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Non-linear least squaresis the form ofleast squaresanalysis used to fit a set ofmobservations with a model that is non-linear innunknown parameters (m≥n). It is used in some forms ofnonlinear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive ite... | https://en.wikipedia.org/wiki/Nonlinear_least_squares |
Instatistics,simple linear regression(SLR) is alinear regressionmodel with a singleexplanatory variable.[1][2][3][4][5]That is, it concerns two-dimensional sample points withone independent variable and one dependent variable(conventionally, thexandycoordinates in aCartesian coordinate system) and finds a linear functi... | https://en.wikipedia.org/wiki/Simple_linear_regression |
Partial least squares (PLS) regressionis astatisticalmethod that bears some relation toprincipal components regressionand is areduced rank regression;[1]instead of findinghyperplanesof maximumvariancebetween the response and independent variables, it finds alinear regressionmodel by projecting thepredicted variablesand... | https://en.wikipedia.org/wiki/Partial_least_squares_regression |
Inmathematics, the termlinear functionrefers to two distinct but related notions:[1]
In calculus,analytic geometryand related areas, a linear function is a polynomial of degree one or less, including thezero polynomial(the latter not being considered to have degree zero).
When the function is of only onevariable, it ... | https://en.wikipedia.org/wiki/Linear_function |
Adocument-term matrixis a mathematicalmatrixthat describes the frequency of terms that occur in each document in a collection. In a document-term matrix, rows correspond to documents in the collection and columns correspond to terms. This matrix is a specific instance of adocument-feature matrixwhere "features" may ref... | https://en.wikipedia.org/wiki/Document-term_matrix |
Alanguage modelis amodelof natural language.[1]Language models are useful for a variety of tasks, includingspeech recognition,[2]machine translation,[3]natural language generation(generating more human-like text),optical character recognition,route optimization,[4]handwriting recognition,[5]grammar induction,[6]andinfo... | https://en.wikipedia.org/wiki/Language_model#Neural_network |
Thought vectoris a term popularized byGeoffrey Hinton, the prominentdeep-learningresearcher, which uses vectors based onnatural language[1]to improve its search results.[2]
Thiscomputer sciencearticle is astub. You can help Wikipedia byexpanding it. | https://en.wikipedia.org/wiki/Thought_vector |
GloVe, coined from Global Vectors, is a model for distributed word representation. The model is anunsupervised learningalgorithm for obtainingvector representationsfor words. This is achieved by mapping words into a meaningful space where the distance between words is related to semantic similarity.[1]Training is perfo... | https://en.wikipedia.org/wiki/GloVe_(machine_learning) |
ELMo(embeddings from language model) is aword embeddingmethod for representing a sequence of words as a corresponding sequence of vectors.[1]It was created by researchers at theAllen Institute for Artificial Intelligence,[2]andUniversity of Washingtonand first released in February 2018. It is a bidirectionalLSTMwhich t... | https://en.wikipedia.org/wiki/ELMo |
Normalized compression distance(NCD) is a way of measuring thesimilaritybetween two objects, be it two documents, two letters, two emails, two music scores, two languages, two programs, two pictures, two systems, two genomes, to name a few. Such a measurement should not be application dependent or arbitrary. A reason... | https://en.wikipedia.org/wiki/Normalized_compression_distance |
TheNetflix Prizewas an open competition for the bestcollaborative filteringalgorithmto predict user ratings forfilms, based on previous ratings without any other information about the users or films, i.e. without the users being identified except by numbers assigned for the contest.
The competition was held byNetflix,... | https://en.wikipedia.org/wiki/Netflix_Prize |
The field ofsystem identificationusesstatistical methodsto buildmathematical modelsofdynamical systemsfrom measured data.[1]System identification also includes theoptimaldesign of experimentsfor efficiently generating informative data forfittingsuch models as well as model reduction. A common approach is to start from ... | https://en.wikipedia.org/wiki/System_identification |
Inmathematics, anasymmetric normon avector spaceis a generalization of the concept of anorm.
Anasymmetric normon arealvector spaceX{\displaystyle X}is afunctionp:X→[0,+∞){\displaystyle p:X\to [0,+\infty )}that has the following properties:
Asymmetric norms differ fromnormsin that they need not satisfy the equalityp(−... | https://en.wikipedia.org/wiki/Asymmetric_norm |
Infunctional analysisand related areas ofmathematics, ametrizable(resp.pseudometrizable)topological vector space(TVS) is a TVS whose topology is induced by a metric (resp.pseudometric). AnLM-spaceis aninductive limitof a sequence oflocally convexmetrizable TVS.
Apseudometricon a setX{\displaystyle X}is a mapd:X×X→R{\d... | https://en.wikipedia.org/wiki/F-seminorm |
Inmathematics, in the field ofadditive combinatorics, aGowers normoruniformity normis a class ofnormsonfunctionson a finitegroupor group-like object which quantify the amount of structure present, or conversely, the amount ofrandomness.[1]They are used in the study ofarithmetic progressionsin the group. They are named... | https://en.wikipedia.org/wiki/Gowers_norm |
Inmathematics, in the areas oftopologyandfunctional analysis, theAnderson–Kadec theoremstates[1]that any twoinfinite-dimensional,separableBanach spaces, or, more generally,Fréchet spaces, arehomeomorphicas topological spaces. The theorem was proved byMikhail Kadec(1966) andRichard Davis Anderson.
Every infinite-dimens... | https://en.wikipedia.org/wiki/Kadec_norm |
Inmathematics, themagnitudeorsizeof amathematical objectis a property which determines whether the object is larger or smaller than other objects of the same kind. More formally, an object's magnitude is the displayed result of anordering(or ranking) of theclassof objects to which it belongs. Magnitude as a concept dat... | https://en.wikipedia.org/wiki/Magnitude_(mathematics) |
In the field ofmathematics,normsare defined for elements within avector space. Specifically, when the vector space comprises matrices, such norms are referred to asmatrix norms. Matrix norms differ from vector norms in that they must also interact with matrix multiplication.
Given afieldK{\displaystyle \ K\ }of either... | https://en.wikipedia.org/wiki/Matrix_norm |
Inmathematics, in the field offunctional analysis, aMinkowski functional(afterHermann Minkowski) orgauge functionis a function that recovers a notion of distance on a linear space.
IfK{\textstyle K}is a subset of arealorcomplexvector spaceX,{\textstyle X,}then theMinkowski functionalorgaugeofK{\textstyle K}is defined ... | https://en.wikipedia.org/wiki/Minkowski_functional |
Inmathematics, theoperator normmeasures the "size" of certainlinear operatorsby assigning each areal numbercalled itsoperator norm. Formally, it is anormdefined on the space ofbounded linear operatorsbetween two givennormed vector spaces. Informally, the operator norm‖T‖{\displaystyle \|T\|}of a linear mapT:X→Y{\displa... | https://en.wikipedia.org/wiki/Operator_norm |
Infunctional analysisand related areas ofmathematics, ametrizable(resp.pseudometrizable)topological vector space(TVS) is a TVS whose topology is induced by a metric (resp.pseudometric). AnLM-spaceis aninductive limitof a sequence oflocally convexmetrizable TVS.
Apseudometricon a setX{\displaystyle X}is a mapd:X×X→R{\d... | https://en.wikipedia.org/wiki/Paranorm |
Inmathematics, ametric spaceis asettogether with a notion ofdistancebetween itselements, usually calledpoints. The distance is measured by afunctioncalled ametricordistance function.[1]Metric spaces are a general setting for studying many of the concepts ofmathematical analysisandgeometry.
The most familiar example o... | https://en.wikipedia.org/wiki/Relation_of_norms_and_metrics |
Inmathematics, particularly infunctional analysis, aseminormis like anormbut need not bepositive definite. Seminorms are intimately connected withconvex sets: every seminorm is theMinkowski functionalof someabsorbingdiskand, conversely, the Minkowski functional of any such set is a seminorm.
Atopological vector space... | https://en.wikipedia.org/wiki/Seminorm |
Inlinear algebra, asublinearfunction (orfunctionalas is more often used infunctional analysis), also called aquasi-seminormor aBanach functional, on avector spaceX{\displaystyle X}is areal-valuedfunctionwith only some of the properties of aseminorm. Unlike seminorms, a sublinear function does not have to benonnegative-... | https://en.wikipedia.org/wiki/Sublinear_function |
Āryabhata's sine tableis a set of twenty-four numbers given in the astronomical treatiseĀryabhatiyacomposed by the fifth centuryIndian mathematicianand astronomerĀryabhata(476–550 CE), for the computation of thehalf-chordsof a certain set of arcs of a circle. The set of numbers appears in verse 12 in Chapter 1Dasagit... | https://en.wikipedia.org/wiki/%C4%80ryabha%E1%B9%ADa%27s_sine_table |
Inmathematics,Bhāskara I's sine approximation formulais arational expressionin onevariablefor thecomputationof theapproximate valuesof thetrigonometric sinesdiscovered byBhāskara I(c. 600 – c. 680), a seventh-century Indianmathematician.[1]Thisformulais given in his treatise titledMahabhaskariya. It is not known how Bh... | https://en.wikipedia.org/wiki/Bhaskara_I%27s_sine_approximation_formula |
Inmathematics, thediscrete sine transform (DST)is aFourier-related transformsimilar to thediscrete Fourier transform(DFT), but using a purelyrealmatrix. It is equivalent to the imaginary parts of a DFT of roughly twice the length, operating on real data withoddsymmetry(since the Fourier transform of a real and odd func... | https://en.wikipedia.org/wiki/Discrete_sine_transform |
In mathematics, theDixon elliptic functionssm and cm are twoelliptic functions(doubly periodicmeromorphic functionson thecomplex plane) that map from eachregular hexagonin ahexagonal tilingto the whole complex plane. Because these functions satisfy the identitycm3z+sm3z=1{\displaystyle \operatorname {cm} ^{3}z+\opera... | https://en.wikipedia.org/wiki/Dixon_elliptic_functions |
Euler's formula, named afterLeonhard Euler, is amathematical formulaincomplex analysisthat establishes the fundamental relationship between thetrigonometric functionsand the complexexponential function. Euler's formula states that, for anyreal numberx, one haseix=cosx+isinx,{\displaystyle e^{ix}=\cos x+i\sin x,}where... | https://en.wikipedia.org/wiki/Euler%27s_formula |
Ordinarytrigonometrystudiestrianglesin theEuclidean planeR2{\displaystyle \mathbb {R} ^{2}}. There are a number of ways of defining the ordinaryEuclidean geometrictrigonometric functionsonreal numbers, for exampleright-angled triangle definitions,unit circle definitions,series definitions[broken anchor],definitions v... | https://en.wikipedia.org/wiki/Generalized_trigonometry |
Inmathematics,hyperbolic functionsare analogues of the ordinarytrigonometric functions, but defined using thehyperbolarather than thecircle. Just as the points(cost, sint)form acircle with a unit radius, the points(cosht, sinht)form the right half of theunit hyperbola. Also, similarly to how the derivatives ofsin(t)and... | https://en.wikipedia.org/wiki/Hyperbolic_function |
Inmathematics, thelemniscate elliptic functionsareelliptic functionsrelated to the arc length of thelemniscate of Bernoulli. They were first studied byGiulio Fagnanoin 1718 and later byLeonhard EulerandCarl Friedrich Gauss, among others.[1]
Thelemniscate sineandlemniscate cosinefunctions, usually written with the symb... | https://en.wikipedia.org/wiki/Lemniscate_elliptic_functions |
Intrigonometry, thelaw of sines(sometimes called thesine formulaorsine rule) is a mathematicalequationrelating thelengthsof the sides of anytriangleto thesinesof itsangles. According to the law,asinα=bsinβ=csinγ=2R,{\displaystyle {\frac {a}{\sin {\alpha }}}\,=\,{\frac {b}{\sin {\beta }}}\,=\,{\frac {c}{\sin {\gamma ... | https://en.wikipedia.org/wiki/Law_of_sines |
This is a list of some well-knownperiodic functions. The constant functionf(x) =c, wherecis independent ofx, is periodic with any period, but lacks afundamental period. A definition is given for some of the following functions, though each function may have many equivalent definitions.
All trigonometric functions list... | https://en.wikipedia.org/wiki/List_of_periodic_functions |
Intrigonometry,trigonometric identitiesareequalitiesthat involvetrigonometric functionsand are true for every value of the occurringvariablesfor which both sides of the equality are defined. Geometrically, these areidentitiesinvolving certain functions of one or moreangles. They are distinct fromtriangle identities, wh... | https://en.wikipedia.org/wiki/List_of_trigonometric_identities |
Inmathematics, aMadhava seriesis one of the threeTaylor seriesexpansions for thesine,cosine, andarctangentfunctionsdiscovered in 14th or 15th century inKerala,Indiaby the mathematician and astronomerMadhava of Sangamagrama(c. 1350 – c. 1425) or his followers in theKerala school of astronomy and mathematics.[1]Using mod... | https://en.wikipedia.org/wiki/Madhava_series |
Madhava's sine tableis thetableoftrigonometric sinesconstructed by the 14th centuryKeralamathematician-astronomerMadhava of Sangamagrama(c. 1340 – c. 1425). The table lists thejya-sor Rsines of the twenty-fouranglesfrom 3.75°to 90° in steps of 3.75° (1/24 of aright angle, 90°). Rsine is just the sine multiplied by a se... | https://en.wikipedia.org/wiki/Madhava%27s_sine_table |
Inoptics, theoptical sine theoremstates that the products of the index, height, andsineof the slope angle of a ray in object space and its corresponding ray inimage spaceare equal. That is:
Thisoptics-related article is astub. You can help Wikipedia byexpanding it. | https://en.wikipedia.org/wiki/Optical_sine_theorem |
Ingeometry, thepolar sinegeneralizes thesine functionofangleto thevertex angleof apolytope. It is denoted bypsin.
Letv1, ...,vn(n≥ 1) be non-zeroEuclidean vectorsinn-dimensional space(Rn) that are directed from avertexof aparallelotope, forming the edges of the parallelotope. The polar sine of the vertex angle is:
wh... | https://en.wikipedia.org/wiki/Polar_sine |
There are several equivalent ways for definingtrigonometric functions, and the proofs of thetrigonometric identitiesbetween them depend on the chosen definition. The oldest and most elementary definitions are based on the geometry ofright trianglesand the ratio between their sides. The proofs given in this article use ... | https://en.wikipedia.org/wiki/Proofs_of_trigonometric_identities |
Inmathematics,physicsandengineering, thesinc function(/ˈsɪŋk/SINK), denoted bysinc(x), has two forms, normalized and unnormalized.[1]
In mathematics, the historicalunnormalized sinc functionis defined forx≠ 0bysinc(x)=sinxx.{\displaystyle \operatorname {sinc} (x)={\frac {\sin x}{x}}.}
Alternatively, the unnormalize... | https://en.wikipedia.org/wiki/Sinc_function |
Inmathematics, the Fouriersine and cosine transformsareintegral equationsthat decompose arbitrary functions into a sum ofsine wavesrepresenting theodd componentof the function plus cosine waves representing the even component of the function. The modernFourier transformconciselycontainsboth the sine and cosine transfor... | https://en.wikipedia.org/wiki/Sine_and_cosine_transforms |
Inmathematics,trigonometric integralsare afamilyofnonelementary integralsinvolvingtrigonometric functions.
The differentsineintegral definitions areSi(x)=∫0xsinttdt{\displaystyle \operatorname {Si} (x)=\int _{0}^{x}{\frac {\sin t}{t}}\,dt}si(x)=−∫x∞sinttdt.{\displaystyle \operatorname {si} (x)=-\int _{x}^{\infty }... | https://en.wikipedia.org/wiki/Sine_integral |
Asine quadrant(Arabic:الربع المجيب,romanized:rub‘ul mujayyab), sometimes known as a "sinecal quadrant", was a type ofquadrantused by medievalArabic astronomers. Theinstrumentcould be used to measurecelestial angles, tell time, find directions, performtrigonometriccomputations, and determine the apparent positions of a... | https://en.wikipedia.org/wiki/Sine_quadrant |
Asine wave,sinusoidal wave, orsinusoid(symbol:∿) is aperiodic wavewhosewaveform(shape) is thetrigonometricsine function. Inmechanics, as a linearmotionover time, this issimple harmonic motion; asrotation, it corresponds touniform circular motion. Sine waves occur often inphysics, includingwind waves,soundwaves, andligh... | https://en.wikipedia.org/wiki/Sine_wave |
Thesine-Gordon equationis a second-ordernonlinear partial differential equationfor a functionφ{\displaystyle \varphi }dependent on two variables typically denotedx{\displaystyle x}andt{\displaystyle t}, involving thewave operatorand thesineofφ{\displaystyle \varphi }.
It was originally introduced byEdmond Bour(1862) i... | https://en.wikipedia.org/wiki/Sine%E2%80%93Gordon_equation |
Instatistics,signal processing, andtime series analysis, asinusoidal modelis used to approximate a sequenceYito asinefunction:
whereCis constant defining ameanlevel, α is anamplitudefor thesine, ω is theangular frequency,Tiis a time variable, φ is thephase-shift, andEiis the error sequence.
This sinusoidal model can ... | https://en.wikipedia.org/wiki/Sinusoidal_model |
Intrigonometry, it is common to usemnemonicsto help remembertrigonometric identitiesand the relationships between the varioustrigonometric functions.
Thesine,cosine, andtangentratios in a right triangle can be remembered by representing them as strings of letters, for instance SOH-CAH-TOA in English:
One way to remem... | https://en.wikipedia.org/wiki/Mnemonics_in_trigonometry#SOH-CAH-TOA |
Inmathematics, thetrigonometric functions(also calledcircular functions,angle functionsorgoniometric functions)[1]arereal functionswhich relate an angle of aright-angled triangleto ratios of two side lengths. They are widely used in all sciences that are related togeometry, such asnavigation,solid mechanics,celestial m... | https://en.wikipedia.org/wiki/Trigonometric_functions |
Inmathematics,trigonometric integralsare afamilyofnonelementary integralsinvolvingtrigonometric functions.
The differentsineintegral definitions areSi(x)=∫0xsinttdt{\displaystyle \operatorname {Si} (x)=\int _{0}^{x}{\frac {\sin t}{t}}\,dt}si(x)=−∫x∞sinttdt.{\displaystyle \operatorname {si} (x)=-\int _{x}^{\infty }... | https://en.wikipedia.org/wiki/Trigonometric_integral |
Instatisticsand, in particular, in the fitting oflinearorlogistic regressionmodels, theelastic netis aregularizedregression method thatlinearly combinestheL1andL2penalties of thelassoandridgemethods.
Nevertheless, elastic net regularization is typically more accurate than both methods with regard to reconstruction.[1]
... | https://en.wikipedia.org/wiki/Elastic_net_regularization |
Inapplied mathematics,antieigenvalue theorywas developed byKarl Gustafsonfrom 1966 to 1968. The theory is applicable tonumerical analysis,wavelets,statistics,quantum mechanics,financeandoptimization.
The antieigenvectorsx{\displaystyle x}are the vectors most turned by a matrix or operatorA{\displaystyle A}, that is to... | https://en.wikipedia.org/wiki/Antieigenvalue_theory |
In mathematics, aneigenoperator,A, of amatrixHis alinear operatorsuch that
whereλ{\displaystyle \lambda }is a correspondingscalarcalled aneigenvalue.[1]
This article aboutmatricesis astub. You can help Wikipedia byexpanding it. | https://en.wikipedia.org/wiki/Eigenoperator |
Inmathematics, aneigenplaneis a two-dimensionalinvariant subspacein a givenvector space. By analogy with the termeigenvectorfor a vector which, when operated on by alinear operatoris another vector which is ascalarmultiple of itself, the termeigenplanecan be used to describe a two-dimensionalplane(a2-plane), such that ... | https://en.wikipedia.org/wiki/Eigenplane |
EigenMoments[1]is a set oforthogonal, noise robust, invariant to rotation, scaling and translation and distribution sensitivemoments. Their application can be found insignal processingandcomputer visionas descriptors of the signal or image. The descriptors can later be used forclassificationpurposes.
It is obtained by... | https://en.wikipedia.org/wiki/Eigenmoments |
Inquantum physics, aquantum stateis a mathematical entity that embodies the knowledge of a quantum system.Quantum mechanicsspecifies the construction, evolution, andmeasurementof a quantum state. The result is a prediction for the system represented by the state. Knowledge of the quantum state, and the rules for the sy... | https://en.wikipedia.org/wiki/Quantum_states |
Inlinear algebra, aJordan normal form, also known as aJordan canonical form,[1][2]is anupper triangular matrixof a particular form called aJordan matrixrepresenting alinear operatoron afinite-dimensionalvector spacewith respect to somebasis. Such a matrix has each non-zero off-diagonal entry equal to 1, immediately abo... | https://en.wikipedia.org/wiki/Jordan_normal_form |
Inmathematics, anonlinear eigenproblem, sometimesnonlinear eigenvalue problem, is a generalization of the (ordinary)eigenvalue problemto equations that dependnonlinearlyon the eigenvalue. Specifically, it refers to equations of the form
wherex≠0{\displaystyle x\neq 0}is avector, andM{\displaystyle M}is amatrix-valuedf... | https://en.wikipedia.org/wiki/Nonlinear_eigenproblem |
In mathematics, specifically inspectral theory, aneigenvalueof aclosed linear operatoris callednormalif the space admits a decomposition into a direct sum of a finite-dimensionalgeneralized eigenspaceand aninvariant subspacewhereA−λI{\displaystyle A-\lambda I}has a bounded inverse.
The set of normal eigenvalues coincid... | https://en.wikipedia.org/wiki/Normal_eigenvalue |
Inmathematics, thequadratic eigenvalue problem[1](QEP), is to findscalareigenvaluesλ{\displaystyle \lambda }, lefteigenvectorsy{\displaystyle y}and right eigenvectorsx{\displaystyle x}such that
whereQ(λ)=λ2M+λC+K{\displaystyle Q(\lambda )=\lambda ^{2}M+\lambda C+K}, with matrix coefficientsM,C,K∈Cn×n{\displaystyle M,\... | https://en.wikipedia.org/wiki/Quadratic_eigenvalue_problem |
Inmathematics, thespectrumof amatrixis thesetof itseigenvalues.[1][2][3]More generally, ifT:V→V{\displaystyle T\colon V\to V}is alinear operatoron anyfinite-dimensionalvector space, its spectrum is the set of scalarsλ{\displaystyle \lambda }such thatT−λI{\displaystyle T-\lambda I}is notinvertible. Thedeterminantof the ... | https://en.wikipedia.org/wiki/Spectrum_of_a_matrix |
Incomputer science, aball tree,balltree[1]ormetric tree, is aspace partitioningdata structurefor organizing points in a multi-dimensional space. A ball tree partitions data points into a nested set ofballs. The resulting data structure has characteristics that make it useful for a number of applications, most notablyne... | https://en.wikipedia.org/wiki/Ball_tree |
Theclosest pair of points problemorclosest pair problemis a problem ofcomputational geometry: givenn{\displaystyle n}points inmetric space, find a pair of points with the smallest distance between them. The closest pair problem for points in the Euclidean plane[1]was among the first geometric problems that were treated... | https://en.wikipedia.org/wiki/Closest_pair_of_points_problem |
Content-based image retrieval, also known asquery by image content(QBIC) andcontent-based visual information retrieval(CBVIR), is the application ofcomputer visiontechniques to theimage retrievalproblem, that is, the problem of searching fordigital imagesin largedatabases(see this survey[1]for a scientific overview of ... | https://en.wikipedia.org/wiki/Content-based_image_retrieval |
Dimensionality reduction, ordimension reduction, is the transformation of data from a high-dimensional space into a low-dimensional space so that the low-dimensional representation retains some meaningful properties of the original data, ideally close to itsintrinsic dimension. Working in high-dimensional spaces can be... | https://en.wikipedia.org/wiki/Dimension_reduction |
Incomputational geometry, thefixed-radius near neighbor problemis a variant of thenearest neighbor searchproblem. In the fixed-radius near neighbor problem, one is given as input a set of points ind-dimensionalEuclidean spaceand a fixed distance Δ. One must design a data structure that, given a query pointq, efficientl... | https://en.wikipedia.org/wiki/Fixed-radius_near_neighbors |
Inmachine learning,instance-based learning(sometimes calledmemory-based learning[1]) is a family of learning algorithms that, instead of performing explicit generalization, compare new problem instances with instances seen in training, which have been stored in memory. Because computation is postponed until a new insta... | https://en.wikipedia.org/wiki/Instance-based_learning |
Instatistics, thek-nearest neighbors algorithm(k-NN) is anon-parametricsupervised learningmethod. It was first developed byEvelyn FixandJoseph Hodgesin 1951,[1]and later expanded byThomas Cover.[2]Most often, it is used forclassification, as ak-NN classifier, the output of which is a class membership. An object is clas... | https://en.wikipedia.org/wiki/K-nearest_neighbor_algorithm |
Incomputer science,locality-sensitive hashing(LSH) is afuzzy hashingtechnique that hashes similar input items into the same "buckets" with high probability.[1](The number of buckets is much smaller than the universe of possible input items.)[1]Since similar items end up in the same buckets, this technique can be used f... | https://en.wikipedia.org/wiki/Locality_sensitive_hashing |
Maximum inner-product search(MIPS) is asearch problem, with a corresponding class ofsearch algorithmswhich attempt to maximise theinner productbetween a query and the data items to be retrieved. MIPS algorithms are used in a wide variety of big data applications, includingrecommendation algorithmsandmachine learning.[1... | https://en.wikipedia.org/wiki/Maximum_inner-product_search |
Instatistics,econometricsand related fields,multidimensional analysis(MDA) is adata analysisprocess that groups data into two categories:data dimensionsand measurements. For example, adata setconsisting of the number of wins for a single football team at each of several years is a single-dimensional (in this case, long... | https://en.wikipedia.org/wiki/Multidimensional_analysis |
Nearest-neighbor interpolation(also known asproximal interpolationor, in some contexts,point sampling) is a simple method ofmultivariate interpolationin one or moredimensions.
Interpolationis the problem of approximating the value of a function for a non-given point in some space when given the value of that function ... | https://en.wikipedia.org/wiki/Nearest-neighbor_interpolation |
Inbioinformatics,neighbor joiningis a bottom-up (agglomerative)clusteringmethod for the creation ofphylogenetic trees, created by Naruya Saitou andMasatoshi Neiin 1987.[1]Usually based onDNAorproteinsequencedata, the algorithm requires knowledge of the distance between each pair oftaxa(e.g., species or sequences) to cr... | https://en.wikipedia.org/wiki/Neighbor_joining |
Incomputer science, therange searchingproblem consists of processing a setSof objects, in order to determine which objects fromSintersect with a query object, called therange. For example, ifSis a set of points corresponding to the coordinates of several cities, find the subset of cities within a given range oflatitude... | https://en.wikipedia.org/wiki/Range_search |
Inmathematics, aVoronoi diagramis apartitionof aplaneinto regions close to each of a given set of objects. It can be classified also as atessellation. In the simplest case, these objects are just finitely many points in the plane (called seeds, sites, or generators). For each seed there is a correspondingregion, called... | https://en.wikipedia.org/wiki/Voronoi_diagram |
Awaveletis awave-likeoscillationwith anamplitudethat begins at zero, increases or decreases, and then returns to zero one or more times. Wavelets are termed a "brief oscillation". A taxonomy of wavelets has been established, based on the number and direction of its pulses. Wavelets are imbued with specific properties t... | https://en.wikipedia.org/wiki/Wavelet |
Asimple polygonthat is notconvexis calledconcave,[1]non-convex[2]orreentrant.[3]A concave polygon will always have at least onereflex interior angle—that is, an angle with a measure that is between 180 degrees and 360 degrees exclusive.[4]
Some lines containing interior points of a concave polygon intersect its bounda... | https://en.wikipedia.org/wiki/Concave_polygon |
Inconvex analysis, anon-negativefunctionf:Rn→R+islogarithmically concave(orlog-concavefor short) if itsdomainis aconvex set, and if it satisfies the inequality
for allx,y∈ domfand0 <θ< 1. Iffis strictly positive, this is equivalent to saying that thelogarithmof the function,log ∘f, isconcave; that is,
for allx,y∈ dom... | https://en.wikipedia.org/wiki/Logarithmically_concave_function |
Inmathematics, aquasiconvex functionis areal-valuedfunctiondefined on anintervalor on aconvex subsetof a realvector spacesuch that theinverse imageof any set of the form(−∞,a){\displaystyle (-\infty ,a)}is aconvex set. For a function of a single variable, along any stretch of the curve the highest point is one of the e... | https://en.wikipedia.org/wiki/Quasiconcave_function |
In mathematics,concavificationis the process of converting a non-concave function to aconcave function. A related concept isconvexification– converting a non-convex function to aconvex function. It is especially important ineconomicsandmathematical optimization.[1]
An important special case of concavification is where... | https://en.wikipedia.org/wiki/Concavification |
Artificial intelligence artusually meansvisual artworkgenerated (or enhanced) through the use ofartificial intelligence(AI) programs.
Artists began to create AI art in the mid to late 20th century, when the discipline was founded. Throughoutits history, AI has raised manyphilosophical concernsrelated to thehuman mind,... | https://en.wikipedia.org/wiki/Artificial_intelligence_art |
Deepfakes(aportmanteauof'deep learning'and'fake'[1]) are images, videos, or audio that have been edited or generatedusing artificial intelligence, AI-based tools or AV editing software. They may depict real or fictional people and are considered a form ofsynthetic media, that is media that is usually created by artific... | https://en.wikipedia.org/wiki/Deepfake |
Inmachine learning,diffusion models, also known asdiffusion-based generative modelsorscore-based generative models, are a class oflatent variablegenerativemodels. A diffusion model consists of two major components: the forward diffusion process, and the reverse sampling process. The goal of diffusion models is to learn... | https://en.wikipedia.org/wiki/Diffusion_model |
Generative artificial intelligence(Generative AI,GenAI,[1]orGAI) is a subfield ofartificial intelligencethat uses generative models to produce text, images, videos, or other forms of data.[2][3][4]These modelslearnthe underlying patterns and structures of theirtraining dataand use them to produce new data[5][6]based on... | https://en.wikipedia.org/wiki/Generative_artificial_intelligence |
Synthetic media(also known asAI-generated media,[1][2]media produced bygenerative AI,[3]personalized media,personalized content,[4]and colloquially asdeepfakes[5]) is a catch-all term for the artificial production, manipulation, and modification of data and media byautomatedmeans, especially through the use ofartificia... | https://en.wikipedia.org/wiki/Synthetic_media |
Inprobabilityandstatistics, the class ofexponential dispersion models(EDM), also calledexponential dispersion family(EDF), is a set ofprobability distributionsthat represents a generalisation of thenatural exponential family.[1][2][3]Exponential dispersion models play an important role instatistical theory, in particu... | https://en.wikipedia.org/wiki/Exponential_dispersion_model |
Inphysicsandmathematics, theGibbs measure, named afterJosiah Willard Gibbs, is aprobability measurefrequently seen in many problems ofprobability theoryandstatistical mechanics. It is a generalization of thecanonical ensembleto infinite systems.
The canonical ensemble gives the probability of the systemXbeing in state... | https://en.wikipedia.org/wiki/Gibbs_measure |
Inprobability theoryandstatistics, themodified half-normal distribution (MHN)[1][2][3][4][5][6][7][8]is a three-parameter family of continuousprobability distributionssupported on the positive part of the real line. It can be viewed as a generalization of multiple families, including thehalf-normal distribution,truncat... | https://en.wikipedia.org/wiki/Modified_half-normal_distribution |
Inprobabilityandstatistics, anatural exponential family(NEF) is a class ofprobability distributionsthat is a special case of anexponential family(EF).
The natural exponential families (NEF) are a subset of theexponential families. A NEF is an exponential family in which the natural parameterηand the natural statisticT... | https://en.wikipedia.org/wiki/Natural_exponential_family |
Inprobability theoryandstatistics, thebinomial distributionwith parametersnandpis thediscrete probability distributionof the number of successes in a sequence ofnindependentexperiments, each asking ayes–no question, and each with its ownBoolean-valuedoutcome:success(with probabilityp) orfailure(with probabilityq= 1 −p)... | https://en.wikipedia.org/wiki/Binomial_distribution |
Inprobability theory, acompound Poisson distributionis theprobability distributionof the sum of a number ofindependent identically-distributed random variables, where the number of terms to be added is itself aPoisson-distributedvariable. The result can be either acontinuousor adiscrete distribution.
Suppose that
i.e... | https://en.wikipedia.org/wiki/Compound_Poisson_distribution |
Inprobability theoryandstatistics, theConway–Maxwell–Poisson (CMP or COM–Poisson) distributionis adiscrete probability distributionnamed afterRichard W. Conway,William L. Maxwell, andSiméon Denis Poissonthat generalizes thePoisson distributionby adding a parameter to modeloverdispersionandunderdispersion. It is a membe... | https://en.wikipedia.org/wiki/Conway%E2%80%93Maxwell%E2%80%93Poisson_distribution |
TheErlang distributionis a two-parameter family of continuousprobability distributionswithsupportx∈[0,∞){\displaystyle x\in [0,\infty )}. The two parameters are:
The Erlang distribution is the distribution of a sum ofk{\displaystyle k}independentexponential variableswith mean1/λ{\displaystyle 1/\lambda }each. Equival... | https://en.wikipedia.org/wiki/Erlang_distribution |
Inprobability theoryandstatistics, theexponential distributionornegative exponential distributionis theprobability distributionof the distance between events in aPoisson point process, i.e., a process in which events occur continuously and independently at a constant average rate; the distance parameter could be any me... | https://en.wikipedia.org/wiki/Exponential_distribution |
Inprobability theoryandstatistics, thegamma distributionis a versatile two-parameterfamily of continuousprobability distributions.[1]Theexponential distribution,Erlang distribution, andchi-squared distributionare special cases of the gamma distribution.[2]There are two equivalent parameterizations in common use:
In ea... | https://en.wikipedia.org/wiki/Gamma_distribution |
Inprobability theoryandstatistics, theHermite distribution, named afterCharles Hermite, is adiscrete probability distributionused to modelcount datawith more than one parameter. This distribution is flexible in terms of its ability to allow a moderateover-dispersionin the data.
The authors C. D. Kemp andA. W. Kemp[1]h... | https://en.wikipedia.org/wiki/Hermite_distribution |
Inprobability theoryandstatistics, theindex of dispersion,[1]dispersion index,coefficient of dispersion,relative variance, orvariance-to-mean ratio(VMR), like thecoefficient of variation, is anormalizedmeasure of thedispersionof aprobability distribution: it is a measure used to quantify whether a set of observed occur... | https://en.wikipedia.org/wiki/Index_of_dispersion |
Inprobability theoryandstatistics, thenegative binomial distributionis adiscrete probability distributionthat models the number of failures in a sequence of independent and identically distributedBernoulli trialsbefore a specified/constant/fixed number of successesr{\displaystyle r}occur.[2]For example, we can define r... | https://en.wikipedia.org/wiki/Negative_binomial_distribution |
Poisson clumping, orPoisson bursts,[1]is a phenomenon whererandomevents may appear to occur in clusters, clumps, orbursts.
Poisson clumping is named for 19th-centuryFrenchmathematicianSiméon Denis Poisson,[1]known for his work ondefinite integrals,electromagnetic theory, andprobability theory, and after whom thePoisso... | https://en.wikipedia.org/wiki/Poisson_clumping |
a0,t+(a0,t)2−(a0,t)2=a0,t{\displaystyle a_{0,t}+(a_{0,t})^{2}-(a_{0,t})^{2}=a_{0,t}}sinceRx(t1,t2)=a0,min(t1,t2)+a0,t1a0,t2{\displaystyle R_{x}(t_{1},t_{2})=a_{0,min(t_{1},t_{2})}+a_{0,t_{1}}a_{0,t_{2}}}
Inprobability theory,statisticsand related fields, aPoisson point process(also known as:Poisson random measure,Pois... | https://en.wikipedia.org/wiki/Poisson_point_process |
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