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Nearest neighbor search : Various solutions to the NNS problem have been proposed. The quality and usefulness of the algorithms are determined by the time complexity of queries as well as the space complexity of any search data structures that must be maintained. The informal observation usually referred to as the curs... |
Nearest neighbor search : There are numerous variants of the NNS problem and the two most well-known are the k-nearest neighbor search and the ε-approximate nearest neighbor search. |
Nearest neighbor search : Shasha, Dennis (2004). High Performance Discovery in Time Series. Berlin: Springer. ISBN 978-0-387-00857-8. |
Nearest neighbor search : Nearest Neighbors and Similarity Search – a website dedicated to educational materials, software, literature, researchers, open problems and events related to NN searching. Maintained by Yury Lifshits Similarity Search Wiki – a collection of links, people, ideas, keywords, papers, slides, code... |
Linear discriminant analysis : Linear discriminant analysis (LDA), normal discriminant analysis (NDA), canonical variates analysis (CVA), or discriminant function analysis is a generalization of Fisher's linear discriminant, a method used in statistics and other fields, to find a linear combination of features that cha... |
Linear discriminant analysis : The original dichotomous discriminant analysis was developed by Sir Ronald Fisher in 1936. It is different from an ANOVA or MANOVA, which is used to predict one (ANOVA) or multiple (MANOVA) continuous dependent variables by one or more independent categorical variables. Discriminant funct... |
Linear discriminant analysis : Consider a set of observations x → (also called features, attributes, variables or measurements) for each sample of an object or event with known class y . This set of samples is called the training set in a supervised learning context. The classification problem is then to find a good ... |
Linear discriminant analysis : The assumptions of discriminant analysis are the same as those for MANOVA. The analysis is quite sensitive to outliers and the size of the smallest group must be larger than the number of predictor variables. Multivariate normality: Independent variables are normal for each level of the g... |
Linear discriminant analysis : Discriminant analysis works by creating one or more linear combinations of predictors, creating a new latent variable for each function. These functions are called discriminant functions. The number of functions possible is either N g − 1 -1 where N g = number of groups, or p (the numbe... |
Linear discriminant analysis : Maximum likelihood: Assigns x to the group that maximizes population (group) density. Bayes Discriminant Rule: Assigns x to the group that maximizes π i f i ( x ) f_(x) , where πi represents the prior probability of that classification, and f i ( x ) (x) represents the population densit... |
Linear discriminant analysis : An eigenvalue in discriminant analysis is the characteristic root of each function. It is an indication of how well that function differentiates the groups, where the larger the eigenvalue, the better the function differentiates. This however, should be interpreted with caution, as eigenv... |
Linear discriminant analysis : Some suggest the use of eigenvalues as effect size measures, however, this is generally not supported. Instead, the canonical correlation is the preferred measure of effect size. It is similar to the eigenvalue, but is the square root of the ratio of SSbetween and SStotal. It is the corre... |
Linear discriminant analysis : Canonical discriminant analysis (CDA) finds axes (k − 1 canonical coordinates, k being the number of classes) that best separate the categories. These linear functions are uncorrelated and define, in effect, an optimal k − 1 space through the n-dimensional cloud of data that best separate... |
Linear discriminant analysis : The terms Fisher's linear discriminant and LDA are often used interchangeably, although Fisher's original article actually describes a slightly different discriminant, which does not make some of the assumptions of LDA such as normally distributed classes or equal class covariances. Suppo... |
Linear discriminant analysis : In the case where there are more than two classes, the analysis used in the derivation of the Fisher discriminant can be extended to find a subspace which appears to contain all of the class variability. This generalization is due to C. R. Rao. Suppose that each of C classes has a mean μ ... |
Linear discriminant analysis : The typical implementation of the LDA technique requires that all the samples are available in advance. However, there are situations where the entire data set is not available and the input data are observed as a stream. In this case, it is desirable for the LDA feature extraction to hav... |
Linear discriminant analysis : In practice, the class means and covariances are not known. They can, however, be estimated from the training set. Either the maximum likelihood estimate or the maximum a posteriori estimate may be used in place of the exact value in the above equations. Although the estimates of the cova... |
Linear discriminant analysis : In addition to the examples given below, LDA is applied in positioning and product management. |
Linear discriminant analysis : Discriminant function analysis is very similar to logistic regression, and both can be used to answer the same research questions. Logistic regression does not have as many assumptions and restrictions as discriminant analysis. However, when discriminant analysis’ assumptions are met, it ... |
Linear discriminant analysis : Geometric anomalies in higher dimensions lead to the well-known curse of dimensionality. Nevertheless, proper utilization of concentration of measure phenomena can make computation easier. An important case of these blessing of dimensionality phenomena was highlighted by Donoho and Tanner... |
Linear discriminant analysis : Data mining Decision tree learning Factor analysis Kernel Fisher discriminant analysis Logit (for logistic regression) Linear regression Multiple discriminant analysis Multidimensional scaling Pattern recognition Preference regression Quadratic classifier Statistical classification |
Linear discriminant analysis : Duda, R. O.; Hart, P. E.; Stork, D. H. (2000). Pattern Classification (2nd ed.). Wiley Interscience. ISBN 978-0-471-05669-0. MR 1802993. Hilbe, J. M. (2009). Logistic Regression Models. Chapman & Hall/CRC Press. ISBN 978-1-4200-7575-5. Mika, S.; et al. (1999). "Fisher discriminant analysi... |
Linear discriminant analysis : Discriminant Correlation Analysis (DCA) of the Haghighat article (see above) ALGLIB contains open-source LDA implementation in C# / C++ / Pascal / VBA. LDA in Python- LDA implementation in Python LDA tutorial using MS Excel Biomedical statistics. Discriminant analysis StatQuest: Linear Di... |
One-class classification : In machine learning, one-class classification (OCC), also known as unary classification or class-modelling, tries to identify objects of a specific class amongst all objects, by primarily learning from a training set containing only the objects of that class, although there exist variants of ... |
One-class classification : The term one-class classification (OCC) was coined by Moya & Hush (1996) and many applications can be found in scientific literature, for example outlier detection, anomaly detection, novelty detection. A feature of OCC is that it uses only sample points from the assigned class, so that a rep... |
One-class classification : SVM based one-class classification (OCC) relies on identifying the smallest hypersphere (with radius r, and center c) consisting of all the data points. This method is called Support Vector Data Description (SVDD). Formally, the problem can be defined in the following constrained optimization... |
One-class classification : Several approaches have been proposed to solve one-class classification (OCC). The approaches can be distinguished into three main categories, density estimation, boundary methods, and reconstruction methods. |
One-class classification : Multiclass classification Anomaly detection Supervised learning == References == |
Operational taxonomic unit : An operational taxonomic unit (OTU) is an operational definition used to classify groups of closely related individuals. The term was originally introduced in 1963 by Robert R. Sokal and Peter H. A. Sneath in the context of numerical taxonomy, where an "operational taxonomic unit" is simply... |
Operational taxonomic unit : There are three main approaches to clustering OTUs: De novo, for which the clustering is based on similarities between sequencing reads. Closed-reference, for which the clustering is performed against a reference database of sequences. Open-reference, where clustering is first performed aga... |
Operational taxonomic unit : Hierarchical clustering algorithms (HCA): uclust & cd-hit & ESPRIT Bayesian clustering: CROP |
Operational taxonomic unit : Phylotype Amplicon sequence variant |
Operational taxonomic unit : Chen, W.; Zhang, C. K.; Cheng, Y.; Zhang, S.; Zhao, H. (2013). "A comparison of methods for clustering 16S rRNA sequences into OTUs.". PLOS ONE. 8 (8): e70837. Bibcode:2013PLoSO...870837C. doi:10.1371/journal.pone.0070837. PMC 3742672. PMID 23967117. |
Optimal discriminant analysis and classification tree analysis : Optimal Discriminant Analysis (ODA) and the related classification tree analysis (CTA) are exact statistical methods that maximize predictive accuracy. For any specific sample and exploratory or confirmatory hypothesis, optimal discriminant analysis (ODA)... |
Optimal discriminant analysis and classification tree analysis : Data mining Decision tree Factor analysis Linear classifier Logit (for logistic regression) Machine learning Multidimensional scaling Perceptron Preference regression Quadratic classifier Statistics |
Optimal discriminant analysis and classification tree analysis : Yarnold, Paul R.; Soltysik, Robert C. (2004). Optimal Data Analysis. American Psychological Association. ISBN 978-1-55798-981-9. Archived from the original on 2008-11-23. Retrieved 2009-09-11. Fisher, R. A. (1936). "The Use of Multiple Measurements in Tax... |
Optimal discriminant analysis and classification tree analysis : LDA tutorial using MS Excel IMSL discriminant analysis function DSCRM, which has many useful mathematical definitions. |
Ordinal regression : In statistics, ordinal regression, also called ordinal classification, is a type of regression analysis used for predicting an ordinal variable, i.e. a variable whose value exists on an arbitrary scale where only the relative ordering between different values is significant. It can be considered an... |
Ordinal regression : Ordinal regression can be performed using a generalized linear model (GLM) that fits both a coefficient vector and a set of thresholds to a dataset. Suppose one has a set of observations, represented by length-p vectors x1 through xn, with associated responses y1 through yn, where each yi is an ord... |
Ordinal regression : In machine learning, alternatives to the latent-variable models of ordinal regression have been proposed. An early result was PRank, a variant of the perceptron algorithm that found multiple parallel hyperplanes separating the various ranks; its output is a weight vector w and a sorted vector of K−... |
Ordinal regression : ORCA (Ordinal Regression and Classification Algorithms) is an Octave/MATLAB framework including a wide set of ordinal regression methods. R packages that provide ordinal regression methods include MASS and Ordinal. |
Ordinal regression : Logistic regression |
Ordinal regression : Agresti, Alan (2010). Analysis of ordinal categorical data. Hoboken, N.J: Wiley. ISBN 978-0470082898. Greene, William H. (2012). Econometric Analysis (Seventh ed.). Boston: Pearson Education. pp. 824–842. ISBN 978-0-273-75356-8. Hardin, James; Hilbe, Joseph (2007). Generalized Linear Models and Ext... |
Probit model : In statistics, a probit model is a type of regression where the dependent variable can take only two values, for example married or not married. The word is a portmanteau, coming from probability + unit. The purpose of the model is to estimate the probability that an observation with particular character... |
Probit model : Suppose a response variable Y is binary, that is it can have only two possible outcomes which we will denote as 1 and 0. For example, Y may represent presence/absence of a certain condition, success/failure of some device, answer yes/no on a survey, etc. We also have a vector of regressors X, which are a... |
Probit model : The suitability of an estimated binary model can be evaluated by counting the number of true observations equaling 1, and the number equaling zero, for which the model assigns a correct predicted classification by treating any estimated probability above 1/2 (or, below 1/2), as an assignment of a predict... |
Probit model : Consider the latent variable model formulation of the probit model. When the variance of ε conditional on x is not constant but dependent on x , then the heteroscedasticity issue arises. For example, suppose y ∗ = β 0 + B 1 x 1 + ε =\beta _+B_x_+\varepsilon and ε ∣ x ∼ N ( 0 , x 1 2 ) ^) where x 1 i... |
Probit model : The probit model is usually credited to Chester Bliss, who coined the term "probit" in 1934, and to John Gaddum (1933), who systematized earlier work. However, the basic model dates to the Weber–Fechner law by Gustav Fechner, published in Fechner (1860), and was repeatedly rediscovered until the 1930s; s... |
Probit model : Generalized linear model Limited dependent variable Logit model Multinomial probit Multivariate probit models Ordered probit and ordered logit model Separation (statistics) Tobit model |
Probit model : Albert, J. H.; Chib, S. (1993). "Bayesian Analysis of Binary and Polychotomous Response Data". Journal of the American Statistical Association. 88 (422): 669–679. doi:10.1080/01621459.1993.10476321. JSTOR 2290350. Amemiya, Takeshi (1985). "Qualitative Response Models". Advanced Econometrics. Oxford: Basi... |
Probit model : Media related to Probit model at Wikimedia Commons Econometrics Lecture (topic: Probit model) on YouTube by Mark Thoma |
Quadratic classifier : In statistics, a quadratic classifier is a statistical classifier that uses a quadratic decision surface to separate measurements of two or more classes of objects or events. It is a more general version of the linear classifier. |
Quadratic classifier : Statistical classification considers a set of vectors of observations x of an object or event, each of which has a known type y. This set is referred to as the training set. The problem is then to determine, for a given new observation vector, what the best class should be. For a quadratic classi... |
Quadratic classifier : Quadratic discriminant analysis (QDA) is closely related to linear discriminant analysis (LDA), where it is assumed that the measurements from each class are normally distributed. Unlike LDA however, in QDA there is no assumption that the covariance of each of the classes is identical. When the n... |
Quadratic classifier : While QDA is the most commonly-used method for obtaining a classifier, other methods are also possible. One such method is to create a longer measurement vector from the old one by adding all pairwise products of individual measurements. For instance, the vector [ x 1 , x 2 , x 3 ] ,\;x_,\;x_] wo... |
Rules extraction system family : The rules extraction system (RULES) family is a family of inductive learning that includes several covering algorithms. This family is used to build a predictive model based on given observation. It works based on the concept of separate-and-conquer to directly induce rules from a given... |
Rules extraction system family : RULES family algorithms are mainly used in data mining to create a model that predicts the actions of a given input features. It goes under the umbrella of inductive learning, which is a machine learning approach. In this type of learning, the agent is usually provided with previous inf... |
Rules extraction system family : To induce the best rules based on a given observation, RULES family start by selecting (separating) a seed example to build a rule, condition by condition. The rule that covers the most positive examples and the least negative examples are chosen as the best rule of the current seed exa... |
Rules extraction system family : Several versions and algorithms have been proposed in RULES family, and can be summarized as follows: RULES-1 [3] is the first version in RULES family and was proposed by prof. Pham and prof. Aksoy in 1995. RULES-2 [4] is an upgraded version of RULES-1, in which every example is studied... |
Rules extraction system family : Covering algorithms, in general, can be applied to any machine learning application field, as long as it supports its data type. Witten, Frank and Hall [20] identified six main fielded applications that are actively used as ML applications, including sales and marketing, judgment decisi... |
Rules extraction system family : Decision Tree WEKA KEEL Machine learning C4.5 algorithm |
Rules extraction system family : [1] L. A. Kurgan, K. J. Cios, and S. Dick, "Highly Scalable and Robust Rule Learner: Performance Evaluation and Comparison," IEEE SYSTEMS, MAN, AND CYBERNETICS—PART B: CYBERNETICS, vol. 36, pp. 32–53, 2006. [2] M. S. Aksoy, "A review of rules family of algorithms," Mathematical and Comp... |
Syntactic pattern recognition : Syntactic pattern recognition, or structural pattern recognition, is a form of pattern recognition in which each object can be represented by a variable-cardinality set of symbolic nominal features. This allows for representing pattern structures, taking into account more complex relatio... |
Syntactic pattern recognition : Grammar induction String matching Hopcroft–Karp algorithm Structural information theory |
Syntactic pattern recognition : Schalkoff, Robert (1992). Pattern recognition - statistical, structural and neural approaches. John Wiley & sons. ISBN 0-471-55238-0. Bunke, Horst (1993). Structural and syntactic pattern recognition, Chen, Pau & Wang (Eds.) Handbook of pattern recognition & computer vision. World Scient... |
Whitening transformation : A whitening transformation or sphering transformation is a linear transformation that transforms a vector of random variables with a known covariance matrix into a set of new variables whose covariance is the identity matrix, meaning that they are uncorrelated and each have variance 1. The tr... |
Whitening transformation : Suppose X is a random (column) vector with non-singular covariance matrix Σ and mean 0 . Then the transformation Y = W X with a whitening matrix W satisfying the condition W T W = Σ − 1 W=\Sigma ^ yields the whitened random vector Y with unit diagonal covariance. If X has non-zero mea... |
Whitening transformation : Whitening a data matrix follows the same transformation as for random variables. An empirical whitening transform is obtained by estimating the covariance (e.g. by maximum likelihood) and subsequently constructing a corresponding estimated whitening matrix (e.g. by Cholesky decomposition). |
Whitening transformation : This modality is a generalization of the pre-whitening procedure extended to more general spaces where X is usually assumed to be a random function or other random objects in a Hilbert space H . One of the main issues of extending whitening to infinite dimensions is that the covariance oper... |
Whitening transformation : An implementation of several whitening procedures in R, including ZCA-whitening and PCA whitening but also CCA whitening, is available in the "whitening" R package published on CRAN. The R package "pfica" allows the computation of high-dimensional whitening representations using basis functio... |
Whitening transformation : Decorrelation Principal component analysis Weighted least squares Canonical correlation Mahalanobis distance (is Euclidean after W. transformation). |
Whitening transformation : http://courses.media.mit.edu/2010fall/mas622j/whiten.pdf The ZCA whitening transformation. Appendix A of Learning Multiple Layers of Features from Tiny Images by A. Krizhevsky. |
Winnow (algorithm) : The winnow algorithm is a technique from machine learning for learning a linear classifier from labeled examples. It is very similar to the perceptron algorithm. However, the perceptron algorithm uses an additive weight-update scheme, while Winnow uses a multiplicative scheme that allows it to perf... |
Winnow (algorithm) : The basic algorithm, Winnow1, is as follows. The instance space is X = n ^ , that is, each instance is described as a set of Boolean-valued features. The algorithm maintains non-negative weights w i for i ∈ , which are initially set to 1, one weight for each feature. When the learner is given a... |
Winnow (algorithm) : In certain circumstances, it can be shown that the number of mistakes Winnow makes as it learns has an upper bound that is independent of the number of instances with which it is presented. If the Winnow1 algorithm uses α > 1 and Θ ≥ 1 / α on a target function that is a k -literal monotone disju... |
Blockmodeling : Blockmodeling is a set or a coherent framework, that is used for analyzing social structure and also for setting procedure(s) for partitioning (clustering) social network's units (nodes, vertices, actors), based on specific patterns, which form a distinctive structure through interconnectivity. It is pr... |
Blockmodeling : A network as a system is composed of (or defined by) two different sets: one set of units (nodes, vertices, actors) and one set of links between the units. Using both sets, it is possible to create a graph, describing the structure of the network. During blockmodeling, the researcher is faced with two p... |
Blockmodeling : Regarding what kind of network is undergoing blockmodeling, a different approach is necessary. Networks can be one–mode or two–mode. In the former all units can be connected to any other unit and where units are of the same type, while in the latter the units are connected only to the unit(s) of a diffe... |
Blockmodeling : Blockmodels (sometimes also block models) are structures in which: vertices (e.g., units, nodes) are assembled within a cluster, with each cluster identified as a vertex; from such vertices a graph can be constructed; combinations of all the links (ties), represented in a block as a single link between ... |
Blockmodeling : Blockmodeling is done with specialized computer programs, dedicated to the analysis of networks or blockmodeling in particular, as: BLOCKS (Tom Snijders), CONCOR, Model (Vladimir Batagelj), Model2 (Vladimir Batagelj), Pajek (Vladimir Batagelj and Andrej Mrvar), R–package Blockmodeling (Aleš Žiberna), St... |
Blockmodeling : Stochastic block model Mathematical sociology Role assignment Multiobjective blockmodeling Blockmodeling linked networks == References == |
Vladimir Batagelj : Vladimir Batagelj (born June 14, 1948 in Idrija, Yugoslavia) is a Slovenian mathematician and an emeritus professor of mathematics at the University of Ljubljana. He is known for his work in discrete mathematics and combinatorial optimization, particularly analysis of social networks and other large... |
Vladimir Batagelj : Vladimir Batagelj completed his Ph.D. at the University of Ljubljana in 1986 under the direction of Tomaž Pisanski. He stayed at the University of Ljubljana as a professor until his retirement, where he was a professor of sociology and statistics, while also being a chair of the Department of Sociol... |
Vladimir Batagelj : Batagelj is particularly known for his work on Pajek, a freely available software for analysis and visualization of large networks. He began work on Pajek in 1996 with Andrej Mrvar, who was then his PhD student. |
Vladimir Batagelj : First prizes for contributions (with Andrej Mrvar) to Graph Drawing Contests in years: 1995, 1996, 1997, 1998, 1999, 2000 and 2005 / Graph Drawing Hall of Fame. In 2007 the book Generalized blockmodeling was awarded the Harrison White Outstanding Book Award by the Mathematical Sociology Section of A... |
Vladimir Batagelj : Vladimir Batagelj, Social Network Analysis, Large-Scale [1]. in R.A. Meyers, ed., Encyclopedia of Complexity and Systems Science, Springer 2009: 8245–8265. Vladimir Batagelj, Complex Networks, Visualization of [2]. in R.A. Meyers, ed., Encyclopedia of Complexity and Systems Science, Springer 2009: 1... |
Vladimir Batagelj : Vladimir Batagelj publications indexed by Google Scholar ResearcherId: B-9105-2008 |
Blockmodeling : Blockmodeling is a set or a coherent framework, that is used for analyzing social structure and also for setting procedure(s) for partitioning (clustering) social network's units (nodes, vertices, actors), based on specific patterns, which form a distinctive structure through interconnectivity. It is pr... |
Blockmodeling : A network as a system is composed of (or defined by) two different sets: one set of units (nodes, vertices, actors) and one set of links between the units. Using both sets, it is possible to create a graph, describing the structure of the network. During blockmodeling, the researcher is faced with two p... |
Blockmodeling : Regarding what kind of network is undergoing blockmodeling, a different approach is necessary. Networks can be one–mode or two–mode. In the former all units can be connected to any other unit and where units are of the same type, while in the latter the units are connected only to the unit(s) of a diffe... |
Blockmodeling : Blockmodels (sometimes also block models) are structures in which: vertices (e.g., units, nodes) are assembled within a cluster, with each cluster identified as a vertex; from such vertices a graph can be constructed; combinations of all the links (ties), represented in a block as a single link between ... |
Blockmodeling : Blockmodeling is done with specialized computer programs, dedicated to the analysis of networks or blockmodeling in particular, as: BLOCKS (Tom Snijders), CONCOR, Model (Vladimir Batagelj), Model2 (Vladimir Batagelj), Pajek (Vladimir Batagelj and Andrej Mrvar), R–package Blockmodeling (Aleš Žiberna), St... |
Blockmodeling : Stochastic block model Mathematical sociology Role assignment Multiobjective blockmodeling Blockmodeling linked networks == References == |
Confirmatory blockmodeling : Confirmatory blockmodeling is a deductive approach in blockmodeling, where a blockmodel (or part of it) is prespecify before the analysis, and then the analysis is fit to this model. When only a part of analysis is prespecify (like individual cluster(s) or location of the block types), it i... |
Deterministic blockmodeling : Deterministic blockmodeling is an approach in blockmodeling that does not assume a probabilistic model, and instead relies on the exact or approximate algorithms, which are used to find blockmodel(s). This approach typically minimizes some inconsistency that can occur with the ideal block ... |
Deterministic blockmodeling : Blockmodeling == References == |
Exploratory blockmodeling : Exploratory blockmodeling is an (inductive) approach (or a group of approaches) in blockmodeling regarding the specification of an ideal blockmodel.: 234 This approach, also known as hypotheses-generating, is the simplest approach, as it "merely involves the definition of the block types per... |
Generalized blockmodeling : In generalized blockmodeling, the blockmodeling is done by "the translation of an equivalence type into a set of permitted block types", which differs from the conventional blockmodeling, which is using the indirect approach. It's a special instance of the direct blockmodeling approach. Gene... |
Generalized blockmodeling : Generalized blockmodeling approach is a direct one, "where the optimal partition(s) is (are) identified based on minimal values of a compatible criterion function defined by the difference between empirical blocks and corresponding ideal blocks". At the same time, the much broader set of blo... |
Generalized blockmodeling : According to Patrick Doreian, the benefits of generalized blockmodeling, are as follows: usage of explicit criterion function, compatible with a given type of equivalence, results to in-built measure of fit, which is integral to the establishment of the blockmodels (in conventional blockmode... |
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