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Incomputer science,Scott encodingis a way to represent(recursive) data typesin thelambda calculus.Church encodingperforms a similar function. The data and operators form a mathematical structure which isembeddedin the lambda calculus.
Whereas Church encoding starts with representations of the basic data types, and bu... | https://en.wikipedia.org/wiki/Mogensen%E2%80%93Scott_encoding |
Inset theory, anordinal number, orordinal, is a generalization ofordinal numerals(first, second,nth, etc.) aimed to extendenumerationtoinfinite sets.[1]
A finite set can be enumerated by successively labeling each element with the leastnatural numberthat has not been previously used. To extend this process to variousi... | https://en.wikipedia.org/wiki/Ordinal_number#Von_Neumann_definition_of_ordinals |
Inmathematics, anantimatroidis aformal systemthat describes processes in which asetis built up by including elements one at a time, and in which an element, once available for inclusion, remains available until it is included.[1]Antimatroids are commonlyaxiomatized in two equivalent ways, either as aset systemmodeling ... | https://en.wikipedia.org/wiki/Antimatroid |
In mathematics,Coxeter matroidsare generalization ofmatroidsdepending on a choice of aCoxeter groupWand aparabolic subgroupP. Ordinary matroids correspond to the case whenPis a maximal parabolic subgroup of a symmetric groupW. They were introduced by Gelfand and Serganova (1987,1987b), who named them afterH. S. M. Cox... | https://en.wikipedia.org/wiki/Coxeter_matroid |
Incombinatorics, agreedoidis a type ofset system. It arises from the notion of thematroid, which was originally introduced byWhitneyin 1935 to studyplanar graphsand was later used byEdmondsto characterize a class of optimization problems that can be solved bygreedy algorithms. Around 1980,KorteandLovászintroduced the g... | https://en.wikipedia.org/wiki/Greedoid |
Anoriented matroidis amathematicalstructurethat abstracts the properties ofdirected graphs,vectorarrangements over ordered fields, andhyperplane arrangementsoverordered fields.[1]In comparison, an ordinary (i.e., non-oriented)matroidabstracts thedependenceproperties that are common both tographs, which are not necessar... | https://en.wikipedia.org/wiki/Oriented_matroid |
In mathematics, apolymatroidis apolytopeassociated with asubmodular function. The notion was introduced byJack Edmondsin 1970.[1]It is also a generalization of the notion of amatroid.
LetE{\displaystyle E}be a finitesetandf:2E→R≥0{\displaystyle f:2^{E}\rightarrow \mathbb {R} _{\geq 0}}a non-decreasingsubmodular functi... | https://en.wikipedia.org/wiki/Polymatroid |
Pregeometry, and in fullcombinatorial pregeometry, are essentially synonyms for "matroid". They were introduced byGian-Carlo Rotawith the intention of providing a less "ineffably cacophonous" alternative term. Also, the termcombinatorial geometry, sometimes abbreviated togeometry, was intended to replace "simple matro... | https://en.wikipedia.org/wiki/Pregeometry_(model_theory) |
Ingraph theory, amatchingin ahypergraphis a set ofhyperedges, in which every two hyperedges aredisjoint. It is an extension of the notion ofmatching in a graph.[1]: 466–470[2]
Recall that ahypergraphHis a pair(V,E), whereVis asetofverticesandEis a set ofsubsetsofVcalledhyperedges. Each hyperedge may contain one or mor... | https://en.wikipedia.org/wiki/Matching_in_hypergraphs |
Ingraph theory, afractional matchingis a generalization of amatchingin which, intuitively, each vertex may be broken into fractions that are matched to different neighbor vertices.
Given agraphG= (V,E), a fractional matching inGis a function that assigns, to each edgeeinE, a fractionf(e) in [0, 1], such that for every... | https://en.wikipedia.org/wiki/Fractional_matching |
Ingraph theory, theDulmage–Mendelsohn decompositionis a partition of the vertices of abipartite graphinto subsets, with the property that two adjacent vertices belong to the same subset if and only if they are paired with each other in aperfect matchingof the graph. It is named after A. L. Dulmage andNathan Mendelsohn,... | https://en.wikipedia.org/wiki/Dulmage%E2%80%93Mendelsohn_decomposition |
Ingraph theory, aproper edge coloringof agraphis an assignment of "colors" to the edges of the graph so that no two incident edges have the same color. For example, the figure to the right shows an edge coloring of a graph by the colors red, blue, and green. Edge colorings are one of several different types ofgraph co... | https://en.wikipedia.org/wiki/Edge_coloring |
Ingraph theory, a branch of mathematics, thematching preclusion numberof a graphG(denoted mp(G)) is the minimum number of edges whose deletion results in the elimination of allperfect matchingsor near-perfect matchings (matchings that cover all but one vertex in a graph with an odd number of vertices).[1]Matching precl... | https://en.wikipedia.org/wiki/Matching_preclusion |
In the mathematical discipline ofgraph theory, arainbow matchingin anedge-colored graphis amatchingin which all the edges have distinct colors.
Given an edge-colored graphG= (V,E), a rainbow matchingMinGis a set of pairwise non-adjacent edges, that is, no two edges share a common vertex, such that all the edges in the... | https://en.wikipedia.org/wiki/Rainbow_matching |
Ingraph theory, a branch of mathematics, askew-symmetric graphis adirected graphthat isisomorphicto its owntranspose graph, the graph formed by reversing all of its edges, under an isomorphism that is aninvolutionwithout anyfixed points. Skew-symmetric graphs are identical to thedouble covering graphsofbidirected grap... | https://en.wikipedia.org/wiki/Skew-symmetric_graph |
Inmathematics,economics, andcomputer science, thestable matching problem[1][2][3]is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element. A matching is abijectionfrom the elements of one set to the elements of the other set. A matching i... | https://en.wikipedia.org/wiki/Stable_matching |
Ingraph theory, anindependent set,stable set,cocliqueoranticliqueis a set ofverticesin agraph, no two of which are adjacent. That is, it is a setS{\displaystyle S}of vertices such that for every two vertices inS{\displaystyle S}, there is noedgeconnecting the two. Equivalently, each edge in the graph has at most one en... | https://en.wikipedia.org/wiki/Independent_vertex_set |
Inmathematics,economics, andcomputer science, thestable matching problem[1][2][3]is the problem of finding a stable matching between two equally sized sets of elements given an ordering of preferences for each element. A matching is abijectionfrom the elements of one set to the elements of the other set. A matching i... | https://en.wikipedia.org/wiki/Stable_marriage_problem |
In the context ofnetwork theory, acomplex networkis agraph(network) with non-trivialtopologicalfeatures—features that do not occur in simple networks such aslatticesorrandom graphsbut often occur in networks representing real systems. The study of complex networks is a young and active area of scientific research[1][2]... | https://en.wikipedia.org/wiki/Complex_network |
Graf(German pronunciation:[ɡʁaːf]ⓘ; feminine:Gräfin[ˈɡʁɛːfɪn]ⓘ) is a historicaltitleof theGerman nobilityand later also of theRussian nobility, usually translated as "count". Considered to be intermediate amongnoble ranks, the title is often treated as equivalent to the British title of "earl" (whose female version is ... | https://en.wikipedia.org/wiki/Graf |
Graffmay refer to: | https://en.wikipedia.org/wiki/Graff_(disambiguation) |
Agraph database(GDB) is adatabasethat usesgraph structuresforsemantic querieswithnodes,edges, and properties to represent and store data.[1]A key concept of the system is thegraph(or edge or relationship). The graph relates the data items in the store to a collection of nodes and edges, the edges representing the relat... | https://en.wikipedia.org/wiki/Graph_database |
Inlinguistics, agraphemeis the smallest functional unit of awriting system.[1]The wordgraphemeis derived fromAncient Greekgráphō('write'), and the suffix-emeby analogy withphonemeand otheremic units. The study of graphemes is calledgraphemics. The concept of graphemes is abstract and similar to the notion incomputingof... | https://en.wikipedia.org/wiki/Grapheme |
Graphemicsorgraphematicsis the linguistic study ofwriting systemsand their basic components, i.e.graphemes.
At the beginning of the development of this area of linguistics,Ignace Gelbcoined the termgrammatologyfor this discipline;[1]later some scholars suggested calling itgraphology[2]to matchphonology, but that name ... | https://en.wikipedia.org/wiki/Graphemics |
Graphicsare two-dimensional images.
Graphic(s)orThe Graphicmay also refer to: | https://en.wikipedia.org/wiki/Graphic_(disambiguation) |
The Englishsuffix-graphymeans a "field of study" or related to "writing" a book, and is an anglicization of the French-graphieinherited from the Latin-graphia, which is a transliterated direct borrowing from Greek. | https://en.wikipedia.org/wiki/-graphy |
This is a list of software to create any kind ofinformation graphics:
Vector graphicssoftware can be used for manual graphing or for editing the output of another program; see:
A few online editors using vector graphics for specific needs have been created.[citation needed]This kind of creativeinterfaceswork well tog... | https://en.wikipedia.org/wiki/List_of_information_graphics_software |
Statistical graphics, also known asstatistical graphical techniques, aregraphicsused in the field ofstatisticsfordata visualization.
Whereasstatisticsanddata analysisprocedures generally yield their output in numeric or tabular form, graphical techniques allow such results to be displayed in some sort of pictorial for... | https://en.wikipedia.org/wiki/Statistical_graphics |
Curve fitting[1][2]is the process of constructing acurve, ormathematical function, that has the best fit to a series ofdata points,[3]possibly subject to constraints.[4][5]Curve fitting can involve eitherinterpolation,[6][7]where an exact fit to the data is required, orsmoothing,[8][9]in which a "smooth" function is co... | https://en.wikipedia.org/wiki/Curve_fitting |
Instatistics,linear regressionis amodelthat estimates the relationship between ascalarresponse (dependent variable) and one or more explanatory variables (regressororindependent variable). A model with exactly one explanatory variable is asimple linear regression; a model with two or more explanatory variables is amult... | https://en.wikipedia.org/wiki/Line_regression |
Local regressionorlocal polynomial regression,[1]also known asmoving regression,[2]is a generalization of themoving averageandpolynomial regression.[3]Its most common methods, initially developed forscatterplot smoothing, areLOESS(locally estimated scatterplot smoothing) andLOWESS(locally weighted scatterplot smoothing... | https://en.wikipedia.org/wiki/Local_polynomial_regression |
Instatistical modeling(especiallyprocess modeling), polynomial functions and rational functions are sometimes used as an empirical technique forcurve fitting.
Apolynomial functionis one that has the form
wherenis a non-negativeintegerthat defines the degree of the polynomial. A polynomial with a degree of 0 is simply... | https://en.wikipedia.org/wiki/Polynomial_and_rational_function_modeling |
Innumerical analysis,polynomial interpolationis theinterpolationof a givendata setby thepolynomialof lowest possible degree that passes through the points in the dataset.
Given a set ofn+ 1data points(x0,y0),…,(xn,yn){\displaystyle (x_{0},y_{0}),\ldots ,(x_{n},y_{n})}, with no twoxj{\displaystyle x_{j}}the same, a pol... | https://en.wikipedia.org/wiki/Polynomial_interpolation |
In statistics,response surface methodology(RSM) explores the relationships between severalexplanatory variablesand one or moreresponse variables. RSM is an empirical model which employs the use of mathematical and statistical techniques to relate input variables, otherwise known as factors, to the response. RSM became ... | https://en.wikipedia.org/wiki/Response_surface_methodology |
Smoothing splinesare function estimates,f^(x){\displaystyle {\hat {f}}(x)}, obtained from a set of noisy observationsyi{\displaystyle y_{i}}of the targetf(xi){\displaystyle f(x_{i})}, in order to balance a measure ofgoodness of fitoff^(xi){\displaystyle {\hat {f}}(x_{i})}toyi{\displaystyle y_{i}}with a derivative based... | https://en.wikipedia.org/wiki/Smoothing_spline |
A variable is considereddependentif it depends on (or is hypothesized to depend on) anindependent variable. Dependent variables are studied under the supposition or demand that they depend, by some law or rule (e.g., by amathematical function), on the values of other variables. Independent variables, on the other hand,... | https://en.wikipedia.org/wiki/Covariate |
Instatistics,datatransformationis the application of adeterministicmathematicalfunctionto each point in adataset—that is, each data pointziis replaced with the transformed valueyi=f(zi), wherefis a function. Transforms are usually applied so that the data appear to more closely meet the assumptions of astatistical infe... | https://en.wikipedia.org/wiki/Data_transformation_(statistics) |
Inmachine learning(ML),feature learningorrepresentation learning[2]is a set of techniques that allow a system to automatically discover the representations needed forfeaturedetection or classification from raw data. This replaces manualfeature engineeringand allows a machine to both learn the features and use them to p... | https://en.wikipedia.org/wiki/Feature_learning |
Inmachine learning,feature hashing, also known as thehashing trick(by analogy to thekernel trick), is a fast and space-efficient way of vectorizingfeatures, i.e. turning arbitrary features into indices in a vector or matrix.[1][2]It works by applying ahash functionto the features and using their hash values as indices ... | https://en.wikipedia.org/wiki/Hashing_trick |
Instatistics,econometrics,epidemiologyand related disciplines, the method ofinstrumental variables(IV) is used to estimatecausal relationshipswhencontrolled experimentsare not feasible or when a treatment is not successfully delivered to every unit in a randomized experiment.[1]Intuitively, IVs are used when an explana... | https://en.wikipedia.org/wiki/Instrumental_variables_estimation |
Thesedatasetsare used inmachine learning (ML)research and have been cited inpeer-reviewedacademic journals. Datasets are an integral part of the field of machine learning. Major advances in this field can result from advances in learningalgorithms(such asdeep learning),computer hardware, and, less-intuitively, the avai... | https://en.wikipedia.org/wiki/List_of_datasets_for_machine_learning_research |
Scale co-occurrence matrix (SCM)is a method for imagefeature extractionwithinscale spaceafterwavelet transformation, proposed by Wu Jun and Zhao Zhongming (Institute of Remote Sensing Application,China). In practice, we first do discrete wavelet transformation for one gray image and get sub images with different scales... | https://en.wikipedia.org/wiki/Scale_co-occurrence_matrix |
Thespace mappingmethodology for modeling and design optimization ofengineering systemswas first discovered byJohn Bandlerin 1993. It uses relevant existing knowledge to speed up model generation and designoptimizationof a system. The knowledge is updated with new validation information from the system when available.
... | https://en.wikipedia.org/wiki/Space_mapping |
Automated machine learning(AutoML) is the process ofautomatingthe tasks of applyingmachine learningto real-world problems. It is the combination of automation and ML.[1]
AutoML potentially includes every stage from beginning with a raw dataset to building a machine learning model ready for deployment. AutoML was propo... | https://en.wikipedia.org/wiki/Automated_machine_learning |
Big dataprimarily refers todata setsthat are too large or complex to be dealt with by traditionaldata-processingsoftware. Data with many entries (rows) offer greaterstatistical power, while data with higher complexity (more attributes or columns) may lead to a higherfalse discovery rate.[1]
Big data analysis challenge... | https://en.wikipedia.org/wiki/Big_data |
Differentiable programmingis aprogramming paradigmin which a numeric computer program can bedifferentiatedthroughout viaautomatic differentiation.[1][2][3][4][5]This allows forgradient-based optimizationof parameters in the program, often viagradient descent, as well as other learning approaches that are based on highe... | https://en.wikipedia.org/wiki/Differentiable_programming |
Thesedatasetsare used inmachine learning (ML)research and have been cited inpeer-reviewedacademic journals. Datasets are an integral part of the field of machine learning. Major advances in this field can result from advances in learningalgorithms(such asdeep learning),computer hardware, and, less-intuitively, the avai... | https://en.wikipedia.org/wiki/List_of_datasets_for_machine-learning_research |
Inmachine learningandcomputer vision,M-theoryis a learning framework inspired by feed-forward processing in theventral streamofvisual cortexand originally developed for recognition and classification of objects in visual scenes. M-theory was later applied to other areas, such asspeech recognition. On certain image reco... | https://en.wikipedia.org/wiki/M-theory_(learning_framework) |
Machine unlearningis a branch ofmachine learningfocused on removing specific undesired element, such as private data, outdated information, copyrighted material, harmful content, dangerous abilities, or misinformation, without needing to rebuild models from the ground up.
Large language models, like the ones poweringC... | https://en.wikipedia.org/wiki/Machine_unlearning |
Solomonoff's theory of inductive inferenceproves that, under its common sense assumptions (axioms), the best possible scientific model is the shortest algorithm that generates the empirical data under consideration. In addition to the choice of data, other assumptions are that, to avoid the post-hoc fallacy, the progr... | https://en.wikipedia.org/wiki/Solomonoff%27s_theory_of_inductive_inference |
Abehavior treeis amathematical modelofplanexecution used incomputer science,robotics,control systemsandvideo games. They describe switchings between a finite set of tasks in a modular fashion. Their strength comes from their ability to create very complex tasks composed of simple tasks, without worrying how the simple ... | https://en.wikipedia.org/wiki/Behavior_tree_(artificial_intelligence,_robotics_and_control) |
Inmachine learning(ML),boostingis anensemblemetaheuristicfor primarily reducingbias (as opposed to variance).[1]It can also improve thestabilityand accuracy of MLclassificationandregressionalgorithms. Hence, it is prevalent insupervised learningfor converting weak learners to strong learners.[2]
The concept of boostin... | https://en.wikipedia.org/wiki/Boosting_(machine_learning) |
Corporate financeis an area offinancethat deals with the sources of funding, and thecapital structureof businesses, the actions that managers take to increase thevalueof the firm to theshareholders, and the tools and analysis used to allocate financial resources. The primary goal of corporate finance is tomaximizeor in... | https://en.wikipedia.org/wiki/Corporate_finance#Valuing_flexibility |
Adecision cycleordecision loop[1]is a sequence of steps used by an entity on a repeated basis toreach and implement decisionsand to learn from the results. The "decision cycle" phrase has a history of use to broadly categorize various methods of making decisions, going upstream to the need, downstream to the outcomes, ... | https://en.wikipedia.org/wiki/Decision_cycle |
Decision listsare a representation for Boolean functions which can be easily learnable from examples.[1]Single term decision lists are more expressive thandisjunctionsandconjunctions; however, 1-term decision lists are less expressive than the generaldisjunctive normal formand theconjunctive normal form.
The language ... | https://en.wikipedia.org/wiki/Decision_list |
Adecision matrixis a list of values in rows and columns that allows an analyst to systematically identify, analyze, and rate the performance of relationships between sets of values and information. Elements of a decision matrix show decisions based on certain decision criteria. The matrix is useful for looking at large... | https://en.wikipedia.org/wiki/Decision_matrix |
Decision tablesare a concise visual representation for specifying which actions to perform depending on given conditions. Decision table is the term used for aControl tableorState-transition tablein the field ofBusiness process modeling; they are usually formatted as the transpose of the way they are formatted inSoftwa... | https://en.wikipedia.org/wiki/Decision_table |
Incomputational complexity theory, thedecision tree modelis themodel of computationin which analgorithmcan be considered to be adecision tree, i.e. a sequence ofqueriesorteststhat are done adaptively, so the outcome of previous tests can influence the tests performed next.
Typically, these tests have a small number of... | https://en.wikipedia.org/wiki/Decision_tree_model |
Adesign rationaleis an explicit documentation of thereasonsbehinddecisionsmade whendesigningasystemorartifact. As initially developed by W.R. Kunz andHorst Rittel, design rationale seeks to provideargumentation-based structure to the political, collaborative process of addressingwicked problems.[1]
A design rationale ... | https://en.wikipedia.org/wiki/Design_rationale |
DRAKON(Russian:Дружелюбный Русский Алгоритмический язык, Который Обеспечивает Наглядность,lit.'Friendly Russian Algorithmic language, Which Provides Clarity') is afree and open sourcealgorithmicvisual programmingandmodeling languagedeveloped as part of the defunct Soviet UnionBuran space program[2]in 1986 following the... | https://en.wikipedia.org/wiki/DRAKON |
In probability theory and statistics, aMarkov chainorMarkov processis astochastic processdescribing asequenceof possible events in which theprobabilityof each event depends only on the state attained in the previous event. Informally, this may be thought of as, "What happens next depends only on the state of affairsnow... | https://en.wikipedia.org/wiki/Markov_chain |
Ordinal priority approach(OPA) is amultiple-criteria decision analysismethod that aids in solving thegroup decision-makingproblems based onpreference relations.
Various methods have been proposed to solve multi-criteria decision-making problems.[1]The basis of methods such asanalytic hierarchy processandanalytic netwo... | https://en.wikipedia.org/wiki/Ordinal_priority_approach |
Indecision theory, theodds algorithm(orBruss algorithm) is a mathematical method for computing optimal strategies for a class of problems that belong to the domain ofoptimal stoppingproblems. Their solution follows from theodds strategy, and the importance of the odds strategy lies in its optimality, as explained belo... | https://en.wikipedia.org/wiki/Odds_algorithm |
Themathematicaldiscipline oftopological combinatoricsis the application oftopologicalandalgebro-topologicalmethods to solving problems incombinatorics.
The discipline ofcombinatorial topologyused combinatorial concepts in topology and in the early 20th century this turned into the field ofalgebraic topology.
In 1978 ... | https://en.wikipedia.org/wiki/Topological_combinatorics |
Atruth tableis amathematical tableused inlogic—specifically in connection withBoolean algebra,Boolean functions, andpropositional calculus—which sets out the functional values of logicalexpressionson each of their functional arguments, that is, for eachcombination of values taken by their logical variables.[1]In partic... | https://en.wikipedia.org/wiki/Truth_table |
In situadaptive tabulation(ISAT) is analgorithmfor the approximation ofnonlinearrelationships. ISAT is based onmultiple linear regressionsthat are dynamically added as additional information is discovered. The technique is adaptive as it adds new linear regressions dynamically to a store of possible retrieval points.... | https://en.wikipedia.org/wiki/In_situ_adaptive_tabulation |
Inmachine learning,kernel machinesare a class of algorithms forpattern analysis, whose best known member is thesupport-vector machine(SVM). These methods involve using linear classifiers to solve nonlinear problems.[1]The general task ofpattern analysisis to find and study general types of relations (for examplecluster... | https://en.wikipedia.org/wiki/Kernel_machines |
Instatistical classification, theFisher kernel, named afterRonald Fisher, is a function thatmeasures the similarityof two objects on the basis of sets of measurements for each object and a statistical model. In a classification procedure, the class for a new object (whose real class is unknown) can be estimated by mini... | https://en.wikipedia.org/wiki/Fisher_kernel |
Inmachine learning,Platt scalingorPlatt calibrationis a way of transforming the outputs of aclassification modelinto aprobability distribution over classes. The method was invented byJohn Plattin the context ofsupport vector machines,[1]replacing an earlier method byVapnik, but can be applied to other classification mo... | https://en.wikipedia.org/wiki/Platt_scaling |
Inmachine learning, thepolynomial kernelis akernel functioncommonly used withsupport vector machines(SVMs) and otherkernelizedmodels, that represents the similarity of vectors (training samples) in a feature space over polynomials of the original variables, allowing learning of non-linear models.
Intuitively, the poly... | https://en.wikipedia.org/wiki/Polynomial_kernel |
Predictive analytics, orpredictive AI, encompasses a variety ofstatisticaltechniques fromdata mining,predictive modeling, andmachine learningthat analyze current and historical facts to makepredictionsabout future or otherwise unknown events.[1]
In business, predictive models exploitpatternsfound in historical and tra... | https://en.wikipedia.org/wiki/Predictive_analytics |
Withinmathematical analysis,Regularization perspectives on support-vector machinesprovide a way of interpretingsupport-vector machines(SVMs) in the context of other regularization-based machine-learning algorithms. SVM algorithms categorize binary data, with the goal of fitting thetraining setdata in a way that minimi... | https://en.wikipedia.org/wiki/Regularization_perspectives_on_support_vector_machines |
Inmathematics, aRelevance Vector Machine (RVM)is amachine learningtechnique that usesBayesian inferenceto obtainparsimonioussolutions forregressionandprobabilistic classification.[1]A greedy optimisation procedure and thus fast version were subsequently developed.[2][3]The RVM has an identical functional form to thesup... | https://en.wikipedia.org/wiki/Relevance_vector_machine |
Sequential minimal optimization(SMO) is an algorithm for solving thequadratic programming(QP) problem that arises during the training ofsupport-vector machines(SVM). It was invented byJohn Plattin 1998 atMicrosoft Research.[1]SMO is widely used for training support vector machines and is implemented by the popularLIBSV... | https://en.wikipedia.org/wiki/Sequential_minimal_optimization |
Thewinnow algorithm[1]is a technique frommachine learningfor learning alinear classifierfrom labeled examples. It is very similar to theperceptron algorithm. However, the perceptron algorithm uses an additive weight-update scheme, while Winnow uses amultiplicative schemethat allows it to perform much better when many... | https://en.wikipedia.org/wiki/Winnow_(algorithm) |
In the field ofmathematical modeling, aradial basis function networkis anartificial neural networkthat usesradial basis functionsasactivation functions. The output of the network is alinear combinationof radial basis functions of the inputs and neuron parameters. Radial basis function networks have many uses, including... | https://en.wikipedia.org/wiki/Radial_basis_function_network |
k-medoidsis a classical partitioning technique of clustering that splits the data set ofnobjects intokclusters, where the numberkof clusters assumed knowna priori(which implies that the programmer must specify k before the execution of ak-medoids algorithm). The "goodness" of the given value ofkcan be assessed with met... | https://en.wikipedia.org/wiki/K-medoids |
TheBFR algorithm, named after its inventors Bradley, Fayyad and Reina, is a variant ofk-means algorithmthat is designed to cluster data in a high-dimensionalEuclidean space. It makes a very strong assumption about the shape of clusters: they must benormally distributedabout acentroid. Themeanandstandard deviationfor a ... | https://en.wikipedia.org/wiki/BFR_algorithm |
Ingeometry, acentroidal Voronoi tessellation(CVT) is a special type ofVoronoi tessellationin which the generating point of each Voronoi cell is also itscentroid(center of mass). It can be viewed as an optimal partition corresponding to an optimal distribution of generators. A number of algorithms can be used to genera... | https://en.wikipedia.org/wiki/Centroidal_Voronoi_tessellation |
Cluster analysisorclusteringis the data analyzing technique in which task of grouping a set of objects in such a way that objects in the same group (called acluster) are moresimilar(in some specific sense defined by the analyst) to each other than to those in other groups (clusters). It is a main task ofexploratory dat... | https://en.wikipedia.org/wiki/Cluster_analysis |
Head/tail breaksis aclustering algorithmfor data with aheavy-tailed distributionsuch aspower lawsandlognormal distributions. The heavy-tailed distribution can be simply referred to the scaling pattern of far more small things than large ones, or alternatively numerous smallest, a very few largest, and some in between t... | https://en.wikipedia.org/wiki/Head/tail_breaks |
Indata miningandmachine learning,kq-flats algorithm[1][2]is an iterative method which aims to partitionmobservations intokclusters where each cluster is close to aq-flat, whereqis a given integer.
It is a generalization of thek-means algorithm. Ink-means algorithm, clusters are formed in the way that each cluster is c... | https://en.wikipedia.org/wiki/K_q-flats |
Indata mining,k-means++[1][2]is an algorithm for choosing the initial values (or "seeds") for thek-means clusteringalgorithm. It was proposed in 2007 by David Arthur and Sergei Vassilvitskii, as an approximation algorithm for theNP-hardk-means problem—a way of avoiding the sometimes poor clusterings found by the stand... | https://en.wikipedia.org/wiki/K-means%2B%2B |
TheLinde–Buzo–Gray algorithm(named after its creators Yoseph Linde, Andrés Buzo andRobert M. Gray, who designed it in 1980)[1]is aniterativevector quantizationalgorithm to improve a small set of vectors (codebook) to represent a larger set of vectors (training set), such that it will belocally optimal. It combinesLloyd... | https://en.wikipedia.org/wiki/Linde%E2%80%93Buzo%E2%80%93Gray_algorithm |
Aself-organizing map(SOM) orself-organizing feature map(SOFM) is anunsupervisedmachine learningtechnique used to produce alow-dimensional(typically two-dimensional) representation of a higher-dimensional data set while preserving thetopological structureof the data. For example, a data set withp{\displaystyle p}variabl... | https://en.wikipedia.org/wiki/Self-organizing_map |
In (unconstrained)mathematical optimization, abacktracking line searchis aline searchmethod to determine the amount to move along a givensearch direction. Its use requires that theobjective functionisdifferentiableand that itsgradientis known.
The method involves starting with a relatively large estimate of thestep si... | https://en.wikipedia.org/wiki/Backtracking_line_search |
Inmathematics, theconjugate gradient methodis analgorithmfor thenumerical solutionof particularsystems of linear equations, namely those whose matrix ispositive-semidefinite. The conjugate gradient method is often implemented as aniterative algorithm, applicable tosparsesystems that are too large to be handled by a dir... | https://en.wikipedia.org/wiki/Conjugate_gradient_method |
Rprop, short for resilientbackpropagation, is a learningheuristicforsupervised learninginfeedforwardartificial neural networks. This is afirst-orderoptimizationalgorithm. This algorithm was created by Martin Riedmiller and Heinrich Braun in 1992.[1]
Similarly to theManhattan update rule, Rprop takes into account only ... | https://en.wikipedia.org/wiki/Rprop |
Inmachine learning, thedelta ruleis agradient descentlearning rule for updating the weights of the inputs toartificial neuronsin asingle-layer neural network.[1]It can be derived as thebackpropagationalgorithm for a single-layer neural network with mean-square error loss function.
For a neuronj{\displaystyle j}withact... | https://en.wikipedia.org/wiki/Delta_rule |
In the unconstrainedminimizationproblem, theWolfe conditionsare a set of inequalities for performing inexactline search, especially inquasi-Newton methods, first published byPhilip Wolfein 1969.[1][2]
In these methods the idea is to findminxf(x){\displaystyle \min _{x}f(\mathbf {x} )}for somesmoothf:Rn→R{\displaystyle... | https://en.wikipedia.org/wiki/Wolfe_conditions |
Inmathematics,preconditioningis the application of a transformation, called thepreconditioner, that conditions a given problem into a form that is more suitable fornumericalsolving methods. Preconditioning is typically related to reducing acondition numberof the problem. The preconditioned problem is then usually solv... | https://en.wikipedia.org/wiki/Preconditioning |
Innumericaloptimization, theBroyden–Fletcher–Goldfarb–Shanno(BFGS)algorithmis aniterative methodfor solving unconstrainednonlinear optimizationproblems.[1]Like the relatedDavidon–Fletcher–Powell method, BFGS determines thedescent directionbypreconditioningthegradientwith curvature information. It does so by gradually i... | https://en.wikipedia.org/wiki/Broyden%E2%80%93Fletcher%E2%80%93Goldfarb%E2%80%93Shanno_algorithm |
TheDavidon–Fletcher–Powell formula(orDFP; named afterWilliam C. Davidon,Roger Fletcher, andMichael J. D. Powell) finds the solution to the secant equation that is closest to the current estimate and satisfies the curvature condition. It was the firstquasi-Newton methodto generalize thesecant methodto a multidimensional... | https://en.wikipedia.org/wiki/Davidon%E2%80%93Fletcher%E2%80%93Powell_formula |
TheNelder–Mead method(alsodownhill simplex method,amoeba method, orpolytope method) is anumerical methodused to find the minimum or maximum of anobjective functionin a multidimensional space. It is adirect searchmethod (based on function comparison) and is often applied to nonlinearoptimizationproblems for which deriva... | https://en.wikipedia.org/wiki/Nelder%E2%80%93Mead_method |
TheGauss–Newton algorithmis used to solvenon-linear least squaresproblems, which is equivalent to minimizing a sum of squared function values. It is an extension ofNewton's methodfor finding aminimumof a non-linearfunction. Since a sum of squares must be nonnegative, the algorithm can be viewed as using Newton's method... | https://en.wikipedia.org/wiki/Gauss%E2%80%93Newton_algorithm |
Innumerical analysis,hill climbingis amathematical optimizationtechnique which belongs to the family oflocal search.
It is aniterative algorithmthat starts with an arbitrary solution to a problem, then attempts to find a better solution by making anincrementalchange to the solution. If the change produces a better sol... | https://en.wikipedia.org/wiki/Hill_climbing |
Quantum annealing(QA) is an optimization process for finding theglobal minimumof a givenobjective functionover a given set of candidate solutions (candidate states), by a process usingquantum fluctuations. Quantum annealing is used mainly for problems where the search space is discrete (combinatorial optimizationproble... | https://en.wikipedia.org/wiki/Quantum_annealing |
Incomputational complexity theory, thecomplexity classTFNPis the class of total function problems which can be solved in nondeterministic polynomial time. That is, it is the class of function problems that are guaranteed to have an answer, and this answer can be checked in polynomial time, or equivalently it is the sub... | https://en.wikipedia.org/wiki/TFNP#CLS |
Neuroevolution, orneuro-evolution, is a form ofartificial intelligencethat usesevolutionary algorithmsto generateartificial neural networks(ANN), parameters, and rules.[1]It is most commonly applied inartificial life,general game playing[2]andevolutionary robotics. The main benefit is that neuroevolution can be applied... | https://en.wikipedia.org/wiki/Neuroevolution |
Instatistics, thebias of an estimator(orbias function) is the difference between thisestimator'sexpected valueand thetrue valueof the parameter being estimated. An estimator or decision rule with zero bias is calledunbiased. In statistics, "bias" is anobjectiveproperty of an estimator. Bias is a distinct concept fromco... | https://en.wikipedia.org/wiki/Bias_of_an_estimator |
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