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INaturalist

iNaturalist is an American 501(c)(3) nonprofit social network of naturalists, citizen scientists, and biologists built on the concept of mapping and sharing observations of biodiversity across the globe. iNaturalist may be accessed via its website or from its mobile applications. iNaturalist includes an automated species identification tool, and users further assist each other in identifying organisms from photographs and sound recordings. As of 5 August 2025, iNaturalist users had contributed nearly 300 million observations of plants, animals, fungi, and other organisms worldwide, and 400,000 users were active in the previous 30 days. iNaturalist serves as an important resource of open data for biodiversity research, conservation, and education, describing itself as "an online social network of people sharing biodiversity information to help each other learn about nature." It is the primary application for crowd-sourced biodiversity data in places such as Mexico, southern Africa, and Australia, and the project has been called "a standard-bearer for natural history mobile applications." Most of iNaturalist's software is open source. It has contributed to over 4,000 research papers and is widely used by scientists, land managers, and conservationists worldwide. The platform has also been active in the discovery of new species and rediscovery of species previously assumed to be extinct. == History == iNaturalist began in 2008 as a UC Berkeley School of Information Master's final project of Nate Agrin, Jessica Kline, and Ken-ichi Ueda. Agrin and Ueda continued work on the site with Sean McGregor, a web developer. In 2011, Ueda began collaboration with Scott Loarie, a research fellow at Stanford University and lecturer at UC Berkeley. Ueda and Loarie are the current co-directors of iNaturalist.org. The organization merged with the California Academy of Sciences on 24 April 2014. In 2017, iNaturalist became a joint initiative between the California Academy of Sciences and the National Geographic Society. With these collaborations and growing popularity of the site since 2012, the number of participants and observations has roughly doubled each year. In 2014, iNaturalist reached 1 million observations. Later, as of October 2023, there were 181 million observations (163 million verifiable). On 11 July 2023 iNaturalist announced its status as a newly independent 501(c)(3) nonprofit organization. === Google AI controversy === On 9 June 2025 Google announced that iNaturalist would be part of its "Generative AI Accelerator". This announcement, paired with the initial lack of information on the iNaturalist site, led to outcry from many iNaturalist users in the blog comments and forum, worrying about the consequences for the environment, volunteer engagement, reliability and raised questions about the decision making within iNaturalist, while some saw the backlash as a sign that people want to resist 'corrosive technologies'. PZ Myers, a biology professor who uses iNaturalist in his teaching, published an article on his website Pharyngula stating that "any decision that drives people away and replaces them with a hallucinating bot is a bad decision". == Platforms == Users can interact with iNaturalist in the following ways: through the iNaturalist.org website, through two mobile apps: iNaturalist (iOS/Android) and Seek by iNaturalist (iOS/Android), or through partner organizations such as the Global Biodiversity Information Facility (GBIF) website. On the iNaturalist.org website, visitors can search the public dataset and interact with other people adding observations and identifications. The website provides tools for registered users to add, identify, and discuss observations, write journal posts, explore information about species, create project pages to recruit participation, and coordinate work on their topics of interest. On the iNaturalist mobile app, users can create and share nature observations to the online dataset, explore observations both nearby and around the world, and learn about different species. Seek by iNaturalist, a separate app marketed to families, requires no online account registration and all observations may remain private. Seek incorporates features of gamification, such as providing a list of nearby organisms to find and encouraging the collection of badges and participation in challenges. Seek was initially released in the spring of 2018. == Observations == The iNaturalist platform is based on crowdsourcing of observations and identifications. An iNaturalist observation records a person's encounter with an individual organism at a particular time and place. An iNaturalist observation may also record evidence of an organism, such as animal tracks, nests, or scat. The scope of iNaturalist excludes natural but inert subjects such as geologic or hydrologic features. Users typically upload photos as evidence of their findings, though audio recordings are also accepted, and such evidence is not a strict requirement. Users may share observation locations publicly, "obscure" them to display a less precise location or make the locations completely private. iNaturalist users can add identifications to each other's observations in order to confirm or improve the identification of the observation. Observations are classified as "Casual", "Needs ID" (needs identification), or "Research Grade" based on the quality of the data provided and the community identification process. Any quality of data can be downloaded from iNaturalist and "Research Grade" observations are often incorporated into other online databases such as the Global Biodiversity Information Facility and the Atlas of Living Australia. === Automated species identification === In addition to observations being identified by others in the community, iNaturalist includes an automated species identification tool, first released in 2017. Images can be identified via a computer vision model which has been trained on the large database of the observations on iNaturalist. Multiple species suggestions are typically provided with the suggestion that the software guesses to be most likely is at the top of the list. A broader taxon such as a genus or family is commonly provided if the model is unsure of the species. It is trained once or twice a year, and the threshold for species included in the training set has changed over time. It can be difficult for the model to guess correctly if the species in question is infrequently observed or hard to identify from images alone, or if the image submitted has poor lighting, is blurry, or contains multiple subjects. In February 2023, iNaturalist released v2.1 of its computer vision model, which was trained on a new source model which performed significantly better than the previous models trained using a different source model. In April 2025 iNaturalist released an updated app for iOS, changing the original version to "iNaturalist Classic." == Projects == Users have created and contributed to tens of thousands of different projects on iNaturalist. The platform is commonly used to record observations during bioblitzes, which are biological surveying events that attempt to record all the species that occur within a designated area, and a specific project type on iNaturalist. Other project types include collections of observations by location or taxon or documenting specific types of observations such as animal tracks and signs, the spread of invasive species, roadkill, fishing catches, or discovering new species. In 2011, iNaturalist was used as a platform to power the Global Amphibian and Global Reptile BioBlitzes, in which observations were used to help monitor the occurrence and distribution of the world's reptiles and amphibian species. The US National Park Service partnered with iNaturalist to record observations from the 2016 National Parks BioBlitz. That project exceeded 100,000 observations in August 2016. In 2017, the United Nations Environment Programme teamed up with iNaturalist to celebrate World Environment Day.. In 2022, Reef Ecologic teamed up with iNaturalist to celebrate World Oceans Day. === City Nature Challenge === In 2016, Lila Higgins from the Natural History Museum of Los Angeles County and Alison Young from the California Academy of Sciences co-founded the City Nature Challenge (CNC). In the first City Nature Challenge, naturalists in Los Angeles and the San Francisco Bay Area documented over 20,000 observations with the iNaturalist platform. In 2017, the CNC expanded to 16 cities across the United States and collected over 125,000 observations of wildlife in 5 days. The CNC expanded to a global audience in 2018, with 68 cities participating from 19 countries, with some cities using community science platforms other than iNaturalist to participate. In 4 days, over 17,000 people cataloged over 440,000 nature observations in urban regions around the world. In 2019, the CNC once again expanded, with 35,000 parti
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Bioz

Bioz is a search engine for life science experimentation. == History == Bioz was founded by Karin Lachmi and Daniel Levitt. Lachmi is a scientist who completed her postdoc in molecular and cellular biology at the Stanford University School of Medicine. During her lab work she found little available data regarding preferable lab tools, reagents and related products for experimentation. There are 50,000 vendors selling 300 million scientific products. She decided to start the company in order to provide researchers with adequate information for that purpose. Co-founder Daniel Levitt is an entrepreneur who sold his company WebAppoint to Microsoft in the year 2000. He also co-founded the company StemRad. At Bioz, Lachmi serves as the Chief Scientific Officer and Levitt serves as the chief executive officer. Bioz claims to have over a million researcher-users from 196 countries. Among the investors are Esther Dyson and the Stanford-StartX Fund. The company's advisory board includes Nobel Laureates in Chemistry Michael Levitt, Roger Kornberg, and Ada Yonath. == Technology == The company uses artificial intelligence, machine learning and natural language processing in order to extract experimentation data from scientific articles, such as the products that researchers used, the companies that supply the products, the protocol conditions that researchers selected, and the types of experiments and techniques. The algorithm ranks products based on how frequently they were used by researchers in their experiments, how recently a product was used, and the impact factor of the journal. The algorithm's output is a Bioz stars score for each product that was mentioned in an article. Bioz is a data-driven platform for product recommendations, which is contrary to platforms such as TripAdvisor and OpenTable that are based on user-generated reviews and ratings. The recommendations and scoring system that the company has developed are meant to assist researchers with the process of developing future medications and finding cures for diseases. They are guided towards products and techniques that were previously used by other researchers when planning and performing experiments. The company's revenue is based on selling SaaS subscriptions to researchers in biopharma companies. They also charge product suppliers for content syndication.
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Latent space

A latent space, also known as a latent feature space or embedding space, is an embedding of a set of items within a manifold in which items resembling each other are positioned closer to one another. Position within the latent space can be viewed as being defined by a set of latent variables that emerge from the resemblances between the objects. In most cases, the dimensionality of the latent space is chosen to be lower than the dimensionality of the feature space from which the data points are drawn, making the construction of a latent space an example of dimensionality reduction, which can also be viewed as a form of data compression. Latent spaces are usually fit via machine learning, and they can then be used as feature spaces in machine learning models, including classifiers and other supervised predictors. The interpretation of latent spaces in machine learning models is an ongoing area of research, but achieving clear interpretations remains challenging. The black-box nature of these models often makes the latent space unintuitive, while its high-dimensional, complex, and nonlinear characteristics further complicate the task of understanding it. Analysis of the latent space geometry of diffusion models reveals a fractal structure of phase transitions in the latent space, characterized by abrupt changes in the Fisher information metric. Some visualization techniques have been developed to connect the latent space to the visual world, but there is often not a direct connection between the latent space interpretation and the model itself. Such techniques include t-distributed stochastic neighbor embedding (t-SNE), where the latent space is mapped to two dimensions for visualization. Latent space distances lack physical units, so the interpretation of these distances may depend on the application. == Embedding models == Several embedding models have been developed to perform this transformation to create latent space embeddings given a set of data items and a similarity function. These models learn the embeddings by leveraging statistical techniques and machine learning algorithms. Here are some commonly used embedding models: Word2Vec: Word2Vec is a popular embedding model used in natural language processing (NLP). It learns word embeddings by training a neural network on a large corpus of text. Word2Vec captures semantic and syntactic relationships between words, allowing for meaningful computations like word analogies. GloVe: GloVe (Global Vectors for Word Representation) is another widely used embedding model for NLP. It combines global statistical information from a corpus with local context information to learn word embeddings. GloVe embeddings are known for capturing both semantic and relational similarities between words. Siamese Networks: Siamese networks are a type of neural network architecture commonly used for similarity-based embedding. They consist of two identical subnetworks that process two input samples and produce their respective embeddings. Siamese networks are often used for tasks like image similarity, recommendation systems, and face recognition. Variational Autoencoders (VAEs): VAEs are generative models that simultaneously learn to encode and decode data. The latent space in VAEs acts as an embedding space. By training VAEs on high-dimensional data, such as images or audio, the model learns to encode the data into a compact latent representation. VAEs are known for their ability to generate new data samples from the learned latent space. == Multimodality == Multimodality refers to the integration and analysis of multiple modes or types of data within a single model or framework. Embedding multimodal data involves capturing relationships and interactions between different data types, such as images, text, audio, and structured data. Multimodal embedding models aim to learn joint representations that fuse information from multiple modalities, allowing for cross-modal analysis and tasks. These models enable applications like image captioning, visual question answering, and multimodal sentiment analysis. To embed multimodal data, specialized architectures such as deep multimodal networks or multimodal transformers are employed. These architectures combine different types of neural network modules to process and integrate information from various modalities. The resulting embeddings capture the complex relationships between different data types, facilitating multimodal analysis and understanding. == Applications == Embedding latent space and multimodal embedding models have found numerous applications across various domains: Information retrieval: Embedding techniques enable efficient similarity search and recommendation systems by representing data points in a compact space. Natural language processing: Word embeddings have revolutionized NLP tasks like sentiment analysis, machine translation, and document classification. Computer vision: Image and video embeddings enable tasks like object recognition, image retrieval, and video summarization. Recommendation systems: Embeddings help capture user preferences and item characteristics, enabling personalized recommendations. Healthcare: Embedding techniques have been applied to electronic health records, medical imaging, and genomic data for disease prediction, diagnosis, and treatment. Social systems: Embedding techniques can be used to learn latent representations of social systems such as internal migration systems, academic citation networks, and world trade networks.
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Ground truth

Ground truth is information that is known to be real or true, provided by direct observation and measurement (i.e. empirical evidence) as opposed to information provided by inference. The term ground truth appeared in remote sensing literature as early as 1972, when NASA described it as essential "data about ... materials on the earth's surface" used to calibrate measurements. It was later adopted by the statistical modeling and machine learning communities. == Etymology == The Oxford English Dictionary (s.v. ground truth) records the use of the word Groundtruth in the sense of 'fundamental truth' from Henry Ellison's poem "The Siberian Exile's Tale", published in 1833. == Usage == The term "ground truth" can be used as a noun, adjective, and verb. Noun: "ground truth" (no hyphen). Example: "The ground truth is essential for training accurate models." Adjective: "ground-truth" (hyphenated compound adjective). Example: "We need to use ground-truth data to validate the model." Verb: "to ground-truth" or "to groundtruth" (compound verb,). Example: "We need to ground-truth the results to ensure their accuracy." == Statistics and machine learning == In statistics and machine learning, ground truth is the ideal expected result, used in statistical models to prove or disprove research hypotheses. "Ground truthing" is the process of gathering the good data for this test. Ground truth is typically included in labeled data. In machine learning, "ground truth" is not necessarily objectively correct or true. For example, in training AI models or relevance rankers, it may be a set of judgments made by people or inferred from user behavior, which may depend on context. For example, in Bayesian spam filtering, a supervised learning system is typically trained by examples labeled as spam and non-spam. Although these labels may be subjective or inaccurate, they are considered ground truth. True ground truth in machine learning is objective data. For example, suppose we are testing a stereo vision system to see how well it can estimate 3D positions. A calibrated laser rangefinder may provide accurate distances as ground truth. == Remote sensing == In remote sensing, "ground truth" refers to information collected at the imaged location. Ground truth allows image data to be related to real features and materials on the ground. The collection of ground truth data enables calibration of remote-sensing data, and aids in the interpretation and analysis of what is being sensed. Examples include cartography, meteorology, analysis of aerial photographs, satellite imagery and other techniques in which data are gathered at a distance. More specifically, ground truth may refer to a process in which "pixels" on a satellite image are compared to what is imaged (at the time of capture) in order to verify the contents of the "pixels" in the image (noting that the concept of "pixel" is imaging-system-dependent). In the case of a classified image, supervised classification can help to determine the accuracy of the classification by the remote sensing system which can minimize error in the classification. Ground truth is usually done on site, correlating what is known with surface observations and measurements of various properties of the features of the ground resolution cells under study in the remotely sensed digital image. The process also involves taking geographic coordinates of the ground resolution cell with GPS technology and comparing those with the coordinates of the "pixel" being studied provided by the remote sensing software to understand and analyze the location errors and how it may affect a particular study. Ground truth is important in the initial supervised classification of an image. When the identity and location of land cover types are known through a combination of field work, maps, and personal experience these areas are known as training sites. The spectral characteristics of these areas are used to train the remote sensing software using decision rules for classifying the rest of the image. These decision rules such as Maximum Likelihood Classification, Parallelopiped Classification, and Minimum Distance Classification offer different techniques to classify an image. Additional ground truth sites allow the remote sensor to establish an error matrix that validates the accuracy of the classification method used. Different classification methods may have different percentages of error for a given classification project. It is important that the remote sensor chooses a classification method that works best with the number of classifications used while providing the least amount of error. Ground truth also helps with atmospheric correction. Since images from satellites have to pass through the atmosphere, they can get distorted because of absorption in the atmosphere. So ground truth can help fully identify objects in satellite photos. === Errors of commission === An example of an error of commission is when a pixel reports the presence of a feature (such a tree) that, in reality, is absent (no tree is actually present). Ground truthing ensures that the error matrices have a higher accuracy percentage than would be the case if no pixels were ground-truthed. This value is the complement of the user's accuracy, i.e. Commission Error = 1 - user's accuracy. === Errors of omission === An example of an error of omission is when pixels of a certain type, for example, maple trees, are not classified as maple trees. The process of ground-truthing helps to ensure that the pixel is classified correctly and the error matrices are more accurate. This value is the complement of the producer's accuracy, i.e. Omission Error = 1 - producer's accuracy == Geographical information systems == In GIS the spatial data is modeled as field (like in remote sensing raster images) or as object (like in vectorial map representation). They are modeled from the real world (also named geographical reality), typically by a cartographic process (illustrated). Geographic information systems such as GIS, GPS, and GNSS, have become so widespread that the term "ground truth" has taken on special meaning in that context. If the location coordinates returned by a location method such as GPS are an estimate of a location, then the "ground truth" is the actual location on Earth. A smart phone might return a set of estimated location coordinates such as 43.87870, −103.45901. The ground truth being estimated by those coordinates is the tip of George Washington's nose on Mount Rushmore. The accuracy of the estimate is the maximum distance between the location coordinates and the ground truth. We could say in this case that the estimate accuracy is 10 meters, meaning that the point on Earth represented by the location coordinates is thought to be within 10 meters of George's nose—the ground truth. In slang, the coordinates indicate where we think George Washington's nose is located, and the ground truth is where it really is. In practice a smart phone or hand-held GPS unit is routinely able to estimate the ground truth within 6–10 meters. Specialized instruments can reduce GPS measurement error to under a centimeter. == Military usage == US military slang uses "ground truth" to refer to the facts comprising a tactical situation—as opposed to intelligence reports, mission plans, and other descriptions reflecting the conative or policy-based projections of the industrial·military complex. The term appears in the title of the Iraq War documentary film The Ground Truth (2006), and also in military publications, for example Stars and Stripes saying: "Stripes decided to figure out what the ground truth was in Iraq."
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Controlled natural language

Controlled natural languages (CNLs) are subsets of natural languages that are obtained by restricting the grammar and vocabulary in order to reduce or eliminate ambiguity and complexity. Traditionally, controlled languages fall into two major types: those that improve readability for human readers (e.g. non-native speakers), and those that enable reliable automatic semantic analysis of the language. The first type of languages (often called "simplified" or "technical" languages), for example ASD Simplified Technical English, Caterpillar Technical English, IBM's Easy English, are used in the industry to increase the quality of technical documentation, and possibly simplify the semi-automatic translation of the documentation. These languages restrict the writer by general rules such as "Keep sentences short", "Avoid the use of pronouns", "Only use dictionary-approved words", and "Use only the active voice". The second type of languages have a formal syntax and formal semantics, and can be mapped to an existing formal language, such as first-order logic. Thus, those languages can be used as knowledge representation languages, and writing of those languages is supported by fully automatic consistency and redundancy checks, query answering, etc. == Languages == Existing controlled natural languages include: == Encoding == IETF has reserved simple as a BCP 47 variant subtag for simplified versions of languages.
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VITAL (machine learning software)

VITAL (Validating Investment Tool for Advancing Life Sciences) was a Board Management Software machine learning proprietary software developed by Aging Analytics, a company registered in Bristol (England) and dissolved in 2017. Andrew Garazha (the firm's Senior Analyst) declared that the project aimed "through iterative releases and updates to create a piece of software capable of making autonomous investment decisions." According to Nick Dyer-Witheford, VITAL 1.0 was a "basic algorithm". On 13 May 2014, Deep Knowledge Ventures, a Hong Kong venture capital firm, claimed to have appointed VITAL to its board of directors in order to prove that artificial intelligence could be an instrument for investment decision-making. The announcement received great press coverage despite the fact commentators consider this a publicity stunt. Fortune reported in 2019 that VITAL is no longer used. == Criticism == Academics and journalists viewed VITAL's board appointment with skepticism. University of Sheffield computer science professor Noel Sharkey called it "a publicity hype". Michael Osborne, a University of Oxford associate professor in machine learning, found it is "a gimmick to call that an actual board member". Simon Sharwood of The Register, wrote there is "a strong whiff of stunt and/or promotion about this". In a 2019 speech, the Chief Scientist of Australia, Alan Finkel, commented, "At the time, most of us probably dismissed Vital as a PR exercise. I admit, I used her story three years ago to get a laugh in one of my speeches." Florian Möslein, a law professor at the University of Marburg, wrote in 2018 that "Vital has widely been acknowledged as the 'world's first artificial intelligence company director'". Vice journalist Jason Koebler suggested that the software did not have any article intelligence capabilities and concluded "VITAL can’t talk, and it can’t hear, and it can’t be a real, functional executive of a company." Sharwood of The Register noted that because VITAL was not a natural person, it could not be a board member under Hong Kong's corporate governance laws. However, in a 2017 interview to The Nikkei, Dmitry Kaminskiy, managing partner of Deep Knowledge Ventures, stated that VITAL had observer status on the board and no voting rights. University of Sheffield computer science professor Noel Sharkey said of VITAL, "On first sight, it looks like a futuristic idea but on reflection it is really a little bit of publicity hype." Vice journalist Jason Koebler said "this is a gimmick" and said "There is literally nothing to suggest that VITAL has any sort of capabilities beyond any other proprietary analysis software". Michael Osborne, a University of Oxford associate professor in machine learning, found VITAL's appointment to be noncredible, saying it is "a bit of a gimmick to call that an actual board member". Osborne said that a core duty of board members to converse with each other, which the algorithm is incapable of doing, so its more likely functionality is to serve as a springboard for conversation among other board members. In a 2019 speech, the Chief Scientist of Australia, Alan Finkel, commented, "At the time, most of us probably dismissed Vital as a PR exercise. I admit, I used her story three years ago to get a laugh in one of my speeches." == Machine intelligence as board member == VITAL was created by a group of programmers employed by Aging Analytics According to Andrew Garazh, Aging Analytics Senior Analyst, VITAL was not a machine learning algorithm as the necessary datasets on investment rounds, intellectual property and clinical trial outcomes are generally not disclosed. Rather, VITAL used fuzzy logic based on 50 parameters to assess risk factors. Aging Analytics licensed the software to Deep Knowledge Ventures. It was used to help the human board members of Deep Knowledge Venture make investment decisions in biotechnology companies. For instance, it supported investments in Insilico Medicine, which creates ways for computers to help find drugs in research into aging. VITAL also supported investing in Pathway Pharmaceuticals, which uses the OncoFinder algorithm to choose and appraise cancer treatments. According to Dmitry Kaminskiy, managing partner of Deep Knowledge Ventures, the motivation for using VITAL was the large number of failed investments in the biotechnology sector and the desire to avoid investing in companies likely to fail. == Ethical and legal implications == Scholars addressed questions around the safety, privacy, accountability transparency and bias in algorithms. Writing in the philosophical journal Multitudes, the academic Ariel Kyrou raised questions about the consequences of a mistake made by an algorithm recommending a dangerous investment. He raised the hypothetical where VITAL was able to persuade the board to invest in a startup that had the facade of doing research into treatment for age-associated ills, but in actuality was run by terrorists who were raising funds. Kyrou raised a series of questions about who society would fault for VITAL's mistake. As the owner of VITAL, should Deep Knowledge Ventures be held accountable, or rather should the companies that supplied data to VITAL or the people who created VITAL be held liable? Simon Sharwood of The Register wrote that because the appointment of a software program to the board directors is not legally feasible in Hong Kong, there is "a strong whiff of stunt and/or promotion about this". Quoting a Thomson Reuters website describing Hong Kong legislation related to corporate governance, Sharwood pointed out that in Hong Kong "the board comprises all of the directors of the company" and "a director must normally be a natural person, except that a private company may have a body corporate as its director if the company is not a member of a listed group." He concluded that since VITAL cannot be considered a "natural person", it is merely a "cosmetic" appointment to the board and that "this software is no more a Board member than Caligula's horse was a senator". Sharwood further argued that corporations frequently purchase directors and officers liability insurance but that it would be practically impossible to get such insurance for VITAL. Sharwood also wrote that were VITAL to be hacked, any misinformation it outputs could be considered "false and misleading communications". In the book Research Handbook on the Law of Artificial Intelligence, Florian Mölein wrote that VITAL could not become a director as defined in Hong Kong's corporate laws, so the other directors just were approaching it as "a member of [the] board with observer status". Lin Shaowei raised concerns in a Journal of East China University of Political Science and Law article about how the software's appearance inspired a complex question about the relationship between corporate law and artificial intelligence. VITAL could be considered either a board director who has voting rights or an observer who does not. Lin said either choice raised questions about whether VITAL is subject to corporate law and who would be held accountable if VITAL recommends a choice that turns out to be damaging to the company. David Theo Goldberg in the Critical Times, a peer reviewed journal in Critical Global Theory, argues that VITAL processed a dataset to predict the most remunerative investment opportunities. Drawing his analysis on an article from Business Insider, Goldberg describes VITAL's decision-making predictiveness based "on surface pattern recognition and the identification of regularities and/or irregularities". In other words, Goldberg asserts that "the normativity of the surface" explains algorithmic knowledge of a "product" like VITAL. In Homo Deus, Yuval Noah Harari mentions VITAL as an example of the future risks that humankind faces. Harari argues that the human mind is being replaced by a world in which algorithms and data make the decisions. Specifically, it is argued that "as algorithms push humans out of the job market," executive boards driven by artificial intelligence are more likely to give priority to algorithms over the humans.
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Mutation (evolutionary algorithm)

Mutation is a genetic operator used to maintain genetic diversity of the chromosomes of a population of an evolutionary algorithm (EA), including genetic algorithms in particular. It is analogous to biological mutation. The classic example of a mutation operator of a binary coded genetic algorithm (GA) involves a probability that an arbitrary bit in a genetic sequence will be flipped from its original state. A common method of implementing the mutation operator involves generating a random variable for each bit in a sequence. This random variable tells whether or not a particular bit will be flipped. This mutation procedure, based on the biological point mutation, is called single point mutation. Other types of mutation operators are commonly used for representations other than binary, such as floating-point encodings or representations for combinatorial problems. The purpose of mutation in EAs is to introduce diversity into the sampled population. Mutation operators are used in an attempt to avoid local minima by preventing the population of chromosomes from becoming too similar to each other, thus slowing or even stopping convergence to the global optimum. This reasoning also leads most EAs to avoid only taking the fittest of the population in generating the next generation, but rather selecting a random (or semi-random) set with a weighting toward those that are fitter. The following requirements apply to all mutation operators used in an EA: every point in the search space must be reachable by one or more mutations. there must be no preference for parts or directions in the search space (no drift). small mutations should be more probable than large ones. For different genome types, different mutation types are suitable. Some mutations are Gaussian, Uniform, Zigzag, Scramble, Insertion, Inversion, Swap, and so on. An overview and more operators than those presented below can be found in the introductory book by Eiben and Smith or in. == Bit string mutation == The mutation of bit strings ensue through bit flips at random positions. Example: The probability of a mutation of a bit is 1 l {\displaystyle {\frac {1}{l}}} , where l {\displaystyle l} is the length of the binary vector. Thus, a mutation rate of 1 {\displaystyle 1} per mutation and individual selected for mutation is reached. == Mutation of real numbers == Many EAs, such as the evolution strategy or the real-coded genetic algorithms, work with real numbers instead of bit strings. This is due to the good experiences that have been made with this type of coding. The value of a real-valued gene can either be changed or redetermined. A mutation that implements the latter should only ever be used in conjunction with the value-changing mutations and then only with comparatively low probability, as it can lead to large changes. In practical applications, the respective value range of the decision variables to be changed of the optimisation problem to be solved is usually limited. Accordingly, the values of the associated genes are each restricted to an interval [ x min , x max ] {\displaystyle [x_{\min },x_{\max }]} . Mutations may or may not take these restrictions into account. In the latter case, suitable post-treatment is then required as described below. === Mutation without consideration of restrictions === A real number x {\displaystyle x} can be mutated using normal distribution N ( 0 , σ ) {\displaystyle {\mathcal {N}}(0,\sigma )} by adding the generated random value to the old value of the gene, resulting in the mutated value x ′ {\displaystyle x'} : x ′ = x + N ( 0 , σ ) {\displaystyle x'=x+{\mathcal {N}}(0,\sigma )} In the case of genes with a restricted range of values, it is a good idea to choose the step size of the mutation σ {\displaystyle \sigma } so that it reasonably fits the range [ x min , x max ] {\displaystyle [x_{\min },x_{\max }]} of the gene to be changed, e.g.: σ = x max − x min 6 {\displaystyle \sigma ={\frac {x_{\text{max}}-x_{\text{min}}}{6}}} The step size can also be adjusted to the smaller permissible change range depending on the current value. In any case, however, it is likely that the new value x ′ {\displaystyle x'} of the gene will be outside the permissible range of values. Such a case must be considered a lethal mutation, since the obvious repair by using the respective violated limit as the new value of the gene would lead to a drift. This is because the limit value would then be selected with the entire probability of the values beyond the limit of the value range. The evolution strategy works with real numbers and mutation based on normal distribution. The step sizes are part of the chromosome and are subject to evolution together with the actual decision variables. === Mutation with consideration of restrictions === One possible form of changing the value of a gene while taking its value range [ x min , x max ] {\displaystyle [x_{\min },x_{\max }]} into account is the mutation relative parameter change of the evolutionary algorithm GLEAM (General Learning Evolutionary Algorithm and Method), in which, as with the mutation presented earlier, small changes are more likely than large ones. First, an equally distributed decision is made as to whether the current value x {\displaystyle x} should be increased or decreased and then the corresponding total change interval is determined. Without loss of generality, an increase is assumed for the explanation and the total change interval is then [ x , x max ] {\displaystyle [x,x_{\max }]} . It is divided into k {\displaystyle k} sub-areas of equal size with the width δ {\displaystyle \delta } , from which k {\displaystyle k} sub-change intervals of different size are formed: i {\displaystyle i} -th sub-change interval: [ x , x + δ ⋅ i ] {\displaystyle [x,x+\delta \cdot i]} with δ = ( x max − x ) k {\displaystyle \delta ={\frac {(x_{\text{max}}-x)}{k}}} and i = 1 , … , k {\displaystyle i=1,\dots ,k} Subsequently, one of the k {\displaystyle k} sub-change intervals is selected in equal distribution and a random number, also equally distributed, is drawn from it as the new value x ′ {\displaystyle x'} of the gene. The resulting summed probabilities of the sub-change intervals result in the probability distribution of the k {\displaystyle k} sub-areas shown in the adjacent figure for the exemplary case of k = 10 {\displaystyle k=10} . This is not a normal distribution as before, but this distribution also clearly favours small changes over larger ones. This mutation for larger values of k {\displaystyle k} , such as 10, is less well suited for tasks where the optimum lies on one of the value range boundaries. This can be remedied by significantly reducing k {\displaystyle k} when a gene value approaches its limits very closely. === Common properties === For both mutation operators for real-valued numbers, the probability of an increase and decrease is independent of the current value and is 50% in each case. In addition, small changes are considerably more likely than large ones. For mixed-integer optimization problems, rounding is usually used. == Mutation of permutations == Mutations of permutations are specially designed for genomes that are themselves permutations of a set. These are often used to solve combinatorial tasks. In the two mutations presented, parts of the genome are rotated or inverted. === Rotation to the right === The presentation of the procedure is illustrated by an example on the right: === Inversion === The presentation of the procedure is illustrated by an example on the right: === Variants with preference for smaller changes === The requirement raised at the beginning for mutations, according to which small changes should be more probable than large ones, is only inadequately fulfilled by the two permutation mutations presented, since the lengths of the partial lists and the number of shift positions are determined in an equally distributed manner. However, the longer the partial list and the shift, the greater the change in gene order. This can be remedied by the following modifications. The end index j {\displaystyle j} of the partial lists is determined as the distance d {\displaystyle d} to the start index i {\displaystyle i} : j = ( i + d ) mod | P 0 | {\displaystyle j=(i+d){\bmod {\left|P_{0}\right|}}} where d {\displaystyle d} is determined randomly according to one of the two procedures for the mutation of real numbers from the interval [ 0 , | P 0 | − 1 ] {\displaystyle \left[0,\left|P_{0}\right|-1\right]} and rounded. For the rotation, k {\displaystyle k} is determined similarly to the distance d {\displaystyle d} , but the value 0 {\displaystyle 0} is forbidden. For the inversion, note that i ≠ j {\displaystyle i\neq j} must hold, so for d {\displaystyle d} the value 0 {\displaystyle 0} must be excluded.
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Gremlin (query language)

Gremlin is a graph traversal language and virtual machine developed by Apache TinkerPop of the Apache Software Foundation. Gremlin works for both OLTP-based graph databases as well as OLAP-based graph processors. Gremlin's automata and functional language foundation enable Gremlin to naturally support imperative and declarative querying, host language agnosticism, user-defined domain specific languages, an extensible compiler/optimizer, single- and multi-machine execution models, and hybrid depth- and breadth-first evaluation with Turing completeness. As an explanatory analogy, Apache TinkerPop and Gremlin are to graph databases what the JDBC and SQL are to relational databases. Likewise, the Gremlin traversal machine is to graph computing as what the Java virtual machine is to general purpose computing. == History == 2009-10-30 the project is born, and immediately named "TinkerPop" 2009-12-25 v0.1 is the first release 2011-05-21 v1.0 is released 2012-05-24 v2.0 is released 2015-01-16 TinkerPop becomes an Apache Incubator project 2015-07-09 v3.0.0-incubating is released 2016-05-23 Apache TinkerPop becomes a top-level project 2016-07-18 v3.1.3 and v3.2.1 are first releases as Apache TinkerPop 2017-12-17 v3.3.1 is released 2018-05-08 v3.3.3 is released 2019-08-05 v3.4.3 is released 2020-02-20 v3.4.6 is released 2021-05-01 v3.5.0 is released 2022-04-04 v3.6.0 is released 2023-07-31 v3.7.0 is released 2025-11-12 v3.8.0 is released == Vendor integration == Gremlin is an Apache2-licensed graph traversal language that can be used by graph system vendors. There are typically two types of graph system vendors: OLTP graph databases and OLAP graph processors. The table below outlines those graph vendors that support Gremlin. == Traversal examples == The following examples of Gremlin queries and responses in a Gremlin-Groovy environment are relative to a graph representation of the MovieLens dataset. The dataset includes users who rate movies. Users each have one occupation, and each movie has one or more categories associated with it. The MovieLens graph schema is detailed below. === Simple traversals === For each vertex in the graph, emit its label, then group and count each distinct label. What year was the oldest movie made? What is Die Hard's average rating? === Projection traversals === For each category, emit a map of its name and the number of movies it represents. For each movie with at least 11 ratings, emit a map of its name and average rating. Sort the maps in decreasing order by their average rating. Emit the first 10 maps (i.e. top 10). === Declarative pattern matching traversals === Gremlin supports declarative graph pattern matching similar to SPARQL. For instance, the following query below uses Gremlin's match()-step. What 80's action movies do 30-something programmers like? Group count the movies by their name and sort the group count map in decreasing order by value. Clip the map to the top 10 and emit the map entries. === OLAP traversal === Which movies are most central in the implicit 5-stars graph? == Gremlin graph traversal machine == Gremlin is a virtual machine composed of an instruction set as well as an execution engine. An analogy is drawn between Gremlin and Java. === Gremlin steps (instruction set) === The following traversal is a Gremlin traversal in the Gremlin-Java8 dialect. The Gremlin language (i.e. the fluent-style of expressing a graph traversal) can be represented in any host language that supports function composition and function nesting. Due to this simple requirement, there exists various Gremlin dialects including Gremlin-Groovy, Gremlin-Scala, Gremlin-Clojure, etc. The above Gremlin-Java8 traversal is ultimately compiled down to a step sequence called a traversal. A string representation of the traversal above provided below. The steps are the primitives of the Gremlin graph traversal machine. They are the parameterized instructions that the machine ultimately executes. The Gremlin instruction set is approximately 30 steps. These steps are sufficient to provide general purpose computing and what is typically required to express the common motifs of any graph traversal query. Given that Gremlin is a language, an instruction set, and a virtual machine, it is possible to design another traversal language that compiles to the Gremlin traversal machine (analogous to how Scala compiles to the JVM). For instance, the popular SPARQL graph pattern match language can be compiled to execute on the Gremlin machine. The following SPARQL query would compile to In Gremlin-Java8, the SPARQL query above would be represented as below and compile to the identical Gremlin step sequence (i.e. traversal). === Gremlin Machine (virtual machine) === The Gremlin graph traversal machine can execute on a single machine or across a multi-machine compute cluster. Execution agnosticism allows Gremlin to run over both graph databases (OLTP) and graph processors (OLAP).
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Visualization (graphics)

Visualization (or visualisation in Commonwealth English; see spelling differences), also known as graphics visualization, is any technique for creating images, diagrams, or animations to communicate a message. Visualization through visual imagery has been an effective way to communicate both abstract and concrete ideas since the dawn of humanity. Examples from history include cave paintings, Egyptian hieroglyphs, Greek geometry, and Leonardo da Vinci's revolutionary methods of technical drawing for engineering purposes that actively involve scientific requirements. Visualization today has ever-expanding applications in science, education, engineering (e.g., product visualization), interactive multimedia, medicine, etc. Typical of a visualization application is the field of computer graphics. The invention of computer graphics (and 3D computer graphics) may be the most important development in visualization since the invention of central perspective in the Renaissance period. The development of animation also helped advance visualization. == Overview == The use of visualization to present information is not a new phenomenon. It has been used in maps, scientific drawings, and data plots for over a thousand years. Examples from cartography include Ptolemy's Geographia (2nd century AD), a map of China (1137 AD), and Minard's map (1861) of Napoleon's invasion of Russia a century and a half ago. Most of the concepts learned in devising these images carry over in a straightforward manner to computer visualization. Edward Tufte has written three critically acclaimed books that explain many of these principles. Computer graphics has from its beginning been used to study scientific problems. However, in its early days the lack of graphics power often limited its usefulness. The recent emphasis on visualization started in 1987 with the publication of Visualization in Scientific Computing, a special issue of Computer Graphics. Since then, there have been several conferences and workshops, co-sponsored by the IEEE Computer Society and ACM SIGGRAPH, devoted to the general topic, and special areas in the field, for example volume visualization. Most people are familiar with the digital animations produced to present meteorological data during weather reports on television, though few can distinguish between those models of reality and the satellite photos that are also shown on such programs. TV also offers scientific visualizations when it shows computer drawn and animated reconstructions of road or airplane accidents. Some of the most popular examples of scientific visualizations are computer-generated images that show real spacecraft in action, out in the void far beyond Earth, or on other planets. Dynamic forms of visualization, such as educational animation or timelines, have the potential to enhance learning about systems that change over time. Apart from the distinction between interactive visualizations and animation, the most useful categorization is probably between abstract and model-based scientific visualizations. The abstract visualizations show completely conceptual constructs in 2D or 3D. These generated shapes are completely arbitrary. The model-based visualizations either place overlays of data on real or digitally constructed images of reality or make a digital construction of a real object directly from the scientific data. Scientific visualization is usually done with specialized software, though there are a few exceptions, noted below. Some of these specialized programs have been released as open source software, having very often its origins in universities, within an academic environment where sharing software tools and giving access to the source code is common. There are also many proprietary software packages of scientific visualization tools. Models and frameworks for building visualizations include the data flow models popularized by systems such as AVS, IRIS Explorer, and VTK toolkit, and data state models in spreadsheet systems such as the Spreadsheet for Visualization and Spreadsheet for Images. == Applications == === Scientific visualization === As a subject in computer science, scientific visualization is the use of interactive, sensory representations, typically visual, of abstract data to reinforce cognition, hypothesis building, and reasoning. Scientific visualization is the transformation, selection, or representation of data from simulations or experiments, with an implicit or explicit geometric structure, to allow the exploration, analysis, and understanding of the data. Scientific visualization focuses and emphasizes the representation of higher order data using primarily graphics and animation techniques. It is a very important part of visualization and maybe the first one, as the visualization of experiments and phenomena is as old as science itself. Traditional areas of scientific visualization are flow visualization, medical visualization, astrophysical visualization, and chemical visualization. There are several different techniques to visualize scientific data, with isosurface reconstruction and direct volume rendering being the more common. === Data and information visualization === Data visualization is a related subcategory of visualization dealing with statistical graphics and geospatial data (as in thematic cartography) that is abstracted in schematic form. Information visualization concentrates on the use of computer-supported tools to explore large amount of abstract data. The term "information visualization" was originally coined by the User Interface Research Group at Xerox PARC and included Jock Mackinlay. Practical application of information visualization in computer programs involves selecting, transforming, and representing abstract data in a form that facilitates human interaction for exploration and understanding. Important aspects of information visualization are dynamics of visual representation and the interactivity. Strong techniques enable the user to modify the visualization in real-time, thus affording unparalleled perception of patterns and structural relations in the abstract data in question. === Educational visualization === Educational visualization is using a simulation to create an image of something so it can be taught about. This is very useful when teaching about a topic that is difficult to otherwise see, for example, atomic structure, because atoms are far too small to be studied easily without expensive and difficult to use scientific equipment. === Knowledge visualization === The use of visual representations to transfer knowledge between at least two persons aims to improve the transfer of knowledge by using computer and non-computer-based visualization methods complementarily. Thus properly designed visualization is an important part of not only data analysis but knowledge transfer process, too. Knowledge transfer may be significantly improved using hybrid designs as it enhances information density but may decrease clarity as well. For example, visualization of a 3D scalar field may be implemented using iso-surfaces for field distribution and textures for the gradient of the field. Examples of such visual formats are sketches, diagrams, images, objects, interactive visualizations, information visualization applications, and imaginary visualizations as in stories. While information visualization concentrates on the use of computer-supported tools to derive new insights, knowledge visualization focuses on transferring insights and creating new knowledge in groups. Beyond the mere transfer of facts, knowledge visualization aims to further transfer insights, experiences, attitudes, values, expectations, perspectives, opinions, and estimates in different fields by using various complementary visualizations. See also: picture dictionary, visual dictionary === Product visualization === Product visualization involves visualization software technology for the viewing and manipulation of 3D models, technical drawing and other related documentation of manufactured components and large assemblies of products. It is a key part of product lifecycle management. Product visualization software typically provides high levels of photorealism so that a product can be viewed before it is actually manufactured. This supports functions ranging from design and styling to sales and marketing. Technical visualization is an important aspect of product development. Originally technical drawings were made by hand, but with the rise of advanced computer graphics the drawing board has been replaced by computer-aided design (CAD). CAD-drawings and models have several advantages over hand-made drawings such as the possibility of 3-D modeling, rapid prototyping, and simulation. 3D product visualization promises more interactive experiences for online shoppers, but also challenges retailers to overcome hurdles in the production of 3D content, as large-scale 3D content production can be extremel
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Variable-order Bayesian network

Variable-order Bayesian network (VOBN) models provide an important extension of both the Bayesian network models and the variable-order Markov models. VOBN models are used in machine learning in general and have shown great potential in bioinformatics applications. These models extend the widely used position weight matrix (PWM) models, Markov models, and Bayesian network (BN) models. In contrast to the BN models, where each random variable depends on a fixed subset of random variables, in VOBN models these subsets may vary based on the specific realization of observed variables. The observed realizations are often called the context and, hence, VOBN models are also known as context-specific Bayesian networks. The flexibility in the definition of conditioning subsets of variables turns out to be a real advantage in classification and analysis applications, as the statistical dependencies between random variables in a sequence of variables (not necessarily adjacent) may be taken into account efficiently, and in a position-specific and context-specific manner.
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LPBoost

Linear Programming Boosting (LPBoost) is a supervised classifier from the boosting family of classifiers. LPBoost maximizes a margin between training samples of different classes, and thus also belongs to the class of margin classifier algorithms. Consider a classification function f : X → { − 1 , 1 } , {\displaystyle f:{\mathcal {X}}\to \{-1,1\},} which classifies samples from a space X {\displaystyle {\mathcal {X}}} into one of two classes, labelled 1 and -1, respectively. LPBoost is an algorithm for learning such a classification function, given a set of training examples with known class labels. LPBoost is a machine learning technique especially suited for joint classification and feature selection in structured domains. == LPBoost overview == As in all boosting classifiers, the final classification function is of the form f ( x ) = ∑ j = 1 J α j h j ( x ) , {\displaystyle f({\boldsymbol {x}})=\sum _{j=1}^{J}\alpha _{j}h_{j}({\boldsymbol {x}}),} where α j {\displaystyle \alpha _{j}} are non-negative weightings for weak classifiers h j : X → { − 1 , 1 } {\displaystyle h_{j}:{\mathcal {X}}\to \{-1,1\}} . Each individual weak classifier h j {\displaystyle h_{j}} may be just a little bit better than random, but the resulting linear combination of many weak classifiers can perform very well. LPBoost constructs f {\displaystyle f} by starting with an empty set of weak classifiers. Iteratively, a single weak classifier to add to the set of considered weak classifiers is selected, added and all the weights α {\displaystyle {\boldsymbol {\alpha }}} for the current set of weak classifiers are adjusted. This is repeated until no weak classifiers to add remain. The property that all classifier weights are adjusted in each iteration is known as totally-corrective property. Early boosting methods, such as AdaBoost do not have this property and converge slower. == Linear program == More generally, let H = { h ( ⋅ ; ω ) | ω ∈ Ω } {\displaystyle {\mathcal {H}}=\{h(\cdot ;\omega )|\omega \in \Omega \}} be the possibly infinite set of weak classifiers, also termed hypotheses. One way to write down the problem LPBoost solves is as a linear program with infinitely many variables. The primal linear program of LPBoost, optimizing over the non-negative weight vector α {\displaystyle {\boldsymbol {\alpha }}} , the non-negative vector ξ {\displaystyle {\boldsymbol {\xi }}} of slack variables and the margin ρ {\displaystyle \rho } is the following. min α , ξ , ρ − ρ + D ∑ n = 1 ℓ ξ n sb.t. ∑ ω ∈ Ω y n α ω h ( x n ; ω ) + ξ n ≥ ρ , n = 1 , … , ℓ , ∑ ω ∈ Ω α ω = 1 , ξ n ≥ 0 , n = 1 , … , ℓ , α ω ≥ 0 , ω ∈ Ω , ρ ∈ R . {\displaystyle {\begin{array}{cl}{\underset {{\boldsymbol {\alpha }},{\boldsymbol {\xi }},\rho }{\min }}&-\rho +D\sum _{n=1}^{\ell }\xi _{n}\\{\textrm {sb.t.}}&\sum _{\omega \in \Omega }y_{n}\alpha _{\omega }h({\boldsymbol {x}}_{n};\omega )+\xi _{n}\geq \rho ,\qquad n=1,\dots ,\ell ,\\&\sum _{\omega \in \Omega }\alpha _{\omega }=1,\\&\xi _{n}\geq 0,\qquad n=1,\dots ,\ell ,\\&\alpha _{\omega }\geq 0,\qquad \omega \in \Omega ,\\&\rho \in {\mathbb {R} }.\end{array}}} Note the effects of slack variables ξ ≥ 0 {\displaystyle {\boldsymbol {\xi }}\geq 0} : their one-norm is penalized in the objective function by a constant factor D {\displaystyle D} , which—if small enough—always leads to a primal feasible linear program. Here we adopted the notation of a parameter space Ω {\displaystyle \Omega } , such that for a choice ω ∈ Ω {\displaystyle \omega \in \Omega } the weak classifier h ( ⋅ ; ω ) : X → { − 1 , 1 } {\displaystyle h(\cdot ;\omega ):{\mathcal {X}}\to \{-1,1\}} is uniquely defined. When the above linear program was first written down in early publications about boosting methods it was disregarded as intractable due to the large number of variables α {\displaystyle {\boldsymbol {\alpha }}} . Only later it was discovered that such linear programs can indeed be solved efficiently using the classic technique of column generation. === Column generation for LPBoost === In a linear program a column corresponds to a primal variable. Column generation is a technique to solve large linear programs. It typically works in a restricted problem, dealing only with a subset of variables. By generating primal variables iteratively and on-demand, eventually the original unrestricted problem with all variables is recovered. By cleverly choosing the columns to generate the problem can be solved such that while still guaranteeing the obtained solution to be optimal for the original full problem, only a small fraction of columns has to be created. ==== LPBoost dual problem ==== Columns in the primal linear program corresponds to rows in the dual linear program. The equivalent dual linear program of LPBoost is the following linear program. max λ , γ γ sb.t. ∑ n = 1 ℓ y n h ( x n ; ω ) λ n + γ ≤ 0 , ω ∈ Ω , 0 ≤ λ n ≤ D , n = 1 , … , ℓ , ∑ n = 1 ℓ λ n = 1 , γ ∈ R . {\displaystyle {\begin{array}{cl}{\underset {{\boldsymbol {\lambda }},\gamma }{\max }}&\gamma \\{\textrm {sb.t.}}&\sum _{n=1}^{\ell }y_{n}h({\boldsymbol {x}}_{n};\omega )\lambda _{n}+\gamma \leq 0,\qquad \omega \in \Omega ,\\&0\leq \lambda _{n}\leq D,\qquad n=1,\dots ,\ell ,\\&\sum _{n=1}^{\ell }\lambda _{n}=1,\\&\gamma \in \mathbb {R} .\end{array}}} For linear programs the optimal value of the primal and dual problem are equal. For the above primal and dual problems, the optimal value is equal to the negative 'soft margin'. The soft margin is the size of the margin separating positive from negative training instances minus positive slack variables that carry penalties for margin-violating samples. Thus, the soft margin may be positive although not all samples are linearly separated by the classification function. The latter is called the 'hard margin' or 'realized margin'. ==== Convergence criterion ==== Consider a subset of the satisfied constraints in the dual problem. For any finite subset we can solve the linear program and thus satisfy all constraints. If we could prove that of all the constraints which we did not add to the dual problem no single constraint is violated, we would have proven that solving our restricted problem is equivalent to solving the original problem. More formally, let γ ∗ {\displaystyle \gamma ^{}} be the optimal objective function value for any restricted instance. Then, we can formulate a search problem for the 'most violated constraint' in the original problem space, namely finding ω ∗ ∈ Ω {\displaystyle \omega ^{}\in \Omega } as ω ∗ = argmax ω ∈ Ω ∑ n = 1 ℓ y n h ( x n ; ω ) λ n . {\displaystyle \omega ^{}={\underset {\omega \in \Omega }{\textrm {argmax}}}\sum _{n=1}^{\ell }y_{n}h({\boldsymbol {x}}_{n};\omega )\lambda _{n}.} That is, we search the space H {\displaystyle {\mathcal {H}}} for a single decision stump h ( ⋅ ; ω ∗ ) {\displaystyle h(\cdot ;\omega ^{})} maximizing the left hand side of the dual constraint. If the constraint cannot be violated by any choice of decision stump, none of the corresponding constraint can be active in the original problem and the restricted problem is equivalent. ==== Penalization constant ==== D {\displaystyle D} The positive value of penalization constant D {\displaystyle D} has to be found using model selection techniques. However, if we choose D = 1 ℓ ν {\displaystyle D={\frac {1}{\ell \nu }}} , where ℓ {\displaystyle \ell } is the number of training samples and 0 < ν < 1 {\displaystyle 0<\nu <1} , then the new parameter ν {\displaystyle \nu } has the following properties. ν {\displaystyle \nu } is an upper bound on the fraction of training errors; that is, if k {\displaystyle k} denotes the number of misclassified training samples, then k ℓ ≤ ν {\displaystyle {\frac {k}{\ell }}\leq \nu } . ν {\displaystyle \nu } is a lower bound on the fraction of training samples outside or on the margin. == Algorithm == Input: Training set X = { x 1 , … , x ℓ } {\displaystyle X=\{{\boldsymbol {x}}_{1},\dots ,{\boldsymbol {x}}_{\ell }\}} , x i ∈ X {\displaystyle {\boldsymbol {x}}_{i}\in {\mathcal {X}}} Training labels Y = { y 1 , … , y ℓ } {\displaystyle Y=\{y_{1},\dots ,y_{\ell }\}} , y i ∈ { − 1 , 1 } {\displaystyle y_{i}\in \{-1,1\}} Convergence threshold θ ≥ 0 {\displaystyle \theta \geq 0} Output: Classification function f : X → { − 1 , 1 } {\displaystyle f:{\mathcal {X}}\to \{-1,1\}} Initialization Weights, uniform λ n ← 1 ℓ , n = 1 , … , ℓ {\displaystyle \lambda _{n}\leftarrow {\frac {1}{\ell }},\quad n=1,\dots ,\ell } Edge γ ← 0 {\displaystyle \gamma \leftarrow 0} Hypothesis count J ← 1 {\displaystyle J\leftarrow 1} Iterate h ^ ← argmax ω ∈ Ω ∑ n = 1 ℓ y n h ( x n ; ω ) λ n {\displaystyle {\hat {h}}\leftarrow {\underset {\omega \in \Omega }{\textrm {argmax}}}\sum _{n=1}^{\ell }y_{n}h({\boldsymbol {x}}_{n};\omega )\lambda _{n}} if ∑ n = 1 ℓ y n h ^ ( x n ) λ n + γ ≤ θ {\displaystyle \sum _{n=1}^{\ell }y_{n}{\hat {h}}({\boldsymbol {x}}_{n})\lambda _{n}+\gamma \leq \theta } then break h J ← h ^ {\displaystyle h_{J}\leftarrow {\hat {h}}} J
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Ilastik

ilastik is free open source software for image classification and segmentation. No previous experience in image processing is required to run the software. Since 2018 ilastik is further developed and maintained by Anna Kreshuk's group at European Molecular Biology Laboratory. == Features == ilastik allows user to annotate an arbitrary number of classes in images with a mouse interface. Using these user annotations and the generic (nonlinear) image features, the user can train a random forest classifier. Trained ilastik classifiers can be applied new data not included in the training set in ilastik via its batch processing functionality, or without using the graphical user interface, in headless mode. ilastik can be integrated into various related tools: Pre-trained workflows can be executed directly from ImageJ/Fiji using the ilastik-ImageJ plugin. Pre-trained ilastik Pixel Classification workflows can be run directly in Python with the ilastik Python package, which is available via conda. ilastik has a CellProfiler module to use ilastik classifiers to process images within a CellProfiler framework. == History == ilastik was first released in 2011 by scientists at the Heidelberg Collaboratory for Image Processing (HCI), University of Heidelberg. == Application == The Interactive Learning and Segmentation Toolkit Carving Cell classification and neuron classification Synapse detection Cell tracking Neural Network Classification == Resources == ilastik project is hosted on GitHub. It is a collaborative project, any contributions such as comments, bug reports, bug fixes or code contributions are welcome. The ilastik team can be contacted for user support on the image.sc forum.
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AIX Toolbox for Linux Applications

The AIX Toolbox for Linux Applications is a collection of GNU tools for IBM AIX. These tools are available for installation using Red Hat's RPM format. == Licensing == Each of these packages includes its own licensing information and while IBM has made the code available to AIX users, the code is provided as is and has not been thoroughly tested. The Toolbox is meant to provide a core set of some of the most common development tools and libraries along with the more popular GNU packages.
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Multilayer perceptron

In deep learning, a multilayer perceptron (MLP) is a kind of modern feedforward neural network consisting of fully connected neurons with nonlinear activation functions, organized in layers, notable for being able to distinguish data that is not linearly separable. Modern neural networks are trained using backpropagation and are colloquially referred to as "vanilla" networks. MLPs grew out of an effort to improve on single-layer perceptrons, which could only be applied to linearly separable data. A perceptron traditionally used a Heaviside step function as its nonlinear activation function. However, the backpropagation algorithm requires that modern MLPs use continuous activation functions such as sigmoid or ReLU. Multilayer perceptrons form the basis of deep learning, and are applicable across a vast set of diverse domains. == Timeline == In 1943, Warren McCulloch and Walter Pitts proposed the binary artificial neuron as a logical model of biological neural networks. In 1958, Frank Rosenblatt proposed the multilayered perceptron model, consisting of an input layer, a hidden layer with randomized weights that did not learn, and an output layer with learnable connections. In 1962, Rosenblatt published many variants and experiments on perceptrons in his book Principles of Neurodynamics, including up to 2 trainable layers by "back-propagating errors". However, it was not the backpropagation algorithm, and he did not have a general method for training multiple layers. In 1965, Alexey Grigorevich Ivakhnenko and Valentin Lapa published Group Method of Data Handling. It was one of the first deep learning methods, used to train an eight-layer neural net in 1971. In 1967, Shun'ichi Amari reported the first multilayered neural network trained by stochastic gradient descent, was able to classify non-linearily separable pattern classes. Amari's student Saito conducted the computer experiments, using a five-layered feedforward network with two learning layers. Backpropagation was independently developed multiple times in early 1970s. The earliest published instance was Seppo Linnainmaa's master thesis (1970). Paul Werbos developed it independently in 1971, but had difficulty publishing it until 1982. In 1986, David E. Rumelhart et al. popularized backpropagation. In 2003, interest in backpropagation networks returned due to the successes of deep learning being applied to language modelling by Yoshua Bengio with co-authors. In 2021, a very simple NN architecture combining two deep MLPs with skip connections and layer normalizations was designed and called MLP-Mixer; its realizations featuring 19 to 431 millions of parameters were shown to be comparable to vision transformers of similar size on ImageNet and similar image classification tasks. == Mathematical foundations == === Activation function === If a multilayer perceptron has a linear activation function in all neurons, that is, a linear function that maps the weighted inputs to the output of each neuron, then linear algebra shows that any number of layers can be reduced to a two-layer input-output model. In MLPs some neurons use a nonlinear activation function that was developed to model the frequency of action potentials, or firing, of biological neurons. The two historically common activation functions are both sigmoids, and are described by y ( v i ) = tanh ⁡ ( v i ) and y ( v i ) = ( 1 + e − v i ) − 1 {\displaystyle y(v_{i})=\tanh(v_{i})~~{\textrm {and}}~~y(v_{i})=(1+e^{-v_{i}})^{-1}} . The first is a hyperbolic tangent that ranges from −1 to 1, while the other is the logistic function, which is similar in shape but ranges from 0 to 1. Here y i {\displaystyle y_{i}} is the output of the i {\displaystyle i} th node (neuron) and v i {\displaystyle v_{i}} is the weighted sum of the input connections. Alternative activation functions have been proposed, including the rectifier and softplus functions. More specialized activation functions include radial basis functions (used in radial basis networks, another class of supervised neural network models). In recent developments of deep learning the rectified linear unit (ReLU) is more frequently used as one of the possible ways to overcome the numerical problems related to the sigmoids. === Layers === The MLP consists of three or more layers (an input and an output layer with one or more hidden layers) of nonlinearly-activating nodes. Since MLPs are fully connected, each node in one layer connects with a certain weight w i j {\displaystyle w_{ij}} to every node in the following layer. === Learning === Learning occurs in the perceptron by changing connection weights after each piece of data is processed, based on the amount of error in the output compared to the expected result. This is an example of supervised learning, and is carried out through backpropagation, a generalization of the least mean squares algorithm in the linear perceptron. We can represent the degree of error in an output node j {\displaystyle j} in the n {\displaystyle n} th data point (training example) by e j ( n ) = d j ( n ) − y j ( n ) {\displaystyle e_{j}(n)=d_{j}(n)-y_{j}(n)} , where d j ( n ) {\displaystyle d_{j}(n)} is the desired target value for n {\displaystyle n} th data point at node j {\displaystyle j} , and y j ( n ) {\displaystyle y_{j}(n)} is the value produced by the perceptron at node j {\displaystyle j} when the n {\displaystyle n} th data point is given as an input. The node weights can then be adjusted based on corrections that minimize the error in the entire output for the n {\displaystyle n} th data point, given by E ( n ) = 1 2 ∑ output node j e j 2 ( n ) {\displaystyle {\mathcal {E}}(n)={\frac {1}{2}}\sum _{{\text{output node }}j}e_{j}^{2}(n)} . Using gradient descent, the change in each weight w i j {\displaystyle w_{ij}} is Δ w j i ( n ) = − η ∂ E ( n ) ∂ v j ( n ) y i ( n ) {\displaystyle \Delta w_{ji}(n)=-\eta {\frac {\partial {\mathcal {E}}(n)}{\partial v_{j}(n)}}y_{i}(n)} where y i ( n ) {\displaystyle y_{i}(n)} is the output of the previous neuron i {\displaystyle i} , and η {\displaystyle \eta } is the learning rate, which is selected to ensure that the weights quickly converge to a response, without oscillations. In the previous expression, ∂ E ( n ) ∂ v j ( n ) {\displaystyle {\frac {\partial {\mathcal {E}}(n)}{\partial v_{j}(n)}}} denotes the partial derivate of the error E ( n ) {\displaystyle {\mathcal {E}}(n)} according to the weighted sum v j ( n ) {\displaystyle v_{j}(n)} of the input connections of neuron i {\displaystyle i} . The derivative to be calculated depends on the induced local field v j {\displaystyle v_{j}} , which itself varies. It is easy to prove that for an output node this derivative can be simplified to − ∂ E ( n ) ∂ v j ( n ) = e j ( n ) ϕ ′ ( v j ( n ) ) {\displaystyle -{\frac {\partial {\mathcal {E}}(n)}{\partial v_{j}(n)}}=e_{j}(n)\phi ^{\prime }(v_{j}(n))} where ϕ ′ {\displaystyle \phi ^{\prime }} is the derivative of the activation function described above, which itself does not vary. The analysis is more difficult for the change in weights to a hidden node, but it can be shown that the relevant derivative is − ∂ E ( n ) ∂ v j ( n ) = ϕ ′ ( v j ( n ) ) ∑ k − ∂ E ( n ) ∂ v k ( n ) w k j ( n ) {\displaystyle -{\frac {\partial {\mathcal {E}}(n)}{\partial v_{j}(n)}}=\phi ^{\prime }(v_{j}(n))\sum _{k}-{\frac {\partial {\mathcal {E}}(n)}{\partial v_{k}(n)}}w_{kj}(n)} . This depends on the change in weights of the k {\displaystyle k} th nodes, which represent the output layer. So to change the hidden layer weights, the output layer weights change according to the derivative of the activation function, and so this algorithm represents a backpropagation of the activation function.
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Implicit blockmodeling

Implicit blockmodeling is an approach in blockmodeling, similar to a valued and homogeneity blockmodeling, where initially an additional normalization is used and then while specifying the parameter of the relevant link is replaced by the block maximum. This approach was first proposed by Batagelj and Ferligoj in 2000, and developed by Aleš Žiberna in 2007/08. Comparing with homogeneity, the implicit blockmodeling will perform similarly with max-regular equivalence, but slightly worse in other settings. It will perform worse than valued and homogeneity blockmodeling with a pre-specified blockmodel.
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