AI Analysis X Ray

AI Analysis X Ray — independent reviews, comparisons, pricing and step-by-step guides on Aizhi.

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  Game Jolt

  Game Jolt is a social community platform for video games, gamers and content creators. Founded by Yaprak and David DeCarmine, it is available on iOS, Android, and on the web and as a desktop app for Windows and Linux. Users share interactive content through a variety of formats including images, videos, live streams, chat rooms, and virtual events. == Features == === Crowd streaming === In 2021 Game Jolt revealed their own live streaming feature called Firesides. Firesides allowed multiple users to simultaneously livestream together with nearly no delay. The feature launched with a virtual concert showcasing its ability to accommodate multiple streamers. On October 16, 2023, Firesides were removed from Game Jolt. === Mobile app === Game Jolt Social by Game Jolt Inc. launched on both the Apple App Store and Google Play Store in March 2022. "It's clear to us that Gen Z is tired of generic social media and they want a place specifically for gaming that supports all types of content they're creating–art, videos, thoughts, and livestreams all in one place." said Game Jolt founder and CEO Yaprak DeCarmine, in a statement to VentureBeat. === Game API === The Game Jolt Application Programming Interface (usually known as the Game Jolt Game API) allows any developer using a game development platform that supports HTTP operations and MD5 or SHA-1. Game Jolt advertises that the API can: Create multiple "scoreboards" which collect high scores from players made publicly available on the game's profile and give user accounts EXP Award player's trophies which give user accounts EXP Store game data on Game Jolt's data servers Log whether a user is currently playing a game they're logged into via the GJAPI == Game jams and competitions == Game Jolt regularly hosts game jams where participants are encouraged to develop games for a chance to win prizes. They hosted their first game jam in 2009, Shocking Contest. In November 2014, Game Jolt announced the "Indies vs PewDiePie" game jam, partnering with the popular YouTuber Felix "PewDiePie" Kjellberg. Developers were given a weekend (21–24 November) to create a game with the theme of "fun to play, fun to watch" to suit the Let's Plays entertainment style. Users could rate entries afterwards until December 1 when the scores were counted up. The prize to the top 10 rated games was Felix playing the games on his channel as a means of promotion for the developers, although later he played other entries. One of the participants of the jam, now known as Outerminds Inc. was discovered and hired by PewDiePie to develop his mobile game, Legend of the Brofist. Game Jolt partnered with Felix, Sean "Jacksepticeye" McLoughlin and Mark "Markiplier" Fischbach to host "Indies vs Gamers" in July 2015. The requirements for entries were arcade games using the Game Jolt Game API highscore tables, to be made between the July 17–20 and the top 5 games were played on the partner's YouTube channels. Following the "Indies vs PewDiePie" game jam in 2014, Game Jolt released their internal jam hosting tools public for all users to use as a service, to create their own game jams that integrated with the main site. Today, Game Jolt focuses on hosting and co-hosting game competitions with established brands in order to bring monetary and educational opportunities to their users. On April 15, 2024, an announcement was made about a collaboration with Pocket Worlds for the "HighRise Game Jam". Pocket Worlds had sold NFTs up until roughly 2022, causing a community outburst. The situation was addressed, and the situation started to disperse. == Contests == == Events == Game Jolt hosts both physical and virtual events to entertain and prank its users, which consists of the following: == History == Game Jolt has supported independent creators with a central platform to manage their content and communities since its start in 2003. David DeCarmine began development of Game Jolt at the age of 14 for a group of hobbyists, making games and sharing on forums in an early iteration known as Holo World. The original intention was to create a platform for gamers where new games could be discoverable and quickly playable, and where feedback could be provided directly to the creators, allowing them to continue improving their games. In 2008, Game Jolt was registered as an LLC, then incorporated as Game Jolt Inc. in September 2020. A new site launched in 2015 featuring a responsive design, automated curation for both games and game news articles which weighs how recent a game was uploaded and how popular it is ("hot") and filtering options on game listings for platform, maturity rating and development status. In March 2022, Game Jolt launched a mobile application simultaneously on the Google Play Store and Apple App Store targeted at Gen Z gamers and creators. While in beta, the mobile app had 100,000 installs pre-launch. === Game store === Game Jolt continues to host a large library of independent games. Game developers can upload their games directly to the site to share or sell. They would allow distribution for downloadable games, later adding support for Adobe Flash, Unity and Java games which allowed support for browser based games. In February 2013, Game Jolt built support for browser-based HTML5 games as well. A user levelling system was released into public beta in April 2013, incorporating the GJAPI trophies and highscores, as well as site activity, to generate 'EXP' (experience points). Game Jolt Jams released in early 2014 as a service to allow users to create their own game jams that integrated with the main site. In April 2016, an online marketplace was announced and released the following month with an exclusive set of game titles, including Bendy and the Ink Machine, allowing developers to sell their games on the site. In January 2016, Game Jolt released source code of the client and site's front end on GitHub under MIT license. In January 2022, Game Jolt banned adult games from appearing on the site, stating in an email to developers that the site had become a "social media platform" and they "had to make decisions around the direction and future of the brand which has now included the removal of hosted games with explicitly adult content." In response to a tweet by Itch.io saying the site is not for prudes, they wrote in their own tweet: "Game Jolt is a platform with a large audience of 13-16 year olds. Our users asked us to clean up, so here we are." == Investments == After bootstrapping Game Jolt with revenue earned from ads on the website for years, the DeCarmines secured venture capital in 2020 from SoftBank, doing so again in 2021 from founders of Twitch, Rec Room, Modio and more.

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  Reservoir computing

  Reservoir computing is a framework for computation derived from recurrent neural network theory that maps input signals into higher dimensional computational spaces through the dynamics of a fixed, non-linear system called a reservoir. After the input signal is fed into the reservoir, which is treated as a "black box," a simple readout mechanism is trained to read the state of the reservoir and map it to the desired output. The first key benefit of this framework is that training is performed only at the readout stage, as the reservoir dynamics are fixed. The second is that the computational power of naturally available systems, both classical and quantum mechanical, can be used to reduce the effective computational cost. == History == The first examples of reservoir neural networks demonstrated that randomly connected recurrent neural networks could be used for sensorimotor sequence learning, and simple forms of interval and speech discrimination. In these early models the memory in the network took the form of both short-term synaptic plasticity and activity mediated by recurrent connections. In other early reservoir neural network models the memory of the recent stimulus history was provided solely by the recurrent activity. Overall, the general concept of reservoir computing stems from the use of recursive connections within neural networks to create a complex dynamical system. It is a generalisation of earlier neural network architectures such as recurrent neural networks, liquid-state machines and echo-state networks. Reservoir computing also extends to physical systems that are not networks in the classical sense, but rather continuous systems in space and/or time: e.g. a literal "bucket of water" can serve as a reservoir that performs computations on inputs given as perturbations of the surface. The resultant complexity of such recurrent neural networks was found to be useful in solving a variety of problems including language processing and dynamic system modeling. However, training of recurrent neural networks is challenging and computationally expensive. Reservoir computing reduces those training-related challenges by fixing the dynamics of the reservoir and only training the linear output layer. A large variety of nonlinear dynamical systems can serve as a reservoir that performs computations. In recent years semiconductor lasers have attracted considerable interest as computation can be fast and energy efficient compared to electrical components. Recent advances in both AI and quantum information theory have given rise to the concept of quantum neural networks. These hold promise in quantum information processing, which is challenging to classical networks, but can also find application in solving classical problems. In 2018, a physical realization of a quantum reservoir computing architecture was demonstrated in the form of nuclear spins within a molecular solid. However, the nuclear spin experiments in did not demonstrate quantum reservoir computing per se as they did not involve processing of sequential data. Rather the data were vector inputs, which makes this more accurately a demonstration of quantum implementation of a random kitchen sink algorithm (also going by the name of extreme learning machines in some communities). In 2019, another possible implementation of quantum reservoir processors was proposed in the form of two-dimensional fermionic lattices. In 2020, realization of reservoir computing on gate-based quantum computers was proposed and demonstrated on cloud-based IBM superconducting near-term quantum computers. Reservoir computers have been used for time-series analysis purposes. In particular, some of their usages involve chaotic time-series prediction, separation of chaotic signals, and link inference of networks from their dynamics. == Classical reservoir computing == === Reservoir === The 'reservoir' in reservoir computing is the internal structure of the computer, and must have two properties: it must be made up of individual, non-linear units, and it must be capable of storing information. The non-linearity describes the response of each unit to input, which is what allows reservoir computers to solve complex problems. Reservoirs are able to store information by connecting the units in recurrent loops, where the previous input affects the next response. The change in reaction due to the past allows the computers to be trained to complete specific tasks. Reservoirs can be virtual or physical. Virtual reservoirs are typically randomly generated and are designed like neural networks. Virtual reservoirs can be designed to have non-linearity and recurrent loops, but, unlike neural networks, the connections between units are randomized and remain unchanged throughout computation. Physical reservoirs are possible because of the inherent non-linearity of certain natural systems. The interaction between ripples on the surface of water contains the nonlinear dynamics required in reservoir creation, and a pattern recognition RC was developed by first inputting ripples with electric motors then recording and analyzing the ripples in the readout. === Readout === The readout is a neural network layer that performs a linear transformation on the output of the reservoir. The weights of the readout layer are trained by analyzing the spatiotemporal patterns of the reservoir after excitation by known inputs, and by utilizing a training method such as a linear regression or a Ridge regression. As its implementation depends on spatiotemporal reservoir patterns, the details of readout methods are tailored to each type of reservoir. For example, the readout for a reservoir computer using a container of liquid as its reservoir might entail observing spatiotemporal patterns on the surface of the liquid. === Types === ==== Context reverberation network ==== An early example of reservoir computing was the context reverberation network. In this architecture, an input layer feeds into a high dimensional dynamical system which is read out by a trainable single-layer perceptron. Two kinds of dynamical system were described: a recurrent neural network with fixed random weights, and a continuous reaction–diffusion system inspired by Alan Turing's model of morphogenesis. At the trainable layer, the perceptron associates current inputs with the signals that reverberate in the dynamical system; the latter were said to provide a dynamic "context" for the inputs. In the language of later work, the reaction–diffusion system served as the reservoir. ==== Echo state network ==== The tree echo state network (TreeESN) model represents a generalization of the reservoir computing framework to tree structured data. ==== Liquid-state machine ==== Chaotic liquid state machine The liquid (i.e. reservoir) of a chaotic liquid state machine (CLSM), or chaotic reservoir, is made from chaotic spiking neurons but which stabilize their activity by settling to a single hypothesis that describes the trained inputs of the machine. This is in contrast to general types of reservoirs that don't stabilize. The liquid stabilization occurs via synaptic plasticity and chaos control that govern neural connections inside the liquid. CLSM showed promising results in learning sensitive time series data. ==== Nonlinear transient computation ==== This type of information processing is most relevant when time-dependent input signals depart from the mechanism's internal dynamics. These departures cause transients or temporary altercations which are represented in the device's output. ==== Deep reservoir computing ==== The extension of the reservoir computing framework towards deep learning, with the introduction of deep reservoir computing and of the deep echo state network (DeepESN) model allows to develop efficiently trained models for hierarchical processing of temporal data, at the same time enabling the investigation on the inherent role of layered composition in recurrent neural networks. == Quantum reservoir computing == Quantum reservoir computing may use the nonlinear nature of quantum mechanical interactions or processes to form the characteristic nonlinear reservoirs but may also be done with linear reservoirs when the injection of the input to the reservoir creates the nonlinearity. The marriage of machine learning and quantum devices is leading to the emergence of quantum neuromorphic computing as a new research area. === Types === ==== Gaussian states of interacting quantum harmonic oscillators ==== Gaussian states are a paradigmatic class of states of continuous variable quantum systems. Although they can nowadays be created and manipulated in, e.g, state-of-the-art optical platforms, naturally robust to decoherence, it is well-known that they are not sufficient for, e.g., universal quantum computing because transformations that preserve the Gaussian nature of a state are linear. Normally, linear dynamics would not be sufficient for nontrivial reser

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  Multilinear subspace learning

  Multilinear subspace learning is an approach for disentangling the causal factor of data formation and performing dimensionality reduction. The Dimensionality reduction can be performed on a data tensor that contains a collection of observations that have been vectorized, or observations that are treated as matrices and concatenated into a data tensor. Here are some examples of data tensors whose observations are vectorized or whose observations are matrices concatenated into data tensor images (2D/3D), video sequences (3D/4D), and hyperspectral cubes (3D/4D). The mapping from a high-dimensional vector space to a set of lower dimensional vector spaces is a multilinear projection. When observations are retained in the same organizational structure as matrices or higher order tensors, their representations are computed by performing linear projections into the column space, row space and fiber space. Multilinear subspace learning algorithms are higher-order generalizations of linear subspace learning methods such as principal component analysis (PCA), independent component analysis (ICA), linear discriminant analysis (LDA) and canonical correlation analysis (CCA). == Background == Multilinear methods may be causal in nature and perform causal inference, or they may be simple regression methods from which no causal conclusion are drawn. Linear subspace learning algorithms are traditional dimensionality reduction techniques that are well suited for datasets that are the result of varying a single causal factor. Unfortunately, they often become inadequate when dealing with datasets that are the result of multiple causal factors. . Multilinear subspace learning can be applied to observations whose measurements were vectorized and organized into a data tensor for causally aware dimensionality reduction. These methods may also be employed in reducing horizontal and vertical redundancies irrespective of the causal factors when the observations are treated as a "matrix" (ie. a collection of independent column/row observations) and concatenated into a tensor. == Algorithms == === Multilinear principal component analysis === Historically, multilinear principal component analysis has been referred to as "M-mode PCA", a terminology which was coined by Peter Kroonenberg. In 2005, Vasilescu and Terzopoulos introduced the Multilinear PCA terminology as a way to better differentiate between multilinear tensor decompositions that computed 2nd order statistics associated with each data tensor mode, and subsequent work on Multilinear Independent Component Analysis that computed higher order statistics for each tensor mode. MPCA is an extension of PCA. === Multilinear independent component analysis === Multilinear independent component analysis is an extension of ICA. === Multilinear linear discriminant analysis === Multilinear extension of LDA TTP-based: Discriminant Analysis with Tensor Representation (DATER) TTP-based: General tensor discriminant analysis (GTDA) TVP-based: Uncorrelated Multilinear Discriminant Analysis (UMLDA) === Multilinear canonical correlation analysis === Multilinear extension of CCA TTP-based: Tensor Canonical Correlation Analysis (TCCA) TVP-based: Multilinear Canonical Correlation Analysis (MCCA) TVP-based: Bayesian Multilinear Canonical Correlation Analysis (BMTF) A TTP is a direct projection of a high-dimensional tensor to a low-dimensional tensor of the same order, using N projection matrices for an Nth-order tensor. It can be performed in N steps with each step performing a tensor-matrix multiplication (product). The N steps are exchangeable. This projection is an extension of the higher-order singular value decomposition (HOSVD) to subspace learning. Hence, its origin is traced back to the Tucker decomposition in 1960s. A TVP is a direct projection of a high-dimensional tensor to a low-dimensional vector, which is also referred to as the rank-one projections. As TVP projects a tensor to a vector, it can be viewed as multiple projections from a tensor to a scalar. Thus, the TVP of a tensor to a P-dimensional vector consists of P projections from the tensor to a scalar. The projection from a tensor to a scalar is an elementary multilinear projection (EMP). In EMP, a tensor is projected to a point through N unit projection vectors. It is the projection of a tensor on a single line (resulting a scalar), with one projection vector in each mode. Thus, the TVP of a tensor object to a vector in a P-dimensional vector space consists of P EMPs. This projection is an extension of the canonical decomposition, also known as the parallel factors (PARAFAC) decomposition. === Typical approach in MSL === There are N sets of parameters to be solved, one in each mode. The solution to one set often depends on the other sets (except when N=1, the linear case). Therefore, the suboptimal iterative procedure in is followed. Initialization of the projections in each mode For each mode, fixing the projection in all the other mode, and solve for the projection in the current mode. Do the mode-wise optimization for a few iterations or until convergence. This is originated from the alternating least square method for multi-way data analysis. == Code == MATLAB Tensor Toolbox by Sandia National Laboratories. The MPCA algorithm written in Matlab (MPCA+LDA included). The UMPCA algorithm written in Matlab (data included). The UMLDA algorithm written in Matlab (data included). == Tensor data sets == 3D gait data (third-order tensors): 128x88x20(21.2M); 64x44x20(9.9M); 32x22x10(3.2M);

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  Universal approximation theorem

  In the field of machine learning, the universal approximation theorems (UATs) state that neural networks with a certain structure can, in principle, approximate any continuous function to any desired degree of accuracy. These theorems provide a mathematical justification for using neural networks, assuring researchers that a sufficiently large or deep network can model the complex, non-linear relationships often found in real-world data. The best-known version of the theorem applies to feedforward networks with a single hidden layer. It states that if the layer's activation function is non-polynomial (which is true for common choices like the sigmoid function or ReLU), then the network can act as a "universal approximator." Universality is achieved by increasing the number of neurons in the hidden layer, making the network "wider." Other versions of the theorem show that universality can also be achieved by keeping the network's width fixed but increasing its number of layers, making it "deeper." These are existence theorems. They guarantee that a network with the right structure exists, but they do not provide a method for finding the network's parameters (training it), nor do they specify exactly how large the network must be for a given function. Finding a suitable network remains a practical challenge that is typically addressed with optimization algorithms like backpropagation. == Setup == Artificial neural networks are combinations of multiple simple mathematical functions that implement more complicated functions from (typically) real-valued vectors to real-valued vectors. The spaces of multivariate functions that can be implemented by a network are determined by the structure of the network, the set of simple functions, and its multiplicative parameters. A great deal of theoretical work has gone into characterizing these function spaces. Most universal approximation theorems are in one of two classes. The first quantifies the approximation capabilities of neural networks with an arbitrary number of artificial neurons ("arbitrary width" case) and the second focuses on the case with an arbitrary number of hidden layers, each containing a limited number of artificial neurons ("arbitrary depth" case). In addition to these two classes, there are also universal approximation theorems for neural networks with bounded number of hidden layers and a limited number of neurons in each layer ("bounded depth and bounded width" case). == History == === Arbitrary width === The first results concerned the arbitrary width case. Ken-ichi Funahashi (May 1989) showed that Rumelhart–Hinton–Williams type backpropagation networks possess universal approximation capability with a class of sigmoidal activation functions, extending the result to multi-output mappings as well. Kurt Hornik, Maxwell Stinchcombe, and Halbert White (July 1989) showed that multilayer feed-forward networks with as few as one hidden layer are universal approximators, provided that the activation function satisfies certain conditions. George Cybenko (December 1989) independently established a related result for sigmoid activation functions using functional-analytic methods. Hornik also showed in 1991 that it is not the specific choice of the activation function but rather the multilayer feed-forward architecture itself that gives neural networks the potential of being universal approximators. Moshe Leshno et al in 1993 and later Allan Pinkus in 1999 showed that the universal approximation property is equivalent to having a nonpolynomial activation function. === Arbitrary depth === The arbitrary depth case was also studied by a number of authors such as Gustaf Gripenberg in 2003, Dmitry Yarotsky, Zhou Lu et al in 2017, Boris Hanin and Mark Sellke in 2018 who focused on neural networks with ReLU activation function. In 2020, Patrick Kidger and Terry Lyons extended those results to neural networks with general activation functions such, e.g. tanh or GeLU. One special case of arbitrary depth is that each composition component comes from a finite set of mappings. In 2024, Cai constructed a finite set of mappings, named a vocabulary, such that any continuous function can be approximated by compositing a sequence from the vocabulary. This is similar to the concept of compositionality in linguistics, which is the idea that a finite vocabulary of basic elements can be combined via grammar to express an infinite range of meanings. === Bounded depth and bounded width === The bounded depth and bounded width case was first studied by Maiorov and Pinkus in 1999. They showed that there exists an analytic sigmoidal activation function such that two hidden layer neural networks with bounded number of units in hidden layers are universal approximators. In 2018, Guliyev and Ismailov constructed a smooth sigmoidal activation function providing universal approximation property for two hidden layer feedforward neural networks with fewer units in hidden layers. In 2018, they also constructed single hidden layer networks with bounded width that are still universal approximators for univariate functions. However, this does not apply for multivariable functions. In 2022, Shen et al. obtained precise quantitative information on the depth and width required to approximate a target function by deep and wide ReLU neural networks. === Quantitative bounds === The question of minimal possible width for universality was first studied in 2021, Park et al obtained the minimum width required for the universal approximation of Lp functions using feed-forward neural networks with ReLU as activation functions. Similar results that can be directly applied to residual neural networks were also obtained in the same year by Paulo Tabuada and Bahman Gharesifard using control-theoretic arguments. In 2023, Cai obtained the optimal minimum width bound for the universal approximation. For the arbitrary depth case, Leonie Papon and Anastasis Kratsios derived explicit depth estimates depending on the regularity of the target function and of the activation function. === Kolmogorov network === The Kolmogorov–Arnold representation theorem is similar in spirit. Indeed, certain neural network families can directly apply the Kolmogorov–Arnold theorem to yield a universal approximation theorem. Robert Hecht-Nielsen showed that a three-layer neural network can approximate any continuous multivariate function. This was extended to the discontinuous case by Vugar Ismailov. In 2024, Ziming Liu and co-authors showed a practical application. === Reservoir computing and quantum reservoir computing === In reservoir computing a sparse recurrent neural network with fixed weights equipped of fading memory and echo state property is followed by a trainable output layer. Its universality has been demonstrated separately for what concerns networks of rate neurons and spiking neurons, respectively. In 2024, the framework has been generalized and extended to quantum reservoirs where the reservoir is based on qubits defined over Hilbert spaces. === Variants === Variants include discontinuous activation functions, noncompact domains, certifiable networks, random neural networks, and alternative network architectures and topologies. The universal approximation property of width-bounded networks has been studied as a dual of classical universal approximation results on depth-bounded networks. For input dimension d x {\displaystyle d_{x}} and output dimension d y {\displaystyle d_{y}} the minimum width required for the universal approximation of the Lp functions is exactly m a x { d x + 1 , d y } {\displaystyle max\{d_{x}+1,d_{y}\}} (for a ReLU network). More generally this also holds if both ReLU and a threshold activation function are used. Universal function approximation on graphs (or rather on graph isomorphism classes) by popular graph convolutional neural networks (GCNs or GNNs) can be made as discriminative as the Weisfeiler–Leman graph isomorphism test. In 2020, a universal approximation theorem result was established by Brüel-Gabrielsson, showing that graph representation with certain injective properties is sufficient for universal function approximation on bounded graphs and restricted universal function approximation on unbounded graphs, with an accompanying O ( | V | ⋅ | E | ) {\displaystyle {\mathcal {O}}(\left|V\right|\cdot \left|E\right|)} -runtime method that performed at state of the art on a collection of benchmarks (where V {\displaystyle V} and E {\displaystyle E} are the sets of nodes and edges of the graph respectively). There are also a variety of results between non-Euclidean spaces and other commonly used architectures and, more generally, algorithmically generated sets of functions, such as the convolutional neural network (CNN) architecture, radial basis functions, or neural networks with specific properties. == Arbitrary-width case == A universal approximation theorem formally states that a family of neural network funct

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  New York Institute of Technology Computer Graphics Lab

  The New York Institute of Technology Computer Graphics Lab is a computer lab located at the New York Institute of Technology (NYIT), founded by Alexander Schure. It was originally located at the "pink building" on the NYIT campus. It has played an important role in the history of computer graphics and animation, as founders of Pixar and Lucasfilm Limited, including Turing Award winners Edwin Catmull and Patrick Hanrahan, began their research there. It is the birthplace of entirely 3D CGI films. The lab was initially founded to produce a short high-quality feature film with the project name of The Works. The feature, which was never completed, was a 90-minute feature that was to be the first entirely computer-generated CGI movie. Production mainly focused around DEC PDP and VAX machines. Many of the original CGL team now form the elite of the CG and computer world with members going on to Silicon Graphics, Microsoft, Cisco, NVIDIA and others, including Pixar president, co-founder and Turing laureate Ed Catmull, Pixar co-founder and Microsoft graphics fellow Alvy Ray Smith, Pixar co-founder Ralph Guggenheim, Walt Disney Animation Studios chief scientist Lance Williams, Netscape and Silicon Graphics founder Jim Clark, Tableau co-founder and Turing laureate Pat Hanrahan, Microsoft graphics fellow Jim Blinn, Thad Beier, Oscar and Bafta nominee Jacques Stroweis, Andrew Glassner, and Tom Brigham. Systems programmer Bruce Perens went on to co-found the Open Source Initiative. Researchers at the New York Institute of Technology Computer Graphics Lab created the tools that made entirely 3D CGI films possible. Among NYIT CG Lab's many innovations was an eight-bit paint system to ease computer animation. NYIT CG Lab was regarded as the top computer animation research and development group in the world during the late 70s and early 80s. == The 21st century == The lab is presently located at NYIT's Long Island campus, and NYIT currently offers a Ph.D. program in Computer Science.

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  Bayesian network

  A Bayesian network (also known as a Bayes network, Bayes net, belief network, or decision network) is a probabilistic graphical model that represents a set of variables and their conditional dependencies via a directed acyclic graph (DAG). While it is one of several forms of causal notation, causal networks are special cases of Bayesian networks. Bayesian networks are ideal for taking an event that occurred and predicting the likelihood that any one of several possible known causes was the contributing factor. For example, a Bayesian network could represent the probabilistic relationships between diseases and symptoms. Given symptoms, the network can be used to compute the probabilities of the presence of various diseases. Efficient algorithms can perform inference and learning in Bayesian networks. Bayesian networks that model sequences of variables (e.g. speech signals or protein sequences) are called dynamic Bayesian networks. Generalizations of Bayesian networks that can represent and solve decision problems under uncertainty are called influence diagrams. == Graphical model == Formally, Bayesian networks are directed acyclic graphs (DAGs) whose nodes represent variables in the Bayesian sense: they may be observable quantities, latent variables, unknown parameters or hypotheses. Each edge represents a direct conditional dependency. Any pair of nodes that are not connected (i.e. no path connects one node to the other) represent variables that are conditionally independent of each other. Each node is associated with a probability function that takes, as input, a particular set of values for the node's parent variables, and gives (as output) the probability (or probability distribution, if applicable) of the variable represented by the node. For example, if m {\displaystyle m} parent nodes represent m {\displaystyle m} Boolean variables, then the probability function could be represented by a table of 2 m {\displaystyle 2^{m}} entries, one entry for each of the 2 m {\displaystyle 2^{m}} possible parent combinations. Similar ideas may be applied to undirected, and possibly cyclic, graphs such as Markov networks. == Example == Suppose we want to model the dependencies between three variables: the sprinkler (or more appropriately, its state - whether it is on or not), the presence or absence of rain and whether the grass is wet or not. Observe that two events can cause the grass to become wet: an active sprinkler or rain. Rain has a direct effect on the use of the sprinkler (namely that when it rains, the sprinkler usually is not active). This situation can be modeled with a Bayesian network (shown to the right). Each variable has two possible values, T (for true) and F (for false). The joint probability function is, by the chain rule of probability, Pr ( G , S , R ) = Pr ( G ∣ S , R ) Pr ( S ∣ R ) Pr ( R ) {\displaystyle \Pr(G,S,R)=\Pr(G\mid S,R)\Pr(S\mid R)\Pr(R)} where G = "Grass wet (true/false)", S = "Sprinkler turned on (true/false)", and R = "Raining (true/false)". The model can answer questions about the presence of a cause given the presence of an effect (so-called inverse probability) like "What is the probability that it is raining, given the grass is wet?" by using the conditional probability formula and summing over all nuisance variables: Pr ( R = T ∣ G = T ) = Pr ( G = T , R = T ) Pr ( G = T ) = ∑ x ∈ { T , F } Pr ( G = T , S = x , R = T ) ∑ x , y ∈ { T , F } Pr ( G = T , S = x , R = y ) {\displaystyle \Pr(R=T\mid G=T)={\frac {\Pr(G=T,R=T)}{\Pr(G=T)}}={\frac {\sum _{x\in \{T,F\}}\Pr(G=T,S=x,R=T)}{\sum _{x,y\in \{T,F\}}\Pr(G=T,S=x,R=y)}}} Using the expansion for the joint probability function Pr ( G , S , R ) {\displaystyle \Pr(G,S,R)} and the conditional probabilities from the conditional probability tables (CPTs) stated in the diagram, one can evaluate each term in the sums in the numerator and denominator. For example, Pr ( G = T , S = T , R = T ) = Pr ( G = T ∣ S = T , R = T ) Pr ( S = T ∣ R = T ) Pr ( R = T ) = 0.99 × 0.01 × 0.2 = 0.00198. {\displaystyle {\begin{aligned}\Pr(G=T,S=T,R=T)&=\Pr(G=T\mid S=T,R=T)\Pr(S=T\mid R=T)\Pr(R=T)\\&=0.99\times 0.01\times 0.2\\&=0.00198.\end{aligned}}} Then the numerical results (subscripted by the associated variable values) are Pr ( R = T ∣ G = T ) = 0.00198 T T T + 0.1584 T F T 0.00198 T T T + 0.288 T T F + 0.1584 T F T + 0.0 T F F = 891 2491 ≈ 35.77 % . {\displaystyle \Pr(R=T\mid G=T)={\frac {0.00198_{TTT}+0.1584_{TFT}}{0.00198_{TTT}+0.288_{TTF}+0.1584_{TFT}+0.0_{TFF}}}={\frac {891}{2491}}\approx 35.77\%.} To answer an interventional question, such as "What is the probability that it would rain, given that we wet the grass?" the answer is governed by the post-intervention joint distribution function Pr ( S , R ∣ do ( G = T ) ) = Pr ( S ∣ R ) Pr ( R ) {\displaystyle \Pr(S,R\mid {\text{do}}(G=T))=\Pr(S\mid R)\Pr(R)} obtained by removing the factor Pr ( G ∣ S , R ) {\displaystyle \Pr(G\mid S,R)} from the pre-intervention distribution. The do operator forces the value of G to be true. The probability of rain is unaffected by the action: Pr ( R ∣ do ( G = T ) ) = Pr ( R ) . {\displaystyle \Pr(R\mid {\text{do}}(G=T))=\Pr(R).} To predict the impact of turning the sprinkler on: Pr ( R , G ∣ do ( S = T ) ) = Pr ( R ) Pr ( G ∣ R , S = T ) {\displaystyle \Pr(R,G\mid {\text{do}}(S=T))=\Pr(R)\Pr(G\mid R,S=T)} with the term Pr ( S = T ∣ R ) {\displaystyle \Pr(S=T\mid R)} removed, showing that the action affects the grass but not the rain. These predictions may not be feasible given unobserved variables, as in most policy evaluation problems. The effect of the action do ( x ) {\displaystyle {\text{do}}(x)} can still be predicted, however, whenever the back-door criterion is satisfied. It states that, if a set Z of nodes can be observed that d-separates (or blocks) all back-door paths from X to Y then Pr ( Y , Z ∣ do ( x ) ) = Pr ( Y , Z , X = x ) Pr ( X = x ∣ Z ) . {\displaystyle \Pr(Y,Z\mid {\text{do}}(x))={\frac {\Pr(Y,Z,X=x)}{\Pr(X=x\mid Z)}}.} A back-door path is one that ends with an arrow into X. Sets that satisfy the back-door criterion are called "sufficient" or "admissible." For example, the set Z = R is admissible for predicting the effect of S = T on G, because R d-separates the (only) back-door path S ← R → G. However, if S is not observed, no other set d-separates this path and the effect of turning the sprinkler on (S = T) on the grass (G) cannot be predicted from passive observations. In that case P(G | do(S = T)) is not "identified". This reflects the fact that, lacking interventional data, the observed dependence between S and G is due to a causal connection or is spurious (apparent dependence arising from a common cause, R). (see Simpson's paradox) To determine whether a causal relation is identified from an arbitrary Bayesian network with unobserved variables, one can use the three rules of "do-calculus" and test whether all do terms can be removed from the expression of that relation, thus confirming that the desired quantity is estimable from frequency data. Using a Bayesian network can save considerable amounts of memory over exhaustive probability tables, if the dependencies in the joint distribution are sparse. For example, a naive way of storing the conditional probabilities of 10 two-valued variables as a table requires storage space for 2 10 = 1024 {\displaystyle 2^{10}=1024} values. If no variable's local distribution depends on more than three parent variables, the Bayesian network representation stores at most 10 ⋅ 2 3 = 80 {\displaystyle 10\cdot 2^{3}=80} values. One advantage of Bayesian networks is that it is intuitively easier for a human to understand (a sparse set of) direct dependencies and local distributions than complete joint distributions. == Inference and learning == Bayesian networks perform three main inference tasks: Inferring unobserved variables Parameter learning for the probability distributions of each node in the network Structure learning of the graphical network === Inferring unobserved variables === Because a Bayesian network is a complete model for its variables and their relationships, it can be used to answer probabilistic queries about them. For example, the network can be used to update knowledge of the state of a subset of variables when other variables (the evidence variables) are observed. This process of computing the posterior distribution of variables given evidence is called probabilistic inference. The posterior gives a universal sufficient statistic for detection applications, when choosing values for the variable subset that minimize some expected loss function, for instance the probability of decision error. A Bayesian network can thus be considered a mechanism for automatically applying Bayes' theorem to complex problems. The most common exact inference methods are: variable elimination, which eliminates (by integration or summation) the non-observed non-query variables one by one by distributing the sum over the prod

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  Memetic algorithm

  In computer science and operations research, a memetic algorithm (MA) is an extension of an evolutionary algorithm (EA) that aims to accelerate the evolutionary search for the optimum. An EA is a metaheuristic that reproduces the basic principles of biological evolution as a computer algorithm in order to solve challenging optimization or planning tasks, at least approximately. An MA uses one or more suitable heuristics or local search techniques to improve the quality of solutions generated by the EA and to speed up the search. The effects on the reliability of finding the global optimum depend on both the use case and the design of the MA. Memetic algorithms represent one of the recent growing areas of research in evolutionary computation. The term MA is now widely used as a synergy of evolutionary or any population-based approach with separate individual learning or local improvement procedures for problem search. Quite often, MAs are also referred to in the literature as Baldwinian evolutionary algorithms, Lamarckian EAs, cultural algorithms, or genetic local search. == Introduction == Inspired by both Darwinian principles of natural evolution and Dawkins' notion of a meme, the term memetic algorithm (MA) was introduced by Pablo Moscato in his technical report in 1989 where he viewed MA as being close to a form of population-based hybrid genetic algorithm (GA) coupled with an individual learning procedure capable of performing local refinements. The metaphorical parallels, on the one hand, to Darwinian evolution and, on the other hand, between memes and domain specific (local search) heuristics are captured within memetic algorithms thus rendering a methodology that balances well between generality and problem specificity. This two-stage nature makes them a special case of dual-phase evolution. The basic idea behind an MA is to combine the advantages of a global search performed by an EA (or another global search method) with the local refinement provided by one or more local search techniques, while avoiding their drawbacks. The main disadvantage of EAs is that, when searching in the vicinity of an optimum, they perform poorly in determining the exact position of that optimum. The downside of local search methods lies simply in the locality of their search relative to the chosen starting point. The combination of these two classes of methods aims to merge global and local search so that the advantages of both approaches can be leveraged. The idea of this approach can be illustrated by the search for the highest mountain in the Alps. A local search method would climb one of the mountains near the starting point, ignoring Mont Blanc as long as the starting point is not in its vicinity. An EA, on the other hand, will likely only find Mont Blanc after examining many other mountains, valleys, and hills, and then it will have difficulty identifying the summit cross. From the perspective of an MA’s global search procedure, however, only the summits of hills and mountains are seen, and its search is limited to finding the best summit. The open question is whether the additional effort required for the local search is worthwhile. This depends not only on the design of the MA but also on the specific application and the local search methods used. In the context of complex optimization, many different instantiations of memetic algorithms have been reported across a wide range of application domains, in general, converging to high-quality solutions more efficiently than their conventional evolutionary counterparts. In general, using the ideas of memetics within a computational framework is called memetic computing or memetic computation (MC). With MC, the traits of universal Darwinism are more appropriately captured. Viewed in this perspective, MA is a more constrained notion of MC. More specifically, MA covers one area of MC, in particular dealing with areas of evolutionary algorithms that marry other deterministic refinement techniques for solving optimization problems. MC extends the notion of memes to cover conceptual entities of knowledge-enhanced procedures or representations. == Theoretical Background == The no-free-lunch theorems of optimization and search state that all optimization strategies are equally effective with respect to the set of all optimization problems. Conversely, this means that one can expect the following: The more efficiently an algorithm solves a problem or class of problems, the less general it is and the more problem-specific knowledge it builds on. This insight leads directly to the recommendation to complement generally applicable metaheuristics with application-specific methods or heuristics, which fits well with the concept of MAs. == The development of MAs == === 1st generation === Pablo Moscato characterized an MA as follows: "Memetic algorithms are a marriage between a population-based global search and the heuristic local search made by each of the individuals. ... The mechanisms to do local search can be to reach a local optimum or to improve (regarding the objective cost function) up to a predetermined level." And he emphasizes "I am not constraining an MA to a genetic representation.". This original definition of MA although encompasses characteristics of cultural evolution (in the form of local refinement) in the search cycle, it may not qualify as a true evolving system according to universal Darwinism, since all the core principles of inheritance/memetic transmission, variation, and selection are missing. This suggests why the term MA stirred up criticisms and controversies among researchers when first introduced. The following pseudo code would correspond to this general definition of an MA: Pseudo code Procedure Memetic Algorithm Initialize: Generate an initial population, evaluate the individuals and assign a quality value to them; while Stopping conditions are not satisfied do Evolve a new population using stochastic search operators. Evaluate all individuals in the population and assign a quality value to them. Select the subset of individuals, Ω i l {\displaystyle \Omega _{il}} , that should undergo the individual improvement procedure. for each individual in Ω i l {\displaystyle \Omega _{il}} do Perform individual learning using meme(s) with frequency or probability of f i l {\displaystyle f_{il}} , with an intensity of t i l {\displaystyle t_{il}} . Proceed with Lamarckian or Baldwinian learning. end for end while Lamarckian learning in this context means to update the chromosome according to the improved solution found by the individual learning step, while Baldwinian learning leaves the chromosome unchanged and uses only the improved fitness. This pseudo code leaves open which steps are based on the fitness of the individuals and which are not. In question are the evolving of the new population and the selection of Ω i l {\displaystyle \Omega _{il}} . Since most MA implementations are based on EAs, the pseudo code of a corresponding representative of the first generation is also given here, following Krasnogor: Pseudo code Procedure Memetic Algorithm Based on an EA Initialization: t = 0 {\displaystyle t=0} ; // Initialization of the generation counter Randomly generate an initial population P ( t ) {\displaystyle P(t)} ; Compute the fitness f ( p ) ∀ p ∈ P ( t ) {\displaystyle f(p)\ \ \forall p\in P(t)} ; while Stopping conditions are not satisfied do Selection: Accordingly to f ( p ) {\displaystyle f(p)} choose a subset of P ( t ) {\displaystyle P(t)} and store it in M ( t ) {\displaystyle M(t)} ; Offspring: Recombine and mutate individuals p ∈ M ( t ) {\displaystyle p\in M(t)} and store them in M ′ ( t ) {\displaystyle M'(t)} ; Learning: Improve p ′ {\displaystyle p'} by local search or heuristic ∀ p ′ ∈ M ′ ( t ) {\displaystyle \forall p'\in M'(t)} ; Evaluation: Compute the fitness f ( p ′ ) ∀ p ′ ∈ M ′ ( t ) {\displaystyle f(p')\ \ \forall p'\in M'(t)} ; if Lamarckian learning then Update chromosome of p ′ {\displaystyle p'} according to improvement ∀ p ′ ∈ M ′ ( t ) {\displaystyle \forall p'\in M'(t)} ; fi New generation: Generate P ( t + 1 ) {\displaystyle P(t+1)} by selecting some individuals from P ( t ) {\displaystyle P(t)} and M ′ ( t ) {\displaystyle M'(t)} ; t = t + 1 {\displaystyle t=t+1} ; // Increment the generation counter end while Return best individual p ∈ P ( t − 1 ) {\displaystyle p\in P(t-1)} as result; There are some alternatives for this MA scheme. For example: All or some of the initial individuals may be improved by the meme(s). The parents may be locally improved instead of the offspring. Instead of all offspring, only a randomly selected or fitness-dependent fraction may undergo local improvement. The latter requires the evaluation of the offspring in M ′ ( t ) {\displaystyle M'(t)} prior to the Learning step. === 2nd generation === Multi-meme, hyper-heuristic and meta-Lamarckian MA are referred to as second generation MA exhibiting the principles of me

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  Scale-invariant feature operator

  In the fields of computer vision and image analysis, the scale-invariant feature operator (or SFOP) is an algorithm to detect local features in images. The algorithm was published by Förstner et al. in 2009. == Algorithm == The scale-invariant feature operator (SFOP) is based on two theoretical concepts: spiral model feature operator Desired properties of keypoint detectors: Invariance and repeatability for object recognition Accuracy to support camera calibration Interpretability: Especially corners and circles, should be part of the detected keypoints (see figure). As few control parameters as possible with clear semantics Complementarity to known detectors scale-invariant corner/circle detector. == Theory == === Maximize the weight === Maximize the weight w {\displaystyle w} = 1/variance of a point p {\displaystyle p} w ( p , α , τ , σ ) = ( N ( σ ) − 2 ) λ m i n ( M ( p , α , τ , σ ) ) Ω ( p , α , τ , σ ) {\displaystyle w(\mathbf {p} ,\alpha ,\tau ,\sigma )=\left(N(\sigma )-2\right){\frac {\lambda _{min}(M(\mathbf {p} ,\alpha ,\tau ,\sigma ))}{\Omega (\mathbf {p} ,\alpha ,\tau ,\sigma )}}} comprising: 1. the image model Ω ( p , α , τ , σ ) = ∑ n = 1 N ( σ ) [ ( q n − p ) T R α ∇ T g ( q n ) ] 2 G σ ( q n − p ) = N ( σ ) t r { R α ∇ τ ∇ τ T R α T ∗ p p T G σ ( p ) } {\displaystyle {\begin{aligned}\Omega (\mathbf {p} ,\alpha ,\tau ,\sigma )&=\sum _{n=1}^{N(\sigma )}[(\mathbf {q} _{n}-\mathbf {p} )^{T}\mathbf {R} _{\alpha }\mathbf {\nabla } _{T}g(\mathbf {q} _{n})]^{2}G_{\sigma }(\mathbf {q} _{n}-\mathbf {p} )\\&=N(\sigma )\mathbf {tr} \left\{R_{\alpha }\mathbf {\nabla } _{\tau }\mathbf {\nabla } _{\tau }^{T}R_{\alpha }^{T}\mathbf {p} \mathbf {p} ^{T}G_{\sigma }(\mathbf {p} )\right\}\end{aligned}}} 2. the smaller eigenvalue of the structure tensor M ( p , α , τ , σ ) ⏟ structure tensor = G σ ( p ) ⏟ weighted summation ∗ ( R σ ∇ τ ∇ τ T R σ T ) ⏟ squared rotated gradients {\displaystyle \underbrace {M(\mathbf {p} ,\alpha ,\tau ,\sigma )} _{\text{structure tensor}}=\underbrace {G_{\sigma }(\mathbf {p} )} _{\text{weighted summation}}\underbrace {(R_{\sigma }\nabla _{\tau }\nabla _{\tau }^{T}R_{\sigma }^{T})} _{\text{squared rotated gradients}}} === Reduce the search space === Reduce the 5-dimensional search space by linking the differentiation scale τ {\displaystyle \tau } to the integration scale τ = σ / 3 {\displaystyle \tau =\sigma /3} solving for the optimal α ^ {\displaystyle {\hat {\alpha }}} using the model Ω ( α ) = a − b cos ⁡ ( 2 α − 2 α 0 ) {\displaystyle \Omega (\alpha )=a-b\cos(2\alpha -2\alpha _{0})} and determining the parameters from three angles, e. g. Ω ( 0 ∘ ) , Ω ( 60 ∘ ) , Ω ( 120 ∘ ) → a , b , α 0 → α ^ {\displaystyle \Omega (0^{\circ }),\Omega (60^{\circ }),\Omega (120^{\circ })\quad \rightarrow \quad a,b,\alpha _{0}\quad \rightarrow \quad {\hat {\alpha }}} pre-selection possible: α = 0 ∘ → junctions , α = 90 ∘ → circular features {\displaystyle \alpha =0^{\circ }\,\rightarrow \,{\mbox{junctions}},\quad \alpha =90^{\circ }\,\rightarrow \,{\mbox{circular features}}} === Filter potential keypoints === non-maxima suppression over scale, space and angle thresholding the isotropy λ 2 ( M ) {\displaystyle \lambda _{2(M)}} :eigenvalues characterize the shape of the keypoint, smallest eigenvalue has to be larger than threshold T λ {\displaystyle T_{\lambda }} derived from noise variance V ( n ) {\displaystyle V(n)} and significance level S {\displaystyle S} : T λ ( V ( n ) , τ , σ , S ) = N ( σ ) 16 π τ 4 V ( n ) χ 2 , S 2 {\displaystyle T_{\lambda }(V(n),\tau ,\sigma ,S)={\frac {N(\sigma )}{16\pi \tau ^{4}}}V(n)\chi _{2,S}^{2}} == Algorithm == == Results == === Interpretability of SFOP keypoints ===

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  Tandem (app)

  Tandem is a mobile language exchange and language learning app. == History == Tandem was founded in Hannover, Germany in 2014 by Arnd Aschentrup, Tobias Dickmeis, and Matthias Kleimann. Prior to founding Tandem, the trio had launched Vive, a members-only mobile video chat platform. Tandem has been criticised for not accepting members into the community immediately, as opposed to competitors including HelloTalk, Speaky or Cafehub. In some countries, there is a waiting list and applicants can wait up to seven days for their application to be processed by human moderators. In 2015, Tandem completed its first funding round (seed funding) of €600,000. Participating investors included business angels such as Atlantic Labs (Christophe Maire), Hannover Beteiligungsfonds, Marcus Englert (Chairman of the Supervisory Board of Rocket Internet SE ), Catagonia, Ludwig zu Salm, Florian Langenscheidt, Heiko Hubertz, Martin Sinner, and Zehden Enterprises. In 2016, the company received a further €2 million from new investors Rubylight and Faber Ventures, as well as from existing investors Hannover Beteiligungsfonds, Atlantic Labs, and Zehden Enterprises. Since 2018, the premium membership Tandem Pro has been available, which offers members unlimited access to all language learning features of the app as well as the removal of advertising for a monthly fee.

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  One-class classification

  In machine learning, one-class classification (OCC), also known as unary classification or class-modelling, is an approach to the training of binary classifiers in which only examples of one of the two classes are used. Examples include the monitoring of helicopter gearboxes, motor failure prediction, or assessing the operational status of a nuclear plant as 'normal': In such scenarios, there are few, if any, examples of the catastrophic system states – rare outliers – that comprise the second class. Alternatively, the class that is being focused on may cover a small, coherent subset of the data and the training may rely on an information bottleneck approach. In practice, counter-examples from the second class may be used in later rounds of training to further refine the algorithm. == Overview == The term one-class classification (OCC) was coined by Moya & Hush (1996) and many applications can be found in scientific literature, for example outlier detection, anomaly detection, novelty detection. A feature of OCC is that it uses only sample points from the assigned class, so that a representative sampling is not strictly required for non-target classes. == Introduction == SVM based one-class classification (OCC) relies on identifying the smallest hypersphere (with radius r, and center c) consisting of all the data points. This method is called Support Vector Data Description (SVDD). Formally, the problem can be defined in the following constrained optimization form, min r , c r 2 subject to, | | Φ ( x i ) − c | | 2 ≤ r 2 ∀ i = 1 , 2 , . . . , n {\displaystyle \min _{r,c}r^{2}{\text{ subject to, }}||\Phi (x_{i})-c||^{2}\leq r^{2}\;\;\forall i=1,2,...,n} However, the above formulation is highly restrictive, and is sensitive to the presence of outliers. Therefore, a flexible formulation, that allow for the presence of outliers is formulated as shown below, min r , c , ζ r 2 + 1 ν n ∑ i = 1 n ζ i {\displaystyle \min _{r,c,\zeta }r^{2}+{\frac {1}{\nu n}}\sum _{i=1}^{n}\zeta _{i}} subject to, | | Φ ( x i ) − c | | 2 ≤ r 2 + ζ i ∀ i = 1 , 2 , . . . , n {\displaystyle {\text{subject to, }}||\Phi (x_{i})-c||^{2}\leq r^{2}+\zeta _{i}\;\;\forall i=1,2,...,n} From the Karush–Kuhn–Tucker conditions for optimality, we get c = ∑ i = 1 n α i Φ ( x i ) , {\displaystyle c=\sum _{i=1}^{n}\alpha _{i}\Phi (x_{i}),} where the α i {\displaystyle \alpha _{i}} 's are the solution to the following optimization problem: max α ∑ i = 1 n α i κ ( x i , x i ) − ∑ i , j = 1 n α i α j κ ( x i , x j ) {\displaystyle \max _{\alpha }\sum _{i=1}^{n}\alpha _{i}\kappa (x_{i},x_{i})-\sum _{i,j=1}^{n}\alpha _{i}\alpha _{j}\kappa (x_{i},x_{j})} subject to, ∑ i = 1 n α i = 1 and 0 ≤ α i ≤ 1 ν n for all i = 1 , 2 , . . . , n . {\displaystyle \sum _{i=1}^{n}\alpha _{i}=1{\text{ and }}0\leq \alpha _{i}\leq {\frac {1}{\nu n}}{\text{for all }}i=1,2,...,n.} The introduction of kernel function provide additional flexibility to the One-class SVM (OSVM) algorithm. === PU (Positive Unlabeled) learning === A similar problem is PU learning, in which a binary classifier is constructed by semi-supervised learning from only positive and unlabeled sample points. In PU learning, two sets of examples are assumed to be available for training: the positive set P {\displaystyle P} and a mixed set U {\displaystyle U} , which is assumed to contain both positive and negative samples, but without these being labeled as such. This contrasts with other forms of semisupervised learning, where it is assumed that a labeled set containing examples of both classes is available in addition to unlabeled samples. A variety of techniques exist to adapt supervised classifiers to the PU learning setting, including variants of the EM algorithm. PU learning has been successfully applied to text, time series, bioinformatics tasks, and remote sensing data. == Approaches == Several approaches have been proposed to solve one-class classification (OCC). The approaches can be distinguished into three main categories, density estimation, boundary methods, and reconstruction methods. === Density estimation methods === Density estimation methods rely on estimating the density of the data points, and set the threshold. These methods rely on assuming distributions, such as Gaussian, or a Poisson distribution. Following which discordancy tests can be used to test the new objects. These methods are robust to scale variance. Gaussian model is one of the simplest methods to create one-class classifiers. Due to Central Limit Theorem (CLT), these methods work best when large number of samples are present, and they are perturbed by small independent error values. The probability distribution for a d-dimensional object is given by: p N ( z ; μ ; Σ ) = 1 ( 2 π ) d 2 | Σ | 1 2 exp ⁡ { − 1 2 ( z − μ ) T Σ − 1 ( z − μ ) } {\displaystyle p_{\mathcal {N}}(z;\mu ;\Sigma )={\frac {1}{(2\pi )^{\frac {d}{2}}|\Sigma |^{\frac {1}{2}}}}\exp \left\{-{\frac {1}{2}}(z-\mu )^{T}\Sigma ^{-1}(z-\mu )\right\}} Where, μ {\displaystyle \mu } is the mean and Σ {\displaystyle \Sigma } is the covariance matrix. Computing the inverse of covariance matrix ( Σ − 1 {\displaystyle \Sigma ^{-1}} ) is the costliest operation, and in the cases where the data is not scaled properly, or data has singular directions pseudo-inverse Σ + {\displaystyle \Sigma ^{+}} is used to approximate the inverse, and is calculated as Σ T ( Σ Σ T ) − 1 {\displaystyle \Sigma ^{T}(\Sigma \Sigma ^{T})^{-1}} . === Boundary methods === Boundary methods focus on setting boundaries around a few set of points, called target points. These methods attempt to optimize the volume. Boundary methods rely on distances, and hence are not robust to scale variance. K-centers method, NN-d, and SVDD are some of the key examples. K-centers In K-center algorithm, k {\displaystyle k} small balls with equal radius are placed to minimize the maximum distance of all minimum distances between training objects and the centers. Formally, the following error is minimized, ε k − c e n t e r = max i ( min k | | x i − μ k | | 2 ) {\displaystyle \varepsilon _{k-center}=\max _{i}(\min _{k}||x_{i}-\mu _{k}||^{2})} The algorithm uses forward search method with random initialization, where the radius is determined by the maximum distance of the object, any given ball should capture. After the centers are determined, for any given test object z {\displaystyle z} the distance can be calculated as, d k − c e n t r ( z ) = min k | | z − μ k | | 2 {\displaystyle d_{k-centr}(z)=\min _{k}||z-\mu _{k}||^{2}} === Reconstruction methods === Reconstruction methods use prior knowledge and generating process to build a generating model that best fits the data. New objects can be described in terms of a state of the generating model. Some examples of reconstruction methods for OCC are, k-means clustering, learning vector quantization, self-organizing maps, etc. == Applications == === Document classification === The basic Support Vector Machine (SVM) paradigm is trained using both positive and negative examples, however studies have shown there are many valid reasons for using only positive examples. When the SVM algorithm is modified to only use positive examples, the process is considered one-class classification. One situation where this type of classification might prove useful to the SVM paradigm is in trying to identify a web browser's sites of interest based only off of the user's browsing history. === Biomedical studies === One-class classification can be particularly useful in biomedical studies where often data from other classes can be difficult or impossible to obtain. In studying biomedical data it can be difficult and/or expensive to obtain the set of labeled data from the second class that would be necessary to perform a two-class classification. A study from The Scientific World Journal found that the typicality approach is the most useful in analysing biomedical data because it can be applied to any type of dataset (continuous, discrete, or nominal). The typicality approach is based on the clustering of data by examining data and placing it into new or existing clusters. To apply typicality to one-class classification for biomedical studies, each new observation, y 0 {\displaystyle y_{0}} , is compared to the target class, C {\displaystyle C} , and identified as an outlier or a member of the target class. === Unsupervised Concept Drift Detection === One-class classification has similarities with unsupervised concept drift detection, where both aim to identify whether the unseen data share similar characteristics to the initial data. A concept is referred to as the fixed probability distribution which data is drawn from. In unsupervised concept drift detection, the goal is to detect if the data distribution changes without utilizing class labels. In one-class classification, the flow of data is not important. Unseen data is classified as typical or outlier depending on its characteristics, whether it is from the initi

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  Vowpal Wabbit

  Vowpal Wabbit (VW) is an open-source fast online interactive machine learning system library and program developed originally at Yahoo! Research, and currently at Microsoft Research. It was started and is led by John Langford. Vowpal Wabbit's interactive learning support is particularly notable including Contextual Bandits, Active Learning, and forms of guided Reinforcement Learning. Vowpal Wabbit provides an efficient scalable out-of-core implementation with support for a number of machine learning reductions, importance weighting, and a selection of different loss functions and optimization algorithms. == Notable features == The VW program supports: Multiple supervised (and semi-supervised) learning problems: Classification (both binary and multi-class) Regression Active learning (partially labeled data) for both regression and classification Multiple learning algorithms (model-types / representations) OLS regression Matrix factorization (sparse matrix SVD) Single layer neural net (with user specified hidden layer node count) Searn (Search and Learn) Latent Dirichlet Allocation (LDA) Stagewise polynomial approximation Recommend top-K out of N One-against-all (OAA) and cost-sensitive OAA reduction for multi-class Weighted all pairs Contextual-bandit (with multiple exploration/exploitation strategies) Multiple loss functions: squared error quantile hinge logistic poisson Multiple optimization algorithms Stochastic gradient descent (SGD) BFGS Conjugate gradient Regularization (L1 norm, L2 norm, & elastic net regularization) Flexible input - input features may be: Binary Numerical Categorical (via flexible feature-naming and the hash trick) Can deal with missing values/sparse-features Other features On the fly generation of feature interactions (quadratic and cubic) On the fly generation of N-grams with optional skips (useful for word/language data-sets) Automatic test-set holdout and early termination on multiple passes bootstrapping User settable online learning progress report + auditing of the model Hyperparameter optimization == Scalability == Vowpal wabbit has been used to learn a tera-feature (1012) data-set on 1000 nodes in one hour. Its scalability is aided by several factors: Out-of-core online learning: no need to load all data into memory The hashing trick: feature identities are converted to a weight index via a hash (uses 32-bit MurmurHash3) Exploiting multi-core CPUs: parsing of input and learning are done in separate threads. Compiled C++ code

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  LIBSVM

  LIBSVM and LIBLINEAR are two popular open source machine learning libraries, both developed at the National Taiwan University and both written in C++ though with a C API. LIBSVM implements the sequential minimal optimization (SMO) algorithm for kernelized support vector machines (SVMs), supporting classification and regression. LIBLINEAR implements linear SVMs and logistic regression models trained using a coordinate descent algorithm. The SVM learning code from both libraries is often reused in other open source machine learning toolkits, including GATE, KNIME, Orange and scikit-learn. Bindings and ports exist for programming languages such as Java, MATLAB, R, Julia, and Python. It is available in e1071 library in R and scikit-learn in Python. Both libraries are free software released under the 3-clause BSD license.

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  Uncertain data

  In computer science, uncertain data is data that contains noise that makes it deviate from the correct, intended or original values. In the age of big data, uncertainty or data veracity is one of the defining characteristics of data. Data is constantly growing in volume, variety, velocity and uncertainty (1/veracity). Uncertain data is found in abundance today on the web, in sensor networks, within enterprises both in their structured and unstructured sources. For example, there may be uncertainty regarding the address of a customer in an enterprise dataset, or the temperature readings captured by a sensor due to aging of the sensor. In 2012 IBM called out managing uncertain data at scale in its global technology outlook report that presents a comprehensive analysis looking three to ten years into the future seeking to identify significant, disruptive technologies that will change the world. In order to make confident business decisions based on real-world data, analyses must necessarily account for many different kinds of uncertainty present in very large amounts of data. Analyses based on uncertain data will have an effect on the quality of subsequent decisions, so the degree and types of inaccuracies in this uncertain data cannot be ignored. Uncertain data is found in the area of sensor networks; text where noisy text is found in abundance on social media, web and within enterprises where the structured and unstructured data may be old, outdated, or plain incorrect; in modeling where the mathematical model may only be an approximation of the actual process. When representing such data in a database, an appropriate uncertain database model needs to be selected. == Example data model for uncertain data == One way to represent uncertain data is through probability distributions. Let us take the example of a relational database. There are three main ways to do represent uncertainty as probability distributions in such a database model. In attribute uncertainty, each uncertain attribute in a tuple is subject to its own independent probability distribution. For example, if readings are taken of temperature and wind speed, each would be described by its own probability distribution, as knowing the reading for one measurement would not provide any information about the other. In correlated uncertainty, multiple attributes may be described by a joint probability distribution. For example, if readings are taken of the position of an object, and the x- and y-coordinates stored, the probability of different values may depend on the distance from the recorded coordinates. As distance depends on both coordinates, it may be appropriate to use a joint distribution for these coordinates, as they are not independent. In tuple uncertainty, all the attributes of a tuple are subject to a joint probability distribution. This covers the case of correlated uncertainty, but also includes the case where there is a probability of a tuple not belonging in the relevant relation, which is indicated by all the probabilities not summing to one. For example, assume we have the following tuple from a probabilistic database: Then, the tuple has 10% chance of not existing in the database.

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  Cartesian genetic programming

  Cartesian genetic programming is a form of genetic programming that uses a graph representation to encode computer programs. It grew from a method of evolving digital circuits developed by Julian F. Miller and Peter Thomson in 1997. The term ‘Cartesian genetic programming’ first appeared in 1999 and was proposed as a general form of genetic programming in 2000. It is called ‘Cartesian’ because it represents a program using a two-dimensional grid of nodes. Miller's keynote explains how CGP works. He edited a book entitled Cartesian Genetic Programming, published in 2011 by Springer. The open source project dCGP implements a differentiable version of CGP developed at the European Space Agency by Dario Izzo, Francesco Biscani and Alessio Mereta able to approach symbolic regression tasks, to find solution to differential equations, find prime integrals of dynamical systems, represent variable topology artificial neural networks and more.

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  Yooreeka

  Yooreeka is a library for data mining, machine learning, soft computing, and mathematical analysis. The project started with the code of the book "Algorithms of the Intelligent Web". Although the term "Web" prevailed in the title, in essence, the algorithms are valuable in any software application. It covers all major algorithms and provides many examples. Yooreeka 2.x is licensed under the Apache License rather than the somewhat more restrictive LGPL (which was the license of v1.x). The library is written 100% in the Java language. == Algorithms == The following algorithms are covered: Clustering Hierarchical—Agglomerative (e.g. MST single link; ROCK) and Divisive Partitional (e.g. k-means) Classification Bayesian Decision trees Neural Networks Rule based (via Drools) Recommendations Collaborative filtering Content based Search PageRank DocRank Personalization

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