information entropy Η from a prior state to a state that takes some information as given: I G ( T , a ) = H ( T ) − H ( T | a ) , {\displaystyle IG(T,a)=\mathrm {H} {(T)}-\mathrm {H} {(T|a)},} where H ( T | a ) {\displaystyle \mathrm {H} {(T|a)}} is the conditional entropy of T {\displaystyle T} given the value of attribute a {\displaystyle a} . This is intuitively plausible when interpreting entropy Η as a measure of uncertainty of a random variable T {\displaystyle T} : by learning (or assuming) a {\displaystyle a} about T {\displaystyle T} , our uncertainty about T {\displaystyle T} is reduced (i.e. I G ( T , a ) {\displaystyle IG(T,a)} is positive), unless of course T {\displaystyle T} is independent of a {\displaystyle a} , in which case H ( T | a ) = H ( T ) {\displaystyle \mathrm {H} (T|a)=\mathrm {H} (T)} , meaning I G ( T , a ) = 0 {\displaystyle IG(T,a)=0} . == Formal definition == Let T denote a set of training examples, each of the form ( x , y ) = ( x 1 , x 2 , x 3 , . . . , x k , y ) {\displaystyle ({\textbf {x}},y)=(x_{1},x_{2},x_{3},...,x_{k},y)} where x a ∈ v a l s ( a ) {\displaystyle x_{a}\in \mathrm {vals} (a)} is the value of the a th {\displaystyle a^{\text{th}}} attribute or feature of example x {\displaystyle {\textbf {x}}} and y is the corresponding class label. The information gain for an attribute a is defined in terms of Shannon entropy H ( − ) {\displaystyle \mathrm {H} (-)} as follows. For a value v taken by attribute a, let S a ( v ) = { x ∈ T | x a = v } {\displaystyle S_{a}{(v)}=\{{\textbf {x}}\in T|x_{a}=v\}} be defined as the set of training inputs of T for which attribute a is equal to v. Then the information gain of T for attribute a is the difference between the a priori Shannon entropy H ( T ) {\displaystyle \mathrm {H} (T)} of the training set and the conditional entropy H ( T | a ) {\displaystyle \mathrm {H} {(T|a)}} . H ( T | a ) = ∑ v ∈ v a l s ( a ) | S a ( v ) | | T | ⋅ H ( S a ( v ) ) . {\displaystyle \mathrm {H} (T|a)=\sum _{v\in \mathrm {vals} (a)}{{\frac {|S_{a}{(v)}|}{|T|}}\cdot \mathrm {H} \left(S_{a}{\left(v\right)}\right)}.} I G ( T , a ) = H ( T ) − H ( T | a ) {\displaystyle IG(T,a)=\mathrm {H} (T)-\mathrm {H} (T|a)} The mutual information is equal to the total entropy for an attribute if for each of the attribute values a unique classification can be made for the result attribute. In this case, the relative entropies subtracted from the total entropy are 0. In particular, the values v ∈ v a l s ( a ) {\displaystyle v\in vals(a)} defines a partition of the training set data T into mutually exclusive and all-inclusive subsets, inducing a categorical probability distribution P a ( v ) {\textstyle P_{a}{(v)}} on the values v ∈ v a l s ( a ) {\textstyle v\in vals(a)} of attribute a. The distribution is given P a ( v ) := | S a ( v ) | | T | {\textstyle P_{a}{(v)}:={\frac {|S_{a}{(v)}|}{|T|}}} . In this representation, the information gain of T given a can be defined as the difference between the unconditional Shannon entropy of T and the expected entropy of T conditioned on a, where the expectation value is taken with respect to the induced distribution on the values of a. I G ( T , a ) = H ( T ) − ∑ v ∈ v a l s ( a ) P a ( v ) H ( S a ( v ) ) = H ( T ) − E P a [ H ( S a ( v ) ) ] = H ( T ) − H ( T | a ) . {\displaystyle {\begin{alignedat}{2}IG(T,a)&=\mathrm {H} (T)-\sum _{v\in \mathrm {vals} (a)}{P_{a}{(v)}\mathrm {H} \left(S_{a}{(v)}\right)}\\&=\mathrm {H} (T)-\mathbb {E} _{P_{a}}{\left[\mathrm {H} {(S_{a}{(v)})}\right]}\\&=\mathrm {H} (T)-\mathrm {H} {(T|a)}.\end{alignedat}}} == Example == In engineering applications, information is analogous to signal, and entropy is analogous to noise. It determines how a decision tree chooses to split data. The leftmost figure below is very impure and has high entropy corresponding to higher disorder and lower information value. As we go to the right, the entropy decreases, and the information value increases. Now, it is clear that information gain is the measure of how much information a feature provides about a class. Let's visualize information gain in a decision tree as shown in the right: The node t is the parent node, and the sub-nodes tL and tR are child nodes. In this case, the parent node t has a collection of cancer and non-cancer samples denoted as C and NC respectively. We can use information gain to determine how good the splitting of nodes is in a decision tree. In terms of entropy, information gain is defined as: To understand this idea, let's start by an example in which we create a simple dataset and want to see if gene mutations could be related to patients with cancer. Given four different gene mutations, as well as seven samples, the training set for a decision can be created as follows: In this dataset, a 1 means the sample has the mutation (True), while a 0 means the sample does not (False). A sample with C denotes that it has been confirmed to be cancerous, while NC means it is non-cancerous. Using this data, a decision tree can be created with information gain used to determine the candidate splits for each node. For the next step, the entropy at parent node t of the above simple decision tree is computed as:H(t) = −[pC,t log2(pC,t) + pNC,t log2(pNC,t)] where, probability of selecting a class ‘C’ sample at node t, pC,t = n(t, C) / n(t), probability of selecting a class ‘NC’ sample at node t, pNC,t = n(t, NC) / n(t), n(t), n(t, C), and n(t, NC) are the number of total samples, ‘C’ samples and ‘NC’ samples at node t respectively.Using this with the example training set, the process for finding information gain beginning with H ( t ) {\displaystyle \mathrm {H} {(t)}} for Mutation 1 is as follows: pC, t = 4/7 pNC, t = 3/7 H ( t ) {\displaystyle \mathrm {H} {(t)}} = −(4/7 × log2(4/7) + 3/7 × log2(3/7)) = 0.985 Note: H ( t ) {\displaystyle \mathrm {H} {(t)}} will be the same for all mutations at the root. The relatively high value of entropy H ( t ) = 0.985 {\displaystyle \mathrm {H} {(t)}=0.985} (1 is the optimal value) suggests that the root node is highly impure and the constituents of the input at the root node would look like the leftmost figure in the above Entropy Diagram. However, such a set of data is good for learning the attributes of the mutations used to split the node. At a certain node, when the homogeneity of the constituents of the input occurs (as shown in the rightmost figure in the above Entropy Diagram), the dataset would no longer be good for learning. Moving on, the entropy at left and right child nodes of the above decision tree is computed using the formulae:H(tL) = −[pC,L log2(pC,L) + pNC,L log2(pNC,L)]H(tR) = −[pC,R log2(pC,R) + pNC,R log2(pNC,R)]where, probability of selecting a class ‘C’ sample at the left child node, pC,L = n(tL, C) / n(tL), probability of selecting a class ‘NC’ sample at the left child node, pNC,L = n(tL, NC) / n(tL), probability of selecting a class ‘C’ sample at the right child node, pC,R = n(tR, C) / n(tR), prob
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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
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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 ==
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Automatic taxonomy construction

Automatic taxonomy construction (ATC) is the use of software programs to generate taxonomical classifications from a body of texts called a corpus. ATC is a branch of natural language processing, which in turn is a branch of artificial intelligence. A taxonomy (or taxonomical classification) is a scheme of classification, especially, a hierarchical classification, in which things are organized into groups or types. Among other things, a taxonomy can be used to organize and index knowledge (stored as documents, articles, videos, etc.), such as in the form of a library classification system, or a search engine taxonomy, so that users can more easily find the information they are searching for. Many taxonomies are hierarchies (and thus, have an intrinsic tree structure), but not all are. Manually developing and maintaining a taxonomy is a labor-intensive task requiring significant time and resources, including familiarity of or expertise in the taxonomy's domain (scope, subject, or field), which drives the costs and limits the scope of such projects. Also, domain modelers have their own points of view which inevitably, even if unintentionally, work their way into the taxonomy. ATC uses artificial intelligence techniques to quickly automatically generate a taxonomy for a domain in order to avoid these problems and remove limitations. == Approaches == There are several approaches to ATC. One approach is to use rules to detect patterns in the corpus and use those patterns to infer relations such as hyponymy. Other approaches use machine learning techniques such as Bayesian inferencing and Artificial Neural Networks. === Keyword extraction === One approach to building a taxonomy is to automatically gather the keywords from a domain using keyword extraction, then analyze the relationships between them (see Hyponymy, below), and then arrange them as a taxonomy based on those relationships. === Hyponymy and "is-a" relations === In ATC programs, one of the most important tasks is the discovery of hypernym and hyponym relations among words. One way to do that from a body of text is to search for certain phrases like "is a" and "such as". In linguistics, is-a relations are called hyponymy. Words that describe categories are called hypernyms and words that are examples of categories are hyponyms. For example, dog is a hypernym and Fido is one of its hyponyms. A word can be both a hyponym and a hypernym. So, dog is a hyponym of mammal and also a hypernym of Fido. Taxonomies are often represented as is-a hierarchies where each level is more specific than (in mathematical language "a subset of") the level above it. For example, a basic biology taxonomy would have concepts such as mammal, which is a subset of animal, and dogs and cats, which are subsets of mammal. This kind of taxonomy is called an is-a model because the specific objects are considered instances of a concept. For example, Fido is-a instance of the concept dog and Fluffy is-a cat. == Applications == ATC can be used to build taxonomies for search engines, to improve search results. ATC systems are a key component of ontology learning (also known as automatic ontology construction), and have been used to automatically generate large ontologies for domains such as insurance and finance. They have also been used to enhance existing large networks such as Wordnet to make them more complete and consistent. == ATC software == == Other names == Other names for automatic taxonomy construction include: Automated outline building Automated outline construction Automated outline creation Automated outline extraction Automated outline generation Automated outline induction Automated outline learning Automated outlining Automated taxonomy building Automated taxonomy construction Automated taxonomy creation Automated taxonomy extraction Automated taxonomy generation Automated taxonomy induction Automated taxonomy learning Automatic outline building Automatic outline construction Automatic outline creation Automatic outline extraction Automatic outline generation Automatic outline induction Automatic outline learning Automatic taxonomy building Automatic taxonomy creation Automatic taxonomy extraction Automatic taxonomy generation Automatic taxonomy induction Automatic taxonomy learning Outline automation Outline building Outline construction Outline creation Outline extraction Outline generation Outline induction Outline learning Semantic taxonomy building Semantic taxonomy construction Semantic taxonomy creation Semantic taxonomy extraction Semantic taxonomy generation Semantic taxonomy induction Semantic taxonomy learning Taxonomy automation Taxonomy building Taxonomy construction Taxonomy creation Taxonomy extraction Taxonomy generation Taxonomy induction Taxonomy learning
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IDistance

In pattern recognition, iDistance is an indexing and query processing technique for k-nearest neighbor queries on point data in multi-dimensional metric spaces. The kNN query is one of the hardest problems on multi-dimensional data, especially when the dimensionality of the data is high. iDistance is designed to process kNN queries in high-dimensional spaces efficiently and performs extremely well for skewed data distributions, which usually occur in real-life data sets. iDistance employs a two-phase search strategy involving an initial filtering of candidate regions and a subsequent refinement of results, an approach aligned with the Filter and Refine Principle (FRP). This means that the index first prunes the search space to eliminate unlikely candidates, then verifies the true nearest neighbors in a refinement step, following the general FRP paradigm used in database search algorithms. The iDistance index can also be augmented with machine learning models to learn data distributions for improved searching and storage of multi-dimensional data. == Indexing == Building the iDistance index has two steps: A number of reference points in the data space are chosen. There are various ways of choosing reference points. Using cluster centers as reference points is the most efficient way. The data points are partitioned into Voronoi cells based on well-chosen reference points. The distance between a data point and its closest reference point is calculated. This distance plus a scaling value is called the point's iDistance. By this means, points in a multi-dimensional space are mapped to one-dimensional values, and then a B+-tree can be adopted to index the points using the iDistance as the key. The figure on the right shows an example where three reference points (O1, O2, O3) are chosen. The data points are then mapped to a one-dimensional space and indexed in a B+-tree. Various extensions have been proposed to make the selection of reference points for effective query performance, including employing machine learning to learn the identification of reference points. == Query processing == To process a kNN query, the query is mapped to a number of one-dimensional range queries, which can be processed efficiently on a B+-tree. In the above figure, the query Q is mapped to a value in the B+-tree while the kNN search ``sphere" is mapped to a range in the B+-tree. The search sphere expands gradually until the k NNs are found. This corresponds to gradually expanding range searches in the B+-tree. The iDistance technique can be viewed as a way of accelerating the sequential scan. Instead of scanning records from the beginning to the end of the data file, the iDistance starts the scan from spots where the nearest neighbors can be obtained early with a very high probability. == Applications == The iDistance has been used in many applications including Image retrieval Video indexing Similarity search in P2P systems Mobile computing Recommender system == Historical background == The iDistance was first proposed by Cui Yu, Beng Chin Ooi, Kian-Lee Tan and H. V. Jagadish in 2001. Later, together with Rui Zhang, they improved the technique and performed a more comprehensive study on it in 2005.
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Multiple discriminant analysis

Multiple Discriminant Analysis (MDA) is a multivariate dimensionality reduction technique. It has been used to predict signals as diverse as neural memory traces and corporate failure. MDA is not directly used to perform classification. It merely supports classification by yielding a compressed signal amenable to classification. The method described in Duda et al. (2001) §3.8.3 projects the multivariate signal down to an M−1 dimensional space where M is the number of categories. MDA is useful because most classifiers are strongly affected by the curse of dimensionality. In other words, when signals are represented in very-high-dimensional spaces, the classifier's performance is catastrophically impaired by the overfitting problem. This problem is reduced by compressing the signal down to a lower-dimensional space as MDA does. MDA has been used to reveal neural codes.
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Local tangent space alignment

Local tangent space alignment (LTSA) is a method for manifold learning, which can efficiently learn a nonlinear embedding into low-dimensional coordinates from high-dimensional data, and can also reconstruct high-dimensional coordinates from embedding coordinates. It is based on the intuition that when a manifold is correctly unfolded, all of the tangent hyperplanes to the manifold will become aligned. It begins by computing the k-nearest neighbors of every point. It computes the tangent space at every point by computing the d-first principal components in each local neighborhood. It then optimizes to find an embedding that aligns the tangent spaces, but it ignores the label information conveyed by data samples, and thus can not be used for classification directly.
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Plane Finder

Plane Finder is a United Kingdom-based real-time flight tracking service launched in 2009, that is able to show flight data globally. The data available includes flight numbers, how fast an aircraft is moving, its elevation and destination of travel. Several variants of the service are available as mobile apps including free, premium 3D and augmented reality versions. The flight tracking map and database can be accessed by web browsers. Plane Finder allows registered users to share their ADS-B and MLAT data via the Plane Finder ADS-B Client, available for macOS, Windows and Linux. Plane Finder supports VFR charts from NATS, and was the first major flight tracking app to introduce a replay feature, allowing users to replay flights dating back to 2011. == Flight tracking == Plane Finder collects data from its own global network of receivers, using the following sources. === Automatic dependent surveillance-broadcast (ADS-B) === A network of automatic dependent surveillance-broadcast (ADS-B) receivers gathers aircraft data such as callsign, position and speed. Plane Finder serves to supplement this data with additional information, including aircraft registration/tail number, departure airport, destination, artwork, and photographs. Plane Finder users can apply for an ADS-B receiver in exchange for their flight data. === Multilateration (MLAT) === To deliver aircraft position data where ADS-B is unavailable, Plane Finder uses multilateration (MLAT). Using three or more receivers running Plane Finder client software, monitoring the aircraft simultaneously, the aircraft’s position is calculated using receiver location and accurate timestamps. While European airspace is widely covered, only some parts of North American airspace are covered. === Federal Aviation Administration (FAA) feed === ADS-B is prevalent across Europe and Australia, but not in North America. Where MLAT or ADS-B data is unavailable, a feed from the Federal Aviation Administration provides flight information. The FAA feed covers United States and Canadian airspace, including bordering areas of the Atlantic and Pacific Oceans. === FLARM feed === Plane Finder collects data from a centralised FLARM feed, for monitoring small aircraft and gliders. == Flight data source == The Plane Finder website and database is widely used as an information source to support articles in the media. The Independent used Plane Finder flight tracking to demonstrate to readers the flight path of flight MT2706, which turned back as a result of last minute Egyptian government flight restrictions on 6 November 2015. The Independent also used Plane Finder information to demonstrate a timeline of the speed/altitude of flight 7K 9268, a Russian plane which crashed on 31 October 2015. The BBC cited Plane Finder in regard to the point at which at British Airways flight turned back to Heathrow Airport to make an emergency landing after smoke was seen coming from its engines. Plane Finder data has also been used to create original imagery for the media, such as the Washington Post, which used Plane Finder as a source to show flight patterns immediately after the Brussels bombings in March 2016.
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Winner-take-all (computing)

Winner-take-all is a computational principle applied in computational models of neural networks by which neurons compete with each other for activation. In the classical form, only the neuron with the highest activation stays active while all other neurons shut down; however, other variations allow more than one neuron to be active, for example the soft winner take-all, by which a power function is applied to the neurons. == Neural networks == In the theory of artificial neural networks, winner-take-all networks are a case of competitive learning in recurrent neural networks. Output nodes in the network mutually inhibit each other, while simultaneously activating themselves through reflexive connections. After some time, only one node in the output layer will be active, namely the one corresponding to the strongest input. Thus the network uses nonlinear inhibition to pick out the largest of a set of inputs. Winner-take-all is a general computational primitive that can be implemented using different types of neural network models, including both continuous-time and spiking networks. Winner-take-all networks are commonly used in computational models of the brain, particularly for distributed decision-making or action selection in the cortex. Important examples include hierarchical models of vision, and models of selective attention and recognition. They are also common in artificial neural networks and neuromorphic analog VLSI circuits. It has been formally proven that the winner-take-all operation is computationally powerful compared to other nonlinear operations, such as thresholding. In many practical cases, there is not only one single neuron which becomes active but there are exactly k neurons which become active for a fixed number k. This principle is referred to as k-winners-take-all. === Example algorithm === Consider a single linear neuron, with inputs x 1 , … , x n {\displaystyle x_{1},\dots ,x_{n}} . Each input has weight w i {\displaystyle w_{i}} , and the output of the neuron is ∑ i w i x i {\displaystyle \sum _{i}w_{i}x_{i}} . In the Instar learning rule, on each input vector, the weight vectors are modified according to Δ w i = η ( x i − w i ) {\displaystyle \Delta w_{i}=\eta (x_{i}-w_{i})} where η {\displaystyle \eta } is the learning rate. This rule is unsupervised, since we need just the input vector, not a reference output. Now, consider multiple linear neurons y 1 , … , y m {\displaystyle y_{1},\dots ,y_{m}} . The output of each satisfies y i = ∑ j w i j x j {\displaystyle y_{i}=\sum _{j}w_{ij}x_{j}} . In the winner-take-all algorithm, the weights are modified as follows. Given an input vector x {\displaystyle x} , each output is computed. The neuron with the largest output is selected, and the weights going into that neuron are modified according to the Instar learning rule. All other weights remain unchanged. The k-winners-take-all rule is similar, except that the Instar learning rule is applied to the weights going into the k neurons with the largest outputs. == Circuit example == A simple, but popular CMOS winner-take-all circuit is shown on the right. This circuit was originally proposed by Lazzaro et al. (1989) using MOS transistors biased to operate in the weak-inversion or subthreshold regime. In the particular case shown there are only two inputs (IIN,1 and IIN,2), but the circuit can be easily extended to multiple inputs in a straightforward way. It operates on continuous-time input signals (currents) in parallel, using only two transistors per input. In addition, the bias current IBIAS is set by a single global transistor that is common to all the inputs. The largest of the input currents sets the common potential VC. As a result, the corresponding output carries almost all the bias current, while the other outputs have currents that are close to zero. Thus, the circuit selects the larger of the two input currents, i.e., if IIN,1 > IIN,2, we get IOUT,1 = IBIAS and IOUT,2 = 0. Similarly, if IIN,2 > IIN,1, we get IOUT,1 = 0 and IOUT,2 = IBIAS. A SPICE-based DC simulation of the CMOS winner-take-all circuit in the two-input case is shown on the right. As shown in the top subplot, the input IIN,1 was fixed at 6nA, while IIN,2 was linearly increased from 0 to 10nA. The bottom subplot shows the two output currents. As expected, the output corresponding to the larger of the two inputs carries the entire bias current (10nA in this case), forcing the other output current nearly to zero. == Other uses == In stereo matching algorithms, following the taxonomy proposed by Scharstein and Szelliski, winner-take-all is a local method for disparity computation. Adopting a winner-take-all strategy, the disparity associated with the minimum or maximum cost value is selected at each pixel. It is axiomatic that in the electronic commerce market, early dominant players such as AOL or Yahoo! get most of the rewards. By 1998, one study found the top 5% of all web sites garnered more than 74% of all traffic. The winner-take-all hypothesis in economics suggests that once a technology or a firm gets ahead, it will do better and better over time, whereas lagging technology and firms will fall further behind. See First-mover advantage.
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Learning classifier system

Learning classifier systems, or LCS, are a paradigm of rule-based machine learning methods that combine a discovery component (e.g. typically a genetic algorithm in evolutionary computation) with a learning component (performing either supervised learning, reinforcement learning, or unsupervised learning). Learning classifier systems seek to identify a set of context-dependent rules that collectively store and apply knowledge in a piecewise manner in order to make predictions (e.g. behavior modeling, classification, data mining, regression, function approximation, or game strategy). This approach allows complex solution spaces to be broken up into smaller, simpler parts for the reinforcement learning that is inside artificial intelligence research. The founding concepts behind learning classifier systems came from attempts to model complex adaptive systems, using rule-based agents to form an artificial cognitive system (i.e. artificial intelligence). == Methodology == The architecture and components of a given learning classifier system can be quite variable. It is useful to think of an LCS as a machine consisting of several interacting components. Components may be added or removed, or existing components modified/exchanged to suit the demands of a given problem domain (like algorithmic building blocks) or to make the algorithm flexible enough to function in many different problem domains. As a result, the LCS paradigm can be flexibly applied to many problem domains that call for machine learning. The major divisions among LCS implementations are as follows: (1) Michigan-style architecture vs. Pittsburgh-style architecture, (2) reinforcement learning vs. supervised learning, (3) incremental learning vs. batch learning, (4) online learning vs. offline learning, (5) strength-based fitness vs. accuracy-based fitness, and (6) complete action mapping vs best action mapping. These divisions are not necessarily mutually exclusive. For example, XCS, the best known and best studied LCS algorithm, is Michigan-style, was designed for reinforcement learning but can also perform supervised learning, applies incremental learning that can be either online or offline, applies accuracy-based fitness, and seeks to generate a complete action mapping. === Elements of a generic LCS algorithm === Keeping in mind that LCS is a paradigm for genetic-based machine learning rather than a specific method, the following outlines key elements of a generic, modern (i.e. post-XCS) LCS algorithm. For simplicity let us focus on Michigan-style architecture with supervised learning. See the illustrations on the right laying out the sequential steps involved in this type of generic LCS. ==== Environment ==== The environment is the source of data upon which an LCS learns. It can be an offline, finite training dataset (characteristic of a data mining, classification, or regression problem), or an online sequential stream of live training instances. Each training instance is assumed to include some number of features (also referred to as attributes, or independent variables), and a single endpoint of interest (also referred to as the class, action, phenotype, prediction, or dependent variable). Part of LCS learning can involve feature selection, therefore not all of the features in the training data need to be informative. The set of feature values of an instance is commonly referred to as the state. For simplicity let's assume an example problem domain with Boolean/binary features and a Boolean/binary class. For Michigan-style systems, one instance from the environment is trained on each learning cycle (i.e. incremental learning). Pittsburgh-style systems perform batch learning, where rule sets are evaluated in each iteration over much or all of the training data. ==== Rule/classifier/population ==== A rule is a context dependent relationship between state values and some prediction. Rules typically take the form of an {IF:THEN} expression, (e.g. {IF 'condition' THEN 'action'}, or as a more specific example, {IF 'red' AND 'octagon' THEN 'stop-sign'}). A critical concept in LCS and rule-based machine learning alike, is that an individual rule is not in itself a model, since the rule is only applicable when its condition is satisfied. Think of a rule as a "local-model" of the solution space. Rules can be represented in many different ways to handle different data types (e.g. binary, discrete-valued, ordinal, continuous-valued). Given binary data LCS traditionally applies a ternary rule representation (i.e. rules can include either a 0, 1, or '#' for each feature in the data). The 'don't care' symbol (i.e. '#') serves as a wild card within a rule's condition allowing rules, and the system as a whole to generalize relationships between features and the target endpoint to be predicted. Consider the following rule (#1###0 ~ 1) (i.e. condition ~ action). This rule can be interpreted as: IF the second feature = 1 AND the sixth feature = 0 THEN the class prediction = 1. We would say that the second and sixth features were specified in this rule, while the others were generalized. This rule, and the corresponding prediction are only applicable to an instance when the condition of the rule is satisfied by the instance. This is more commonly referred to as matching. In Michigan-style LCS, each rule has its own fitness, as well as a number of other rule-parameters associated with it that can describe the number of copies of that rule that exist (i.e. the numerosity), the age of the rule, its accuracy, or the accuracy of its reward predictions, and other descriptive or experiential statistics. A rule along with its parameters is often referred to as a classifier. In Michigan-style systems, classifiers are contained within a population [P] that has a user defined maximum number of classifiers. Unlike most stochastic search algorithms (e.g. evolutionary algorithms), LCS populations start out empty (i.e. there is no need to randomly initialize a rule population). Classifiers will instead be initially introduced to the population with a covering mechanism. In any LCS, the trained model is a set of rules/classifiers, rather than any single rule/classifier. In Michigan-style LCS, the entire trained (and optionally, compacted) classifier population forms the prediction model. ==== Matching ==== One of the most critical and often time-consuming elements of an LCS is the matching process. The first step in an LCS learning cycle takes a single training instance from the environment and passes it to [P] where matching takes place. In step two, every rule in [P] is now compared to the training instance to see which rules match (i.e. are contextually relevant to the current instance). In step three, any matching rules are moved to a match set [M]. A rule matches a training instance if all feature values specified in the rule condition are equivalent to the corresponding feature value in the training instance. For example, assuming the training instance is (001001 ~ 0), these rules would match: (###0## ~ 0), (00###1 ~ 0), (#01001 ~ 1), but these rules would not (1##### ~ 0), (000##1 ~ 0), (#0#1#0 ~ 1). Notice that in matching, the endpoint/action specified by the rule is not taken into consideration. As a result, the match set may contain classifiers that propose conflicting actions. In the fourth step, since we are performing supervised learning, [M] is divided into a correct set [C] and an incorrect set [I]. A matching rule goes into the correct set if it proposes the correct action (based on the known action of the training instance), otherwise it goes into [I]. In reinforcement learning LCS, an action set [A] would be formed here instead, since the correct action is not known. ==== Covering ==== At this point in the learning cycle, if no classifiers made it into either [M] or [C] (as would be the case when the population starts off empty), the covering mechanism is applied (fifth step). Covering is a form of online smart population initialization. Covering randomly generates a rule that matches the current training instance (and in the case of supervised learning, that rule is also generated with the correct action. Assuming the training instance is (001001 ~ 0), covering might generate any of the following rules: (#0#0## ~ 0), (001001 ~ 0), (#010## ~ 0). Covering not only ensures that each learning cycle there is at least one correct, matching rule in [C], but that any rule initialized into the population will match at least one training instance. This prevents LCS from exploring the search space of rules that do not match any training instances. ==== Parameter updates/credit assignment/learning ==== In the sixth step, the rule parameters of any rule in [M] are updated to reflect the new experience gained from the current training instance. Depending on the LCS algorithm, a number of updates can take place at this step. For supervised learning, we can simply update the accuracy/error of a
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Semidefinite embedding

Maximum Variance Unfolding (MVU), also known as Semidefinite Embedding (SDE), is an algorithm in computer science that uses semidefinite programming to perform non-linear dimensionality reduction of high-dimensional vectorial input data. It is motivated by the observation that kernel Principal Component Analysis (kPCA) does not reduce the data dimensionality, as it leverages the Kernel trick to non-linearly map the original data into an inner-product space. == Algorithm == MVU creates a mapping from the high dimensional input vectors to some low dimensional Euclidean vector space in the following steps: A neighbourhood graph is created. Each input is connected with its k-nearest input vectors (according to Euclidean distance metric) and all k-nearest neighbors are connected with each other. If the data is sampled well enough, the resulting graph is a discrete approximation of the underlying manifold. The neighbourhood graph is "unfolded" with the help of semidefinite programming. Instead of learning the output vectors directly, the semidefinite programming aims to find an inner product matrix that maximizes the pairwise distances between any two inputs that are not connected in the neighbourhood graph while preserving the nearest neighbors distances. The low-dimensional embedding is finally obtained by application of multidimensional scaling on the learned inner product matrix. The steps of applying semidefinite programming followed by a linear dimensionality reduction step to recover a low-dimensional embedding into a Euclidean space were first proposed by Linial, London, and Rabinovich. == Optimization formulation == Let X {\displaystyle X\,\!} be the original input and Y {\displaystyle Y\,\!} be the embedding. If i , j {\displaystyle i,j\,\!} are two neighbors, then the local isometry constraint that needs to be satisfied is: | X i − X j | 2 = | Y i − Y j | 2 {\displaystyle |X_{i}-X_{j}|^{2}=|Y_{i}-Y_{j}|^{2}\,\!} Let G , K {\displaystyle G,K\,\!} be the Gram matrices of X {\displaystyle X\,\!} and Y {\displaystyle Y\,\!} (i.e.: G i j = X i ⋅ X j , K i j = Y i ⋅ Y j {\displaystyle G_{ij}=X_{i}\cdot X_{j},K_{ij}=Y_{i}\cdot Y_{j}\,\!} ). We can express the above constraint for every neighbor points i , j {\displaystyle i,j\,\!} in term of G , K {\displaystyle G,K\,\!} : G i i + G j j − G i j − G j i = K i i + K j j − K i j − K j i {\displaystyle G_{ii}+G_{jj}-G_{ij}-G_{ji}=K_{ii}+K_{jj}-K_{ij}-K_{ji}\,\!} In addition, we also want to constrain the embedding Y {\displaystyle Y\,\!} to center at the origin: 0 = | ∑ i Y i | 2 ⇔ ( ∑ i Y i ) ⋅ ( ∑ i Y i ) ⇔ ∑ i , j Y i ⋅ Y j ⇔ ∑ i , j K i j {\displaystyle 0=|\sum _{i}Y_{i}|^{2}\Leftrightarrow (\sum _{i}Y_{i})\cdot (\sum _{i}Y_{i})\Leftrightarrow \sum _{i,j}Y_{i}\cdot Y_{j}\Leftrightarrow \sum _{i,j}K_{ij}} As described above, except the distances of neighbor points are preserved, the algorithm aims to maximize the pairwise distance of every pair of points. The objective function to be maximized is: T ( Y ) = 1 2 N ∑ i , j | Y i − Y j | 2 {\displaystyle T(Y)={\dfrac {1}{2N}}\sum _{i,j}|Y_{i}-Y_{j}|^{2}} Intuitively, maximizing the function above is equivalent to pulling the points as far away from each other as possible and therefore "unfold" the manifold. The local isometry constraint Let τ = m a x { η i j | Y i − Y j | 2 } {\displaystyle \tau =max\{\eta _{ij}|Y_{i}-Y_{j}|^{2}\}\,\!} where η i j := { 1 if i is a neighbour of j 0 otherwise . {\displaystyle \eta _{ij}:={\begin{cases}1&{\mbox{if}}\ i{\mbox{ is a neighbour of }}j\\0&{\mbox{otherwise}}.\end{cases}}} prevents the objective function from diverging (going to infinity). Since the graph has N points, the distance between any two points | Y i − Y j | 2 ≤ N τ {\displaystyle |Y_{i}-Y_{j}|^{2}\leq N\tau \,\!} . We can then bound the objective function as follows: T ( Y ) = 1 2 N ∑ i , j | Y i − Y j | 2 ≤ 1 2 N ∑ i , j ( N τ ) 2 = N 3 τ 2 2 {\displaystyle T(Y)={\dfrac {1}{2N}}\sum _{i,j}|Y_{i}-Y_{j}|^{2}\leq {\dfrac {1}{2N}}\sum _{i,j}(N\tau )^{2}={\dfrac {N^{3}\tau ^{2}}{2}}\,\!} The objective function can be rewritten purely in the form of the Gram matrix: T ( Y ) = 1 2 N ∑ i , j | Y i − Y j | 2 = 1 2 N ∑ i , j ( Y i 2 + Y j 2 − Y i ⋅ Y j − Y j ⋅ Y i ) = 1 2 N ( ∑ i , j Y i 2 + ∑ i , j Y j 2 − ∑ i , j Y i ⋅ Y j − ∑ i , j Y j ⋅ Y i ) = 1 2 N ( ∑ i , j Y i 2 + ∑ i , j Y j 2 − 0 − 0 ) = 1 N ( ∑ i Y i 2 ) = 1 N ( T r ( K ) ) {\displaystyle {\begin{aligned}T(Y)&{}={\dfrac {1}{2N}}\sum _{i,j}|Y_{i}-Y_{j}|^{2}\\&{}={\dfrac {1}{2N}}\sum _{i,j}(Y_{i}^{2}+Y_{j}^{2}-Y_{i}\cdot Y_{j}-Y_{j}\cdot Y_{i})\\&{}={\dfrac {1}{2N}}(\sum _{i,j}Y_{i}^{2}+\sum _{i,j}Y_{j}^{2}-\sum _{i,j}Y_{i}\cdot Y_{j}-\sum _{i,j}Y_{j}\cdot Y_{i})\\&{}={\dfrac {1}{2N}}(\sum _{i,j}Y_{i}^{2}+\sum _{i,j}Y_{j}^{2}-0-0)\\&{}={\dfrac {1}{N}}(\sum _{i}Y_{i}^{2})={\dfrac {1}{N}}(Tr(K))\\\end{aligned}}\,\!} Finally, the optimization can be formulated as: Maximize T r ( K ) subject to K ⪰ 0 , ∑ i j K i j = 0 and G i i + G j j − G i j − G j i = K i i + K j j − K i j − K j i , ∀ i , j where η i j = 1 , {\displaystyle {\begin{aligned}&{\text{Maximize}}&&Tr(\mathbf {K} )\\&{\text{subject to}}&&\mathbf {K} \succeq 0,\sum _{ij}\mathbf {K} _{ij}=0\\&{\text{and}}&&G_{ii}+G_{jj}-G_{ij}-G_{ji}=K_{ii}+K_{jj}-K_{ij}-K_{ji},\forall i,j{\mbox{ where }}\eta _{ij}=1,\end{aligned}}} After the Gram matrix K {\displaystyle K\,\!} is learned by semidefinite programming, the output Y {\displaystyle Y\,\!} can be obtained via Cholesky decomposition. In particular, the Gram matrix can be written as K i j = ∑ α = 1 N ( λ α V α i V α j ) {\displaystyle K_{ij}=\sum _{\alpha =1}^{N}(\lambda _{\alpha }V_{\alpha i}V_{\alpha j})\,\!} where V α i {\displaystyle V_{\alpha i}\,\!} is the i-th element of eigenvector V α {\displaystyle V_{\alpha }\,\!} of the eigenvalue λ α {\displaystyle \lambda _{\alpha }\,\!} . It follows that the α {\displaystyle \alpha \,\!} -th element of the output Y i {\displaystyle Y_{i}\,\!} is λ α V α i {\displaystyle {\sqrt {\lambda _{\alpha }}}V_{\alpha i}\,\!} .
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AI-complete

In the field of artificial intelligence (AI), tasks that are hypothesized to require artificial general intelligence to solve are informally known as AI-complete or AI-hard. Calling a problem AI-complete reflects the belief that it cannot be solved by a simple specific algorithm. Prior to 2013, problems supposed to be AI-complete included computer vision, natural language understanding, and dealing with unexpected circumstances while solving any real-world problem. AI-complete tasks were notably considered useful for distinguishing humans from automated agents, as CAPTCHAs aim to do. == History == The term was coined by Fanya Montalvo by analogy with NP-complete and NP-hard in complexity theory, which formally describes the most famous class of difficult problems. Early uses of the term are in Erik Mueller's 1987 PhD dissertation and in Eric Raymond's 1991 Jargon File. Expert systems, that were popular in the 1980s, were able to solve very simple and/or restricted versions of AI-complete problems, but never in their full generality. When AI researchers attempted to "scale up" their systems to handle more complicated, real-world situations, the programs tended to become excessively brittle without commonsense knowledge or a rudimentary understanding of the situation: they would fail as unexpected circumstances outside of its original problem context would begin to appear. When human beings are dealing with new situations in the world, they are helped by their awareness of the general context: they know what the things around them are, why they are there, what they are likely to do and so on. They can recognize unusual situations and adjust accordingly. Expert systems lacked this adaptability and were brittle when facing new situations. DeepMind published a work in May 2022 in which they trained a single model to do several things at the same time. The model, named Gato, can "play Atari, caption images, chat, stack blocks with a real robot arm and much more, deciding based on its context whether to output text, joint torques, button presses, or other tokens." Similarly, some tasks once considered to be AI-complete, like machine translation, are among the capabilities of large language models. == AI-complete problems == AI-complete problems have been hypothesized to include: AI peer review (composite natural language understanding, automated reasoning, automated theorem proving, formalized logic expert system) Bongard problems Computer vision (and subproblems such as object recognition) Natural language understanding (and subproblems such as text mining, machine translation, and word-sense disambiguation) Autonomous driving Dealing with unexpected circumstances while solving any real world problem, whether navigation, planning, or even the kind of reasoning done by expert systems. == Formalization == Computational complexity theory deals with the relative computational difficulty of computable functions. By definition, it does not cover problems whose solution is unknown or has not been characterized formally. Since many AI problems have no formalization yet, conventional complexity theory does not enable a formal definition of AI-completeness. == Research == Roman Yampolskiy suggests that a problem C {\displaystyle C} is AI-Complete if it has two properties: It is in the set of AI problems (Human Oracle-solvable). Any AI problem can be converted into C {\displaystyle C} by some polynomial time algorithm. On the other hand, a problem H {\displaystyle H} is AI-Hard if and only if there is an AI-Complete problem C {\displaystyle C} that is polynomial time Turing-reducible to H {\displaystyle H} . This also gives as a consequence the existence of AI-Easy problems, that are solvable in polynomial time by a deterministic Turing machine with an oracle for some problem. Yampolskiy has also hypothesized that the Turing Test is a defining feature of AI-completeness. Groppe and Jain classify problems which require artificial general intelligence to reach human-level machine performance as AI-complete, while only restricted versions of AI-complete problems can be solved by the current AI systems. For Šekrst, getting a polynomial solution to AI-complete problems would not necessarily be equal to solving the issue of artificial general intelligence, while emphasizing the lack of computational complexity research being the limiting factor towards achieving artificial general intelligence. For Kwee-Bintoro and Velez, solving AI-complete problems would have strong repercussions on society.
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Canonical correspondence analysis

In multivariate analysis, canonical correspondence analysis (CCA) is an ordination technique that determines axes from the response data as a unimodal combination of measured predictors. CCA is commonly used in ecology in order to extract gradients that drive the composition of ecological communities. CCA extends correspondence analysis (CA) with regression, in order to incorporate predictor variables. == History == CCA was developed in 1986 by Cajo ter Braak and implemented in the program CANOCO, an extension of DECORANA. To date, CCA is one of the most popular multivariate methods in ecology, despite the availability of contemporary alternatives. CCA was originally derived and implemented using an algorithm of weighted averaging, though Legendre & Legendre (1998) derived an alternative algorithm. == Assumptions == The requirements of a CCA are that the samples are random and independent. Also, the data are categorical and that the independent variables are consistent within the sample site and error-free. The original publication states the need for equal species tolerances, equal species maxima, and equispaced or uniformly distributed species optima and site scores.
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Semantic mapping (statistics)

Semantic mapping (SM) is a statistical method for dimensionality reduction (the transformation of data from a high-dimensional space into a low-dimensional space). SM can be used in a set of multidimensional vectors of features to extract a few new features that preserves the main data characteristics. SM performs dimensionality reduction by clustering the original features in semantic clusters and combining features mapped in the same cluster to generate an extracted feature. Given a data set, this method constructs a projection matrix that can be used to map a data element from a high-dimensional space into a reduced dimensional space. SM can be applied in construction of text mining and information retrieval systems, as well as systems managing vectors of high dimensionality. SM is an alternative to random mapping, principal components analysis and latent semantic indexing methods.
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