AI Chatbot Robot

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  Blobotics

  Blobotics is a term describing research into chemical-based computer processors based on ions rather than electrons. Andrew Adamatzky, a computer scientist at the University of the West of England, Bristol used the term in an article in New Scientist March 28, 2005 [1]. The aim is to create 'liquid logic gates' which would be 'infinitely reconfigurable and self-healing'. The process relies on the Belousov–Zhabotinsky reaction, a repeating cycle of three separate sets of reactions. Such a processor could form the basis of a robot which, using artificial sensors, interact with its surroundings in a way which mimics living creatures. The coining of the term was featured by ABC radio in Australia [2].

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  Multi-label classification

  In machine learning, multi-label classification or multi-output classification is a variant of the classification problem where multiple nonexclusive labels may be assigned to each instance. Multi-label classification is a generalization of multiclass classification, which is the single-label problem of categorizing instances into precisely one of several (greater than or equal to two) classes. In the multi-label problem the labels are nonexclusive and there is no constraint on how many of the classes the instance can be assigned to. The formulation of multi-label learning was first introduced by Shen et al. in the context of Semantic Scene Classification, and later gained popularity across various areas of machine learning. Formally, multi-label classification is the problem of finding a model that maps inputs x to binary vectors y; that is, it assigns a value of 0 or 1 for each element (label) in y. == Problem transformation methods == Several problem transformation methods exist for multi-label classification, and can be roughly broken down into: === Transformation into binary classification problems === The baseline approach, called the binary relevance method, amounts to independently training one binary classifier for each label. Given an unseen sample, the combined model then predicts all labels for this sample for which the respective classifiers predict a positive result. Although this method of dividing the task into multiple binary tasks may resemble superficially the one-vs.-all (OvA) and one-vs.-rest (OvR) methods for multiclass classification, it is essentially different from both, because a single classifier under binary relevance deals with a single label, without any regard to other labels whatsoever. A classifier chain is an alternative method for transforming a multi-label classification problem into several binary classification problems. It differs from binary relevance in that labels are predicted sequentially, and the output of all previous classifiers (i.e. positive or negative for a particular label) are input as features to subsequent classifiers. Classifier chains have been applied, for instance, in HIV drug resistance prediction. Bayesian network has also been applied to optimally order classifiers in Classifier chains. In case of transforming the problem to multiple binary classifications, the likelihood function reads L = ∏ i = 1 n ( ∏ k ( ∏ j k ( p k , j k ( x i ) δ y i , k , j k ) ) ) {\displaystyle L=\prod _{i=1}^{n}(\prod _{k}(\prod _{j_{k}}(p_{k,j_{k}}(x_{i})^{\delta _{y_{i,k},j_{k}}})))} where index i {\displaystyle i} runs over the samples, index k {\displaystyle k} runs over the labels, j k {\displaystyle j_{k}} indicates the binary outcomes 0 or 1, δ a , b {\displaystyle \delta _{a,b}} indicates the Kronecker delta, y i , k ∈ 0 , 1 {\displaystyle y_{i,k}\in {0,1}} indicates the multiple hot encoded labels of sample i {\displaystyle i} . === Transformation into multi-class classification problem === The label powerset (LP) transformation creates one binary classifier for every label combination present in the training set. For example, if possible labels for an example were A, B, and C, the label powerset representation of this problem is a multi-class classification problem with the classes [0 0 0], [1 0 0], [0 1 0], [0 0 1], [1 1 0], [1 0 1], [0 1 1], and [1 1 1] where for example [1 0 1] denotes an example where labels A and C are present and label B is absent. === Ensemble methods === A set of multi-class classifiers can be used to create a multi-label ensemble classifier. For a given example, each classifier outputs a single class (corresponding to a single label in the multi-label problem). These predictions are then combined by an ensemble method, usually a voting scheme where every class that receives a requisite percentage of votes from individual classifiers (often referred to as the discrimination threshold) is predicted as a present label in the multi-label output. However, more complex ensemble methods exist, such as committee machines. Another variation is the random k-labelsets (RAKEL) algorithm, which uses multiple LP classifiers, each trained on a random subset of the actual labels; label prediction is then carried out by a voting scheme. A set of multi-label classifiers can be used in a similar way to create a multi-label ensemble classifier. In this case, each classifier votes once for each label it predicts rather than for a single label. == Adapted algorithms == Some classification algorithms/models have been adapted to the multi-label task, without requiring problem transformations. Examples of these including for multi-label data are k-nearest neighbors: the ML-kNN algorithm extends the k-NN classifier to multi-label data. decision trees: "Clare" is an adapted C4.5 algorithm for multi-label classification; the modification involves the entropy calculations. MMC, MMDT, and SSC refined MMDT, can classify multi-labeled data based on multi-valued attributes without transforming the attributes into single-values. They are also named multi-valued and multi-labeled decision tree classification methods. kernel methods for vector output neural networks: BP-MLL is an adaptation of the popular back-propagation algorithm for multi-label learning. == Learning paradigms == Based on learning paradigms, the existing multi-label classification techniques can be classified into batch learning and online machine learning. Batch learning algorithms require all the data samples to be available beforehand. It trains the model using the entire training data and then predicts the test sample using the found relationship. The online learning algorithms, on the other hand, incrementally build their models in sequential iterations. In iteration t, an online algorithm receives a sample, xt and predicts its label(s) ŷt using the current model; the algorithm then receives yt, the true label(s) of xt and updates its model based on the sample-label pair: (xt, yt). == Multi-label stream classification == Data streams are possibly infinite sequences of data that continuously and rapidly grow over time. Multi-label stream classification (MLSC) is the version of multi-label classification task that takes place in data streams. It is sometimes also called online multi-label classification. The difficulties of multi-label classification (exponential number of possible label sets, capturing dependencies between labels) are combined with difficulties of data streams (time and memory constraints, addressing infinite stream with finite means, concept drifts). Many MLSC methods resort to ensemble methods in order to increase their predictive performance and deal with concept drifts. Below are the most widely used ensemble methods in the literature: Online Bagging (OzaBagging)-based methods: Observing the probability of having K many of a certain data point in a bootstrap sample is approximately Poisson(1) for big datasets, each incoming data instance in a data stream can be weighted proportional to Poisson(1) distribution to mimic bootstrapping in an online setting. This is called Online Bagging (OzaBagging). Many multi-label methods that use Online Bagging are proposed in the literature, each of which utilizes different problem transformation methods. EBR, ECC, EPS, EBRT, EBMT, ML-Random Rules are examples of such methods. ADWIN Bagging-based methods: Online Bagging methods for MLSC are sometimes combined with explicit concept drift detection mechanisms such as ADWIN (Adaptive Window). ADWIN keeps a variable-sized window to detect changes in the distribution of the data, and improves the ensemble by resetting the components that perform poorly when there is a drift in the incoming data. Generally, the letter 'a' is used as a subscript in the name of such ensembles to indicate the usage of ADWIN change detector. EaBR, EaCC, EaHTPS are examples of such multi-label ensembles. GOOWE-ML-based methods: Interpreting the relevance scores of each component of the ensemble as vectors in the label space and solving a least squares problem at the end of each batch, Geometrically-Optimum Online-Weighted Ensemble for Multi-label Classification (GOOWE-ML) is proposed. The ensemble tries to minimize the distance between the weighted prediction of its components and the ground truth vector for each instance over a batch. Unlike Online Bagging and ADWIN Bagging, GOOWE-ML utilizes a weighted voting scheme where better performing components of the ensemble are given more weight. The GOOWE-ML ensemble grows over time, and the lowest weight component is replaced by a new component when it is full at the end of a batch. GOBR, GOCC, GOPS, GORT are the proposed GOOWE-ML-based multi-label ensembles. Multiple Windows : Here, BR models that use a sliding window are replaced with two windows for each label, one for relevant and one for non-relevant examples. Instances are oversampled or undersampled according to a load factor that is kept

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  Multispectral pattern recognition

  Multispectral remote sensing is the collection and analysis of reflected, emitted, or back-scattered energy from an object or an area of interest in multiple bands of regions of the electromagnetic spectrum (Jensen, 2005). Subcategories of multispectral remote sensing include hyperspectral, in which hundreds of bands are collected and analyzed, and ultraspectral remote sensing where many hundreds of bands are used (Logicon, 1997). The main purpose of multispectral imaging is the potential to classify the image using multispectral classification. This is a much faster method of image analysis than is possible by human interpretation. == Multispectral remote sensing systems == Remote sensing systems gather data via instruments typically carried on satellites in orbit around the Earth. The remote sensing scanner detects the energy that radiates from the object or area of interest. This energy is recorded as an analog electrical signal and converted into a digital value though an A-to-D conversion. There are several multispectral remote sensing systems that can be categorized in the following way: === Multispectral imaging using discrete detectors and scanning mirrors === Landsat Multispectral Scanner (MSS) Landsat Thematic Mapper (TM) NOAA Geostationary Operational Environmental Satellite (GOES) NOAA Advanced Very High Resolution Radiometer (AVHRR) NASA and ORBIMAGE, Inc., Sea-viewing Wide field-of-view Sensor (SeaWiFS) Daedalus, Inc., Aircraft Multispectral Scanner (AMS) NASA Airborne Terrestrial Applications Sensor (ATLAS) === Multispectral imaging using linear arrays === SPOT 1, 2, and 3 High Resolution Visible (HRV) sensors and Spot 4 and 5 High Resolution Visible Infrared (HRVIR) and vegetation sensor Indian Remote Sensing System (IRS) Linear Imaging Self-scanning Sensor (LISS) Space Imaging, Inc. (IKONOS) Digital Globe, Inc. (QuickBird) ORBIMAGE, Inc. (OrbView-3) ImageSat International, Inc. (EROS A1) NASA Terra Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) NASA Terra Multiangle Imaging Spectroradiometer (MISR) === Imaging spectrometry using linear and area arrays === NASA Jet Propulsion Laboratory Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) Compact Airborne Spectrographic Imager 3 (CASI 3) NASA Terra Moderate Resolution Imaging Spectrometer (MODIS) NASA Earth Observer (EO-1) Advanced Land Imager (ALI), Hyperion, and LEISA Atmospheric Corrector (LAC) === Satellite analog and digital photographic systems === Russian SPIN-2 TK-350, and KVR-1000 NASA Space Shuttle and International Space Station Imagery == Multispectral classification methods == A variety of methods can be used for the multispectral classification of images: Algorithms based on parametric and nonparametric statistics that use ratio-and interval-scaled data and nonmetric methods that can also incorporate nominal scale data (Duda et al., 2001), Supervised or unsupervised classification logic, Hard or soft (fuzzy) set classification logic to create hard or fuzzy thematic output products, Per-pixel or object-oriented classification logic, and Hybrid approaches == Supervised classification == In this classification method, the identity and location of some of the land-cover types are obtained beforehand from a combination of fieldwork, interpretation of aerial photography, map analysis, and personal experience. The analyst would locate sites that have similar characteristics to the known land-cover types. These areas are known as training sites because the known characteristics of these sites are used to train the classification algorithm for eventual land-cover mapping of the remainder of the image. Multivariate statistical parameters (means, standard deviations, covariance matrices, correlation matrices, etc.) are calculated for each training site. All pixels inside and outside of the training sites are evaluated and allocated to the class with the more similar characteristics. === Classification scheme === The first step in the supervised classification method is to identify the land-cover and land-use classes to be used. Land-cover refers to the type of material present on the site (e.g. water, crops, forest, wet land, asphalt, and concrete). Land-use refers to the modifications made by people to the land cover (e.g. agriculture, commerce, settlement). All classes should be selected and defined carefully to properly classify remotely sensed data into the correct land-use and/or land-cover information. To achieve this purpose, it is necessary to use a classification system that contains taxonomically correct definitions of classes. If a hard classification is desired, the following classes should be used: Mutually exclusive: there is not any taxonomic overlap of any classes (i.e., rain forest and evergreen forest are distinct classes). Exhaustive: all land-covers in the area have been included. Hierarchical: sub-level classes (e.g., single-family residential, multiple-family residential) are created, allowing that these classes can be included in a higher category (e.g., residential). Some examples of hard classification schemes are: American Planning Association Land-Based Classification System United States Geological Survey Land-use/Land-cover Classification System for Use with Remote Sensor Data U.S. Department of the Interior Fish and Wildlife Service U.S. National Vegetation and Classification System International Geosphere-Biosphere Program IGBP Land Cover Classification System === Training sites === Once the classification scheme is adopted, the image analyst may select training sites in the image that are representative of the land-cover or land-use of interest. If the environment where the data was collected is relatively homogeneous, the training data can be used. If different conditions are found in the site, it would not be possible to extend the remote sensing training data to the site. To solve this problem, a geographical stratification should be done during the preliminary stages of the project. All differences should be recorded (e.g. soil type, water turbidity, crop species, etc.). These differences should be recorded on the imagery and the selection training sites made based on the geographical stratification of this data. The final classification map would be a composite of the individual stratum classifications. After the data are organized in different training sites, a measurement vector is created. This vector would contain the brightness values for each pixel in each band in each training class. The mean, standard deviation, variance-covariance matrix, and correlation matrix are calculated from the measurement vectors. Once the statistics from each training site are determined, the most effective bands for each class should be selected. The objective of this discrimination is to eliminate the bands that can provide redundant information. Graphical and statistical methods can be used to achieve this objective. Some of the graphic methods are: Bar graph spectral plots Cospectral mean vector plots Feature space plots Cospectral parallelepiped or ellipse plots === Classification algorithm === The last step in supervised classification is selecting an appropriate algorithm. The choice of a specific algorithm depends on the input data and the desired output. Parametric algorithms are based on the fact that the data is normally distributed. If the data is not normally distributed, nonparametric algorithms should be used. The more common nonparametric algorithms are: One-dimensional density slicing Parallelipiped Minimum distance Nearest-neighbor Expert system analysis Convolutional neural network == Unsupervised classification == Unsupervised classification (also known as clustering) is a method of partitioning remote sensor image data in multispectral feature space and extracting land-cover information. Unsupervised classification require less input information from the analyst compared to supervised classification because clustering does not require training data. This process consists in a series of numerical operations to search for the spectral properties of pixels. From this process, a map with m spectral classes is obtained. Using the map, the analyst tries to assign or transform the spectral classes into thematic information of interest (i.e. forest, agriculture, urban). This process may not be easy because some spectral clusters represent mixed classes of surface materials and may not be useful. The analyst has to understand the spectral characteristics of the terrain to be able to label clusters as a specific information class. There are hundreds of clustering algorithms. Two of the most conceptually simple algorithms are the chain method and the ISODATA method. === Chain method === The algorithm used in this method operates in a two-pass mode (it passes through the multispectral dataset two times. In the first pass, the program reads through the dataset and sequentially builds clusters (groups of p

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  Canonical correspondence analysis

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

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  Microsoft Fresh Paint

  Fresh Paint is a painting app developed by Microsoft and released on May 25, 2012. == History == Fresh Paint originated from a Microsoft Research project known as Project Gustav, an endeavor to reproduce the behavior of physical oil paint on a digital medium. To push the boundaries of simulating oil on a digital medium, the research team created a physics model that precisely replicated on a screen what would happen in the real world if you combined oil, a surface and a tool such as a paint brush. Two publications, Detail-Preserving Paint Modeling for 3D Brushes and Simple Data-Driven Modeling of Brushes, were released as a result of the team’s findings. After a variety of internal testing Project, Gustav was codenamed Digital Art. Partnering with The Museum of Modern Art, Digital Art was tested for a year by 60,000 people. With feedback culled from MoMA, developers expanded the existing physics model, experimenting with how real oil paint blended and reacted to the texture of a canvas. After final adjustments were made, Digital Art was rebranded as Fresh Paint. It was released to the public on 25 May 2012.

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  Stochastic variance reduction

  (Stochastic) variance reduction is an algorithmic approach to minimizing functions that can be decomposed into finite sums. By exploiting the finite sum structure, variance reduction techniques are able to achieve convergence rates that are impossible to achieve with methods that treat the objective as an infinite sum, as in the classical Stochastic approximation setting. Variance reduction approaches are widely used for training machine learning models such as logistic regression and support vector machines as these problems have finite-sum structure and uniform conditioning that make them ideal candidates for variance reduction. == Finite sum objectives == A function f {\displaystyle f} is considered to have finite sum structure if it can be decomposed into a summation or average: f ( x ) = 1 n ∑ i = 1 n f i ( x ) , {\displaystyle f(x)={\frac {1}{n}}\sum _{i=1}^{n}f_{i}(x),} where the function value and derivative of each f i {\displaystyle f_{i}} can be queried independently. Although variance reduction methods can be applied for any positive n {\displaystyle n} and any f i {\displaystyle f_{i}} structure, their favorable theoretical and practical properties arise when n {\displaystyle n} is large compared to the condition number of each f i {\displaystyle f_{i}} , and when the f i {\displaystyle f_{i}} have similar (but not necessarily identical) Lipschitz smoothness and strong convexity constants. The finite sum structure should be contrasted with the stochastic approximation setting which deals with functions of the form f ( θ ) = E ξ ⁡ [ F ( θ , ξ ) ] {\textstyle f(\theta )=\operatorname {E} _{\xi }[F(\theta ,\xi )]} which is the expected value of a function depending on a random variable ξ {\textstyle \xi } . Any finite sum problem can be optimized using a stochastic approximation algorithm by using F ( ⋅ , ξ ) = f ξ {\displaystyle F(\cdot ,\xi )=f_{\xi }} . == Rapid Convergence == Stochastic variance reduced methods without acceleration are able to find a minima of f {\displaystyle f} within accuracy ϵ > {\displaystyle \epsilon >} , i.e. f ( x ) − f ( x ∗ ) ≤ ϵ {\displaystyle f(x)-f(x_{})\leq \epsilon } in a number of steps of the order: O ( ( L μ + n ) log ⁡ ( 1 ϵ ) ) . {\displaystyle O\left(\left({\frac {L}{\mu }}+n\right)\log \left({\frac {1}{\epsilon }}\right)\right).} The number of steps depends only logarithmically on the level of accuracy required, in contrast to the stochastic approximation framework, where the number of steps O ( L / ( μ ϵ ) ) {\displaystyle O{\bigl (}L/(\mu \epsilon ){\bigr )}} required grows proportionally to the accuracy required. Stochastic variance reduction methods converge almost as fast as the gradient descent method's O ( ( L / μ ) log ⁡ ( 1 / ϵ ) ) {\displaystyle O{\bigl (}(L/\mu )\log(1/\epsilon ){\bigr )}} rate, despite using only a stochastic gradient, at a 1 / n {\displaystyle 1/n} lower cost than gradient descent. Accelerated methods in the stochastic variance reduction framework achieve even faster convergence rates, requiring only O ( ( n L μ + n ) log ⁡ ( 1 ϵ ) ) {\displaystyle O\left(\left({\sqrt {\frac {nL}{\mu }}}+n\right)\log \left({\frac {1}{\epsilon }}\right)\right)} steps to reach ϵ {\displaystyle \epsilon } accuracy, potentially n {\displaystyle {\sqrt {n}}} faster than non-accelerated methods. Lower complexity bounds. for the finite sum class establish that this rate is the fastest possible for smooth strongly convex problems. == Approaches == Variance reduction approaches fall within four main categories: table averaging methods, full-gradient snapshot methods, recursive estimator methods (e.g., SARAH), and dual methods. Each category contains methods designed for dealing with convex, non-smooth, and non-convex problems, each differing in hyper-parameter settings and other algorithmic details. === SAGA === In the SAGA method, the prototypical table averaging approach, a table of size n {\displaystyle n} is maintained that contains the last gradient witnessed for each f i {\displaystyle f_{i}} term, which we denote g i {\displaystyle g_{i}} . At each step, an index i {\displaystyle i} is sampled, and a new gradient ∇ f i ( x k ) {\displaystyle \nabla f_{i}(x_{k})} is computed. The iterate x k {\displaystyle x_{k}} is updated with: x k + 1 = x k − γ [ ∇ f i ( x k ) − g i + 1 n ∑ i = 1 n g i ] , {\displaystyle x_{k+1}=x_{k}-\gamma \left[\nabla f_{i}(x_{k})-g_{i}+{\frac {1}{n}}\sum _{i=1}^{n}g_{i}\right],} and afterwards table entry i {\displaystyle i} is updated with g i = ∇ f i ( x k ) {\displaystyle g_{i}=\nabla f_{i}(x_{k})} . SAGA is among the most popular of the variance reduction methods due to its simplicity, easily adaptable theory, and excellent performance. It is the successor of the SAG method, improving on its flexibility and performance. === SVRG === The stochastic variance reduced gradient method (SVRG), the prototypical snapshot method, uses a similar update except instead of using the average of a table it instead uses a full-gradient that is reevaluated at a snapshot point x ~ {\displaystyle {\tilde {x}}} at regular intervals of m ≥ n {\displaystyle m\geq n} iterations. The update becomes: x k + 1 = x k − γ [ ∇ f i ( x k ) − ∇ f i ( x ~ ) + ∇ f ( x ~ ) ] , {\displaystyle x_{k+1}=x_{k}-\gamma [\nabla f_{i}(x_{k})-\nabla f_{i}({\tilde {x}})+\nabla f({\tilde {x}})],} This approach requires two stochastic gradient evaluations per step, one to compute ∇ f i ( x k ) {\displaystyle \nabla f_{i}(x_{k})} and one to compute ∇ f i ( x ~ ) , {\displaystyle \nabla f_{i}({\tilde {x}}),} where-as table averaging approaches need only one. Despite the high computational cost, SVRG is popular as its simple convergence theory is highly adaptable to new optimization settings. It also has lower storage requirements than tabular averaging approaches, which make it applicable in many settings where tabular methods can not be used. === SARAH === The SARAH (stochastic recursive gradient) method maintains a recursive estimator of the gradient rather than storing a table of past gradients (as in SAGA) or computing periodic full-gradient snapshots (as in SVRG). At the start of an inner loop, a full gradient is computed at a reference point x ~ {\displaystyle {\tilde {x}}} : v 0 = ∇ f ( x ~ ) {\displaystyle v_{0}=\nabla f({\tilde {x}})} . For inner iterations, with a sampled index i k {\displaystyle i_{k}} , the gradient estimator and iterate are updated by: v k = ∇ f i k ( x k ) − ∇ f i k ( x k − 1 ) + v k − 1 , x k + 1 = x k − γ v k . {\displaystyle v_{k}=\nabla f_{i_{k}}(x_{k})-\nabla f_{i_{k}}(x_{k-1})+v_{k-1},\qquad x_{k+1}=x_{k}-\gamma v_{k}.} This recursion requires two component-gradient evaluations per step ∇ f i k ( x k ) {\displaystyle \nabla f_{i_{k}}(x_{k})} and ∇ f i k ( x k − 1 ) {\displaystyle \nabla f_{i_{k}}(x_{k-1})} but does not need to store per-sample gradients, resulting in lower memory cost than table-averaging methods. SARAH admits linear convergence for strongly convex functions and has been extended to more general nonconvex and composite problems. === SDCA === Exploiting the dual representation of the objective leads to another variance reduction approach that is particularly suited to finite-sums where each term has a structure that makes computing the convex conjugate f i ∗ , {\displaystyle f_{i}^{},} or its proximal operator tractable. The standard SDCA method considers finite sums that have additional structure compared to generic finite sum setting: f ( x ) = 1 n ∑ i = 1 n f i ( x T v i ) + λ 2 ‖ x ‖ 2 , {\displaystyle f(x)={\frac {1}{n}}\sum _{i=1}^{n}f_{i}(x^{T}v_{i})+{\frac {\lambda }{2}}\|x\|^{2},} where each f i {\displaystyle f_{i}} is 1 dimensional and each v i {\displaystyle v_{i}} is a data point associated with f i {\displaystyle f_{i}} . SDCA solves the dual problem: max α ∈ R n − 1 n ∑ i = 1 n f i ∗ ( − α i ) − λ 2 ‖ 1 λ n ∑ i = 1 n α i v i ‖ 2 , {\displaystyle \max _{\alpha \in \mathbb {R} ^{n}}-{\frac {1}{n}}\sum _{i=1}^{n}f_{i}^{}(-\alpha _{i})-{\frac {\lambda }{2}}\left\|{\frac {1}{\lambda n}}\sum _{i=1}^{n}\alpha _{i}v_{i}\right\|^{2},} by a stochastic coordinate ascent procedure, where at each step the objective is optimized with respect to a randomly chosen coordinate α i {\displaystyle \alpha _{i}} , leaving all other coordinates the same. An approximate primal solution x {\displaystyle x} can be recovered from the α {\displaystyle \alpha } values: x = 1 λ n ∑ i = 1 n α i v i {\displaystyle x={\frac {1}{\lambda n}}\sum _{i=1}^{n}\alpha _{i}v_{i}} . This method obtains similar theoretical rates of convergence to other stochastic variance reduced methods, while avoiding the need to specify a step-size parameter. It is fast in practice when λ {\displaystyle \lambda } is large, but significantly slower than the other approaches when λ {\displaystyle \lambda } is small. == Accelerated approaches == Accelerated variance reduction methods are built upon the standard methods above. The earliest approaches make use of proximal operators t

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  Fitness function

  A fitness function is a particular type of objective or cost function that is used to summarize, as a single figure of merit, how close a given candidate solution is to achieving the set aims. It is an important component of evolutionary algorithms (EA), such as genetic programming, evolution strategies or genetic algorithms. 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. For this purpose, many candidate solutions are generated, which are evaluated using a fitness function in order to guide the evolutionary development towards the desired goal. Similar quality functions are also used in other metaheuristics, such as ant colony optimization or particle swarm optimization. In the field of EAs, each candidate solution, also called an individual, is commonly represented as a string of numbers (referred to as a chromosome). After each round of testing or simulation the idea is to delete the n worst individuals, and to breed n new ones from the best solutions. Each individual must therefore to be assigned a quality number indicating how close it has come to the overall specification, and this is generated by applying the fitness function to the test or simulation results obtained from that candidate solution. Two main classes of fitness functions exist: one where the fitness function does not change, as in optimizing a fixed function or testing with a fixed set of test cases; and one where the fitness function is mutable, as in niche differentiation or co-evolving the set of test cases. Another way of looking at fitness functions is in terms of a fitness landscape, which shows the fitness for each possible chromosome. In the following, it is assumed that the fitness is determined based on an evaluation that remains unchanged during an optimization run. A fitness function does not necessarily have to be able to calculate an absolute value, as it is sometimes sufficient to compare candidates in order to select the better one. A relative indication of fitness (candidate a is better than b) is sufficient in some cases, such as tournament selection or Pareto optimization. == Requirements of evaluation and fitness function == The quality of the evaluation and calculation of a fitness function is fundamental to the success of an EA optimisation. It implements Darwin's principle of "survival of the fittest". Without fitness-based selection mechanisms for mate selection and offspring acceptance, EA search would be blind and hardly distinguishable from the Monte Carlo method. When setting up a fitness function, one must always be aware that it is about more than just describing the desired target state. Rather, the evolutionary search on the way to the optimum should also be supported as much as possible (see also section on auxiliary objectives), if and insofar as this is not already done by the fitness function alone. If the fitness function is designed badly, the algorithm will either converge on an inappropriate solution, or will have difficulty converging at all. Definition of the fitness function is not straightforward in many cases and often is performed iteratively if the fittest solutions produced by an EA is not what is desired. Interactive genetic algorithms address this difficulty by outsourcing evaluation to external agents which are normally humans. == Computational efficiency == The fitness function should not only closely align with the designer's goal, but also be computationally efficient. Execution speed is crucial, as a typical evolutionary algorithm must be iterated many times in order to produce a usable result for a non-trivial problem. Fitness approximation may be appropriate, especially in the following cases: Fitness computation time of a single solution is extremely high Precise model for fitness computation is missing The fitness function is uncertain or noisy. Alternatively or also in addition to the fitness approximation, the fitness calculations can also be distributed to a parallel computer in order to reduce the execution times. Depending on the population model of the EA used, both the EA itself and the fitness calculations of all offspring of one generation can be executed in parallel. == Multi-objective optimization == Practical applications usually aim at optimizing multiple and at least partially conflicting objectives. Two fundamentally different approaches are often used for this purpose, Pareto optimization and optimization based on fitness calculated using the weighted sum. === Weighted sum and penalty functions === When optimizing with the weighted sum, the single values of the O {\displaystyle O} objectives are first normalized so that they can be compared. This can be done with the help of costs or by specifying target values and determining the current value as the degree of fulfillment. Costs or degrees of fulfillment can then be compared with each other and, if required, can also be mapped to a uniform fitness scale. Without loss of generality, fitness is assumed to represent a value to be maximized. Each objective o i {\displaystyle o_{i}} is assigned a weight w i {\displaystyle w_{i}} in the form of a percentage value so that the overall raw fitness f r a w {\displaystyle f_{raw}} can be calculated as a weighted sum: f r a w = ∑ i = 1 O o i ⋅ w i w i t h ∑ i = 1 O w i = 1 {\displaystyle f_{raw}=\sum _{i=1}^{O}{o_{i}\cdot w_{i}}\quad {\mathsf {with}}\quad \sum _{i=1}^{O}{w_{i}}=1} A violation of R {\displaystyle R} restrictions r j {\displaystyle r_{j}} can be included in the fitness determined in this way in the form of penalty functions. For this purpose, a function p f j ( r j ) {\displaystyle pf_{j}(r_{j})} can be defined for each restriction which returns a value between 0 {\displaystyle 0} and 1 {\displaystyle 1} depending on the degree of violation, with the result being 1 {\displaystyle 1} if there is no violation. The previously determined raw fitness is multiplied by the penalty function(s) and the result is then the final fitness f f i n a l {\displaystyle f_{final}} : f f i n a l = f r a w ⋅ ∏ j = 1 R p f j ( r j ) = ∑ i = 1 O ( o i ⋅ w i ) ⋅ ∏ j = 1 R p f j ( r j ) {\displaystyle f_{final}=f_{raw}\cdot \prod _{j=1}^{R}{pf_{j}(r_{j})}=\sum _{i=1}^{O}{(o_{i}\cdot w_{i})}\cdot \prod _{j=1}^{R}{pf_{j}(r_{j})}} This approach is simple and has the advantage of being able to combine any number of objectives and restrictions. The disadvantage is that different objectives can compensate each other and that the weights have to be defined before the optimization. This means that the compromise lines must be defined before optimization, which is why optimization with the weighted sum is also referred to as the a priori method. In addition, certain solutions may not be obtained, see the section on the comparison of both types of optimization. === Pareto optimization === A solution is called Pareto-optimal if the improvement of one objective is only possible with a deterioration of at least one other objective. The set of all Pareto-optimal solutions, also called Pareto set, represents the set of all optimal compromises between the objectives. The figure below on the right shows an example of the Pareto set of two objectives f 1 {\displaystyle f_{1}} and f 2 {\displaystyle f_{2}} to be maximized. The elements of the set form the Pareto front (green line). From this set, a human decision maker must subsequently select the desired compromise solution. Constraints are included in Pareto optimization in that solutions without constraint violations are per se better than those with violations. If two solutions to be compared each have constraint violations, the respective extent of the violations decides. It was recognized early on that EAs with their simultaneously considered solution set are well suited to finding solutions in one run that cover the Pareto front sufficiently well. They are therefore well suited as a-posteriori methods for multi-objective optimization, in which the final decision is made by a human decision maker after optimization and determination of the Pareto front. Besides the SPEA2, the NSGA-II and NSGA-III have established themselves as standard methods. The advantage of Pareto optimization is that, in contrast to the weighted sum, it provides all alternatives that are equivalent in terms of the objectives as an overall solution. The disadvantage is that a visualization of the alternatives becomes problematic or even impossible from four objectives on. Furthermore, the effort increases exponentially with the number of objectives. If there are more than three or four objectives, some have to be combined using the weighted sum or other aggregation methods. === Comparison of both types of assessment === With the help of the weighted sum, the total Pareto front can be obtained by a suitable choice of weights, provided that it is convex

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  ID3 algorithm

  In decision tree learning, ID3 (Iterative Dichotomiser 3) is a greedy algorithm invented by Ross Quinlan used to generate a decision tree from a dataset. ID3 is the precursor to the C4.5 algorithm. The 3 in the name is meant to signify that this was Quinlan's third attempt at a model based on entropy-based splitting, and the term dichotimser is a misnomer as it implies a binary split, but the ID3 algorithm can split on multi-valued attributes. == Algorithm == The ID3 algorithm begins with the original set S {\displaystyle S} as the root node. On each iteration of the algorithm, it iterates through every unused attribute of the set S {\displaystyle S} and calculates the entropy H ( S ) {\displaystyle \mathrm {H} {(S)}} or the information gain I G ( S ) {\displaystyle IG(S)} of that attribute. It then selects the attribute which has the smallest entropy (or largest information gain) value. The set S {\displaystyle S} is then split or partitioned by the selected attribute to produce subsets of the data. (For example, a node can be split into child nodes based upon the subsets of the population whose ages are less than 50, between 50 and 100, and greater than 100.) The algorithm continues to recurse on each subset, considering only attributes never selected before. Recursion on a subset may stop in one of these cases: every element in the subset belongs to the same class; in which case the node is turned into a leaf node and labelled with the class of the examples. there are no more attributes to be selected, but the examples still do not belong to the same class. In this case, the node is made a leaf node and labelled with the most common class of the examples in the subset. there are no examples in the subset, which happens when no example in the parent set was found to match a specific value of the selected attribute. An example could be the absence of a person among the population with age over 100 years. Then a leaf node is created and labelled with the most common class of the examples in the parent node's set. Throughout the algorithm, the decision tree is constructed with each non-terminal node (internal node) representing the selected attribute on which the data was split, and terminal nodes (leaf nodes) representing the class label of the final subset of this branch. === Summary === Calculate the entropy of every attribute a {\displaystyle a} of the data set S {\displaystyle S} . Partition ("split") the set S {\displaystyle S} into subsets using the attribute for which the resulting entropy after splitting is minimized; or, equivalently, information gain is maximum. Make a decision tree node containing that attribute. Recurse on subsets using the remaining attributes. === Properties === ID3 does not guarantee an optimal solution. It can converge upon local optima. It uses a greedy strategy by selecting the locally best attribute to split the dataset on each iteration. The algorithm's optimality can be improved by using backtracking during the search for the optimal decision tree at the cost of possibly taking longer. ID3 can overfit the training data. To avoid overfitting, smaller decision trees should be preferred over larger ones. This algorithm usually produces small trees, but it does not always produce the smallest possible decision tree. ID3 is harder to use on continuous data than on factored data (factored data has a discrete number of possible values, thus reducing the possible branch points). If the values of any given attribute are continuous, then there are many more places to split the data on this attribute, and searching for the best value to split by can be time-consuming. === Usage === The ID3 algorithm is used by training on a data set S {\displaystyle S} to produce a decision tree which is stored in memory. At runtime, this decision tree is used to classify new test cases (feature vectors) by traversing the decision tree using the features of the datum to arrive at a leaf node. == The ID3 metrics == === Entropy === Entropy H ( S ) {\displaystyle \mathrm {H} {(S)}} is a measure of the amount of uncertainty in the (data) set S {\displaystyle S} (i.e. entropy characterizes the (data) set S {\displaystyle S} ). H ( S ) = ∑ x ∈ X − p ( x ) log 2 ⁡ p ( x ) {\displaystyle \mathrm {H} {(S)}=\sum _{x\in X}{-p(x)\log _{2}p(x)}} Where, S {\displaystyle S} – The current dataset for which entropy is being calculated This changes at each step of the ID3 algorithm, either to a subset of the previous set in the case of splitting on an attribute or to a "sibling" partition of the parent in case the recursion terminated previously. X {\displaystyle X} – The set of classes in S {\displaystyle S} p ( x ) {\displaystyle p(x)} – The proportion of the number of elements in class x {\displaystyle x} to the number of elements in set S {\displaystyle S} When H ( S ) = 0 {\displaystyle \mathrm {H} {(S)}=0} , the set S {\displaystyle S} is perfectly classified (i.e. all elements in S {\displaystyle S} are of the same class). In ID3, entropy is calculated for each remaining attribute. The attribute with the smallest entropy is used to split the set S {\displaystyle S} on this iteration. Entropy in information theory measures how much information is expected to be gained upon measuring a random variable; as such, it can also be used to quantify the amount to which the distribution of the quantity's values is unknown. A constant quantity has zero entropy, as its distribution is perfectly known. In contrast, a uniformly distributed random variable (discretely or continuously uniform) maximizes entropy. Therefore, the greater the entropy at a node, the less information is known about the classification of data at this stage of the tree; and therefore, the greater the potential to improve the classification here. As such, ID3 is a greedy heuristic performing a best-first search for locally optimal entropy values. Its accuracy can be improved by preprocessing the data. === Information gain === Information gain I G ( A ) {\displaystyle IG(A)} is the measure of the difference in entropy from before to after the set S {\displaystyle S} is split on an attribute A {\displaystyle A} . In other words, how much uncertainty in S {\displaystyle S} was reduced after splitting set S {\displaystyle S} on attribute A {\displaystyle A} . I G ( S , A ) = H ( S ) − ∑ t ∈ T p ( t ) H ( t ) = H ( S ) − H ( S | A ) . {\displaystyle IG(S,A)=\mathrm {H} {(S)}-\sum _{t\in T}p(t)\mathrm {H} {(t)}=\mathrm {H} {(S)}-\mathrm {H} {(S|A)}.} Where, H ( S ) {\displaystyle \mathrm {H} (S)} – Entropy of set S {\displaystyle S} T {\displaystyle T} – The subsets created from splitting set S {\displaystyle S} by attribute A {\displaystyle A} such that S = ⋃ t ∈ T t {\displaystyle S=\bigcup _{t\in T}t} p ( t ) {\displaystyle p(t)} – The proportion of the number of elements in t {\displaystyle t} to the number of elements in set S {\displaystyle S} H ( t ) {\displaystyle \mathrm {H} (t)} – Entropy of subset t {\displaystyle t} In ID3, information gain can be calculated (instead of entropy) for each remaining attribute. The attribute with the largest information gain is used to split the set S {\displaystyle S} on this iteration.

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  Clapper (service)

  Clapper is an American short-form video-hosting service headquartered in Dallas, Texas. It was founded in 2020 by Edison Chen as an alternative for TikTok for mature audiences. The app is functionally similar to TikTok and includes tipping and e-commerce features. Following an influx of far-right content in early 2021, Clapper strengthened its moderation practices. It achieved 2 million monthly active users by 2023, and the number of downloads increased after a U.S. bill that would potentially ban TikTok in the country was signed in 2024. == History == With its offices in Dallas, Texas, Clapper was founded in July 2020 by Chinese-American entrepreneur Edison Chen. Chen considered that most online platforms, such as TikTok, were being targeted to young generations, such as Generation Z. He then concepted Clapper as a service with short-form content for mature audiences among Generation X and millennials, while not intending to compete directly with TikTok. Clapper averaged fewer than ten thousand daily active users during 2020, reaching 500 thousand downloads in the next year. Initially without paying for external advertising, the company raised about $3 million during a 2021 seed funding round. In 2023, the app reportedly reached about 300 to 400 thousand daily active users and 2 million monthly active users. The average user was between the ages of 35 and 55. Following the April 2024 signing of the Protecting Americans from Foreign Adversary Controlled Applications Act, which would potentially enact a ban on TikTok in the U.S. in January 2025, Clapper averaged 200 thousand weekly downloads. In 2025, before the day scheduled for the ban (January 19), TikTok users migrated to other apps. As a result, Clapper received 1.4 million new downloads in a week preceding the date. It was listed as the third most-downloaded free app on Apple's App Store on January 14, behind Xiaohongshu and Lemon8, and the term "TikTok refugee" became a trending term. == Features == Clapper presents similarities with TikTok in its layout, including "Following" and "For You" tabs with videos up to three minutes long that can be liked, commented on or shared. A "Clapback" feature allows users to create responses to videos from others. Users can create livestreams and chat rooms in the app. Users can tip Clapper creators through its Clapper Fam monetization feature, in place of in-app advertisements. The Clapper Shop allows for e-commerce between users. The service had distributed $10 million to its users in total by 2023, according to Clapper CEO Chen. == Content == Clapper includes a policy requiring users to be at least 17 years of age, although Clapper CEO Chen described that "there is no adult content" on the platform. Lindsay Dodgson of Business Insider described the content as generally outdated and "reminiscent of 'getting owned' compilations of the earlier internet." The Washington Post's Tatum Hunter characterized Clapper as including sexual or engagement baiting content more prevalently than TikTok. === Moderation === Clapper's team, which had fifteen employees in early 2021, initially stated it would not moderate content as strictly as TikTok and would mostly rely on user reports. Following that year's January 6 United States Capitol attack, far-right conservative videos promoting QAnon and anti-vaccine conspiracy theories appeared on Clapper's "For You" page to a substantial degree for weeks. The videos were made in protest against decisions by platforms, particularly TikTok, to ban such content. Clapper's team stated in January 10 that its rules prohibiting incitements to violence would be strictly enforced. By February, videos and accounts promoting the conspiracy theories had been removed, and QAnon-related content was banned permanently. Clapper's team hired more content auditors and implemented moderation by artificial intelligence for further community guideline violations.

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  Canonical correspondence analysis

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

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  Causal Markov condition

  The Causal Markov (CM) condition states that, conditional on the set of all its direct causes, a node is independent of all variables which are not effects or direct causes of that node. In the event that the structure of a Bayesian network accurately depicts causality, the two conditions are equivalent. This is related to the Markov condition, an assumption made in Bayesian probability theory, that every node in a Bayesian network is conditionally independent of its nondescendants, given its parents. Stated loosely, it is assumed that a node has no bearing on nodes which do not descend from it. In a DAG, this local Markov condition is equivalent to the global Markov condition, which states that d-separations in the graph also correspond to conditional independence relations. This also means that a node is conditionally independent of the entire network, given its Markov blanket. A network may accurately embody the Markov condition without depicting causality, in which case it should not be assumed to embody the causal Markov condition. == Motivation == Statisticians are enormously interested in the ways in which certain events and variables are connected. The precise notion of what constitutes a cause and effect is necessary to understand the connections between them. The central idea behind the philosophical study of probabilistic causation is that causes raise the probabilities of their effects, all else being equal. A deterministic interpretation of causation means that if A causes B, then A must always be followed by B. In this sense, smoking does not cause cancer because some smokers never develop cancer. On the other hand, a probabilistic interpretation simply means that causes raise the probability of their effects. In this sense, changes in meteorological readings associated with a storm do cause that storm, since they raise its probability. (However, simply looking at a barometer does not change the probability of the storm, for a more detailed analysis, see:). == Examples == In a simple view, releasing one's hand from a hammer causes the hammer to fall. However, doing so in outer space does not produce the same outcome, calling into question if releasing one's fingers from a hammer always causes it to fall. A causal graph could be created to acknowledge that both the presence of gravity and the release of the hammer contribute to its falling. However, it would be very surprising if the surface underneath the hammer affected its falling. This essentially states the Causal Markov Condition, that given the existence of gravity the release of the hammer, it will fall regardless of what is beneath it. == Implications == === Dependence and Causation === It follows from the definition that if X and Y are in V and are probabilistically dependent, then either X causes Y, Y causes X, or X and Y are both effects of some common cause Z in V. This definition was seminally introduced by Hans Reichenbach as the Common Cause Principle (CCP). === Screening === It once again follows from the definition that the parents of X screen X from other "indirect causes" of X (parents of Parents(X)) and other effects of Parents(X) which are not also effects of X.

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  Win–stay, lose–switch

  In psychology, game theory, statistics, and machine learning, win–stay, lose–switch (also win–stay, lose–shift or Pavlov, named after Ivan Pavlov) is a heuristic learning strategy used to model learning in decision situations. It was first invented as an improvement over randomization in bandit problems. It was later applied to the prisoner's dilemma in order to model the evolution of altruism. In most versions, it starts either with a cooperate, then proceeds as always, or starts with a "probe" of cooperate-defect-cooperate to determine the other player's strategy. A mutual cooperation is regarded as a win. The learning rule bases its decision only on the outcome of the previous play. Outcomes are divided into successes (wins) and failures (losses). If the play on the previous round resulted in a success, then the agent plays the same strategy on the next round. Alternatively, if the play resulted in a failure the agent switches to another action. A large-scale empirical study of players of the game rock, paper, scissors shows that a variation of this strategy is adopted by real-world players of the game, instead of the Nash equilibrium strategy of choosing entirely at random between the three options.

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  Gerrit (software)

  Gerrit ( GERR-it) is a free, web-based team code collaboration tool. Software developers in a team can review each other's modifications on their source code using a Web browser and approve or reject those changes. It integrates closely with Git, a distributed version control system. Gerrit is a fork of Rietveld, a code review tool for Subversion. Both are named after Dutch designer Gerrit Rietveld. == History == Originally written in Python like Rietveld, it is now written in Java (Java EE Servlet) with SQL since version 2 and a custom-made Git-based database (NoteDb) since version 3. In versions 2.0–2.16 Gerrit used Google Web Toolkit for its browser-based front-end. After being developed and used in parallel with GWT for versions 2.14–2.16, a new Polymer web UI replaced the GWT UI in version 3.0.

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  Recursive neural network

  A recursive neural network is a kind of deep neural network created by applying the same set of weights recursively over a structured input, to produce a structured prediction over variable-size input structures, or a scalar prediction on it, by traversing a given structure in topological order. These networks were first introduced to learn distributed representations of structure (such as logical terms), but have been successful in multiple applications, for instance in learning sequence and tree structures in natural language processing (mainly continuous representations of phrases and sentences based on word embeddings). == Architectures == === Basic === In the simplest architecture, nodes are combined into parents using a weight matrix (which is shared across the whole network) and a non-linearity such as the tanh {\displaystyle \tanh } hyperbolic function. If c 1 {\displaystyle c_{1}} and c 2 {\displaystyle c_{2}} are n {\displaystyle n} -dimensional vector representations of nodes, their parent will also be an n {\displaystyle n} -dimensional vector, defined as: p 1 , 2 = tanh ⁡ ( W [ c 1 ; c 2 ] ) {\displaystyle p_{1,2}=\tanh(W[c_{1};c_{2}])} where W {\displaystyle W} is a learned n × 2 n {\displaystyle n\times 2n} weight matrix. This architecture, with a few improvements, has been used for successfully parsing natural scenes, syntactic parsing of natural language sentences, and recursive autoencoding and generative modeling of 3D shape structures in the form of cuboid abstractions. === Recursive cascade correlation (RecCC) === RecCC is a constructive neural network approach to deal with tree domains with pioneering applications to chemistry and extension to directed acyclic graphs. === Unsupervised RNN === A framework for unsupervised RNN has been introduced in 2004. === Tensor === Recursive neural tensor networks use a single tensor-based composition function for all nodes in the tree. == Training == === Stochastic gradient descent === Typically, stochastic gradient descent (SGD) is used to train the network. The gradient is computed using backpropagation through structure (BPTS), a variant of backpropagation through time used for recurrent neural networks. == Properties == The universal approximation capability of RNNs over trees has been proved in literature. == Related models == === Recurrent neural networks === Recurrent neural networks are recursive artificial neural networks with a certain structure: that of a linear chain. Whereas recursive neural networks operate on any hierarchical structure, combining child representations into parent representations, recurrent neural networks operate on the linear progression of time, combining the previous time step and a hidden representation into the representation for the current time step. === Tree Echo State Networks === An efficient approach to implement recursive neural networks is given by the Tree Echo State Network within the reservoir computing paradigm. === Extension to graphs === Extensions to graphs include graph neural network (GNN), Neural Network for Graphs (NN4G), and more recently convolutional neural networks for graphs.

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  Automated Pain Recognition

  Automated Pain Recognition (APR) is a method for objectively measuring pain and at the same time represents an interdisciplinary research area that comprises elements of medicine, psychology, psychobiology, and computer science. The focus is on computer-aided objective recognition of pain, implemented on the basis of machine learning. Automated pain recognition allows for the valid, reliable detection and monitoring of pain in people who are unable to communicate verbally. The underlying machine learning processes are trained and validated in advance by means of unimodal or multimodal body signals. Signals used to detect pain may include facial expressions or gestures and may also be of a (psycho-)physiological or paralinguistic nature. To date, the focus has been on identifying pain intensity, but visionary efforts are also being made to recognize the quality, site, and temporal course of pain. However, the clinical implementation of this approach is a controversial topic in the field of pain research. Critics of automated pain recognition argue that pain diagnosis can only be performed subjectively by humans. == Background == Pain diagnosis under conditions where verbal reporting is restricted - such as in verbally and/or cognitively impaired people or in patients who are sedated or mechanically ventilated - is based on behavioral observations by trained professionals. However, all known observation procedures (e.g., Zurich Observation Pain Assessment (ZOPA)); Pain Assessment in Advanced Dementia Scale (PAINAD) require a great deal of specialist expertise. These procedures can be made more difficult by perception- and interpretation-related misjudgments on the part of the observer. With regard to the differences in design, methodology, evaluation sample, and conceptualization of the phenomenon of pain, it is difficult to compare the quality criteria of the various tools. Even if trained personnel could theoretically record pain intensity several times a day using observation instruments, it would not be possible to measure it every minute or second. In this respect, the goal of automated pain recognition is to use valid, robust pain response patterns that can be recorded multimodally for a temporally dynamic, high-resolution, automated pain intensity recognition system. == Procedure == For automated pain recognition, pain-relevant parameters are usually recorded using non-invasive sensor technology, which captures data on the (physical) responses of the person in pain. This can be achieved with camera technology that captures facial expressions, gestures, or posture, while audio sensors record paralinguistic features. (Psycho-)physiological information such as muscle tone and heart rate can be collected via biopotential sensors (electrodes). Pain recognition requires the extraction of meaningful characteristics or patterns from the data collected. This is achieved using machine learning techniques that are able to provide an assessment of the pain after training (learning), e.g., "no pain," "mild pain," or "severe pain." == Parameters == Although the phenomenon of pain comprises different components (sensory discriminative, affective (emotional), cognitive, vegetative, and (psycho-)motor), automated pain recognition currently relies on the measurable parameters of pain responses. These can be divided roughly into the two main categories of "physiological responses" and "behavioral responses". === Physiological responses === In humans, pain almost always initiates autonomic nervous processes that are reflected measurably in various physiological signals. ==== Physiological signals ==== Measurements can include electrodermal activity (EDA, also skin conductance), electromyography (EMG), electrocardiogram (ECG), blood volume pulse (BVP), electroencephalogram (EEG), respiration, and body temperature, which are regulatory mechanisms of the sympathetic and parasympathetic systems. Physiological signals are mainly recorded using special non-invasive surface electrodes (for EDA, EMG, ECG, and EEG), a blood volume pulse sensor (BVP), a respiratory belt (respiration), and a thermal sensor (body temperature). Endocrinological and immunological parameters can also be recorded, but this requires measures that are somewhat invasive (e.g., blood sampling). === Behavioral responses === Behavioral responses to pain fulfil two functions: protection of the body (e.g., through protective reflexes) and external communication of the pain (e.g., as a cry for help). The responses are particularly evident in facial expressions, gestures, and paralinguistic features. ==== Facial expressions ==== Behavioral signals captured comprise facial expression patterns (expressive behavior), which are measured with the aid of video signals. Facial expression recognition is based on the everyday clinical observation that pain often manifests itself in the patient's facial expressions but that this is not necessarily always the case, since facial expressions can be inhibited through self-control. Despite the possibility that facial expressions may be influenced consciously, facial expression behavior represents an essential source of information for pain diagnosis and is thus also a source of information for automatic pain recognition. One advantage of video-based facial expression recognition is the contact-free measurement of the face, provided that it can be captured on video, which is not possible in every position (e.g., lying face down) or may be limited by bandages covering the face. Facial expression analysis relies on rapid, spontaneous, and temporary changes in neuromuscular activity that lead to visually detectable changes in the face. ==== Gestures ==== Gestures are also captured predominantly using non-contact camera technology. Motor pain responses vary and are strongly dependent on the type and cause of the pain. They range from abrupt protective reflexes (e.g., spontaneous retraction of extremities or doubling up) to agitation (pathological restlessness) and avoidance behavior (hesitant, cautious movements). ==== Paralinguistic features of language ==== Among other things, pain leads to nonverbal linguistic behavior that manifests itself in sounds such as sighing, gasping, moaning, whining, etc. Paralinguistic features are usually recorded using highly sensitive microphones. == Algorithms == After the recording, pre-processing (e.g., filtering), and extraction of relevant features, an optional information fusion can be performed. During this process, modalities from different signal sources are merged to generate new or more precise knowledge. The pain is classified using machine learning processes. The method chosen has a significant influence on the recognition rate and depends greatly on the quality and granularity of the underlying data. Similar to the field of affective computing, the following classifiers are currently being used: Support Vector Machine (SVM): The goal of an SVM is to find a clearly defined optimal hyperplane with the greatest minimal distance to two (or more) classes to be separated. The hyperplane acts as a decision function for classifying an unknown pattern. Random Forest (RF): RF is based on the composition of random, uncorrelated decision trees. An unknown pattern is judged individually by each tree and assigned to a class. The final classification of the patterns by the RF is then based on a majority decision. k-Nearest Neighbors (k-NN): The k-NN algorithm classifies an unknown object using the class label that most commonly classifies the k neighbors closest to it. Its neighbors are determined using a selected similarity measure (e.g., Euclidean distance, Jaccard coefficient, etc.). Artificial neural networks (ANNs): ANNs are inspired by biological neural networks and model their organizational principles and processes in a very simplified manner. Class patterns are learned by adjusting the weights of the individual neuronal connections. == Databases == In order to classify pain in a valid manner, it is necessary to create representative, reliable, and valid pain databases that are available to the machine learner for training. An ideal database would be sufficiently large and would consist of natural (not experimental), high-quality pain responses. However, natural responses are difficult to record and can only be obtained to a limited extent; in most cases they are characterized by suboptimal quality. The databases currently available therefore contain experimental or quasi-experimental pain responses, and each database is based on a different pain model. The following list shows a selection of the most relevant pain databases (last updated: April 2020): UNBC-McMaster Shoulder Pain BioVid Heat Pain EmoPain SenseEmotion X-ITE Pain

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