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help improve the lead of this article if you can august 2026 learn how and when to remove this message when classification is performed by a computer statistical methods are normally used to develop the algorithm often the individual observations are analyzed into a set of quantifiable properties known variously as explanatory variables or features these properties may variously be categorical e g a b ab or o for blood type ordinal e g large medium or small integer valued e g the number of occurrences of a particular word in an email or real valued e g a measurement of blood pressure other classifiers work by comparing observations to previous observations by means of a similarity or distance function an algorithm that implements classification especially in a concrete implementation is known as a classifier the term classifier sometimes also refers to the mathematical function implemented by a classification algorithm that maps input data to a category terminology across fields is quite varied in statistics where classification is often done with logistic regression or a similar procedure the properties of observations are termed explanatory variables or independent variables regressors etc and the categories to be predicted are known as outcomes which are considered to be possible values of the dependent variable in machine learning the observations are often known as instances the explanatory variables are termed features grouped into a feature vector and the possible categories to be predicted are classes other fields may use different terminology e g in community ecology the term classification normally refers to cluster analysis relation to other problems edit classification and clustering are examples of the more general problem of pattern recognition which is the assignment of some sort of output value to a given input value other examples are regression which assigns a real valued output to each input sequence labeling which assigns a class to each member of a sequence of values for example part of speech tagging which assigns a part of speech to each word in an input sentence parsing which assigns a parse tree to an input sentence describing the syntactic structure of the sentence etc a common subclass of classification is probabilistic classification algorithms of this nature use statistical inference to find the best class for a given instance unlike other algorithms which simply output a best class probabilistic algorithms output a probability of the instance being a member of each of the possible classes the best class is normally then selected as the one with the highest probability however such an algorithm has numerous advantages over non probabilistic classifiers it can output a confidence value associated with its choice in general a classifier that can do this is known as a confidence weighted classifier correspondingly it can abstain when its confidence of choosing any particular output is too low because of the probabilities which are generated probabilistic classifiers can be more effectively incorporated into larger machine learning tasks in a way that partially or completely avoids the problem of error propagation frequentist procedures edit early work on statistical classification was undertaken by fisher 1 2 in the context of two group problems leading to fisher s linear discriminant function as the rule for assigning a group to a new observation 3 this early work assumed that data values within each of the two groups had a multivariate normal distribution the extension of this same context to more than two groups has also been considered with a restriction imposed that the classification rule should be linear 3 4 later work for the multivariate normal distribution allowed the classifier to be nonlinear 5 several classification rules can be derived based on different adjustments of the mahalanobis distance with a new observation being assigned to the group whose centre has the lowest adjusted distance from the observation bayesian procedures edit unlike frequentist procedures bayesian classification procedures provide a natural way of taking into account any available information about the relative sizes of the different groups within the overall population 6 bayesian procedures tend to be computationally expensive and in the days before markov chain monte carlo computations were developed approximations for bayesian clustering rules were devised 7 some bayesian procedures involve the calculation of group membership probabilities these provide a more informative outcome than a simple attribution of a single group label to each new observation binary and multiclass classification edit classification can be thought of as two separate problems binary classification and multiclass classification in binary classification a better understood task only two classes are involved whereas multiclass classification involves assigning an object to one of several classes 8 since many classification methods have been developed specifically for binary classification multiclass classification often requires the combined use of multiple binary classifiers feature vectors edit main article feature vector most algorithms describe an individual instance whose category is to be predicted using a feature vector of individual measurable properties of the instance each property is termed a feature also known in statistics as an explanatory variable or independent variable although features may or may not be statistically independent features may variously be binary e g on or off categorical e g a b ab or o for blood type ordinal e g large medium or small integer valued e g the number of occurrences of a particular word in an email or real valued e g a measurement of blood pressure if the instance is an image the feature values might correspond to the pixels of an image if the instance is a piece of text the feature values might be occurrence frequencies of different words some algorithms work only in terms of discrete data and require that real valued or integer valued data be discretized into groups e g less than 5 between 5 and 10 or greater than 10 linear classifiers edit main article linear classifier a large number of algorithms for classification can be phrased in terms of a linear function that assigns a score to each possible category k by combining the feature vector of an instance with a vector of weights using a dot product the predicted category is the one with the highest score this type of score function is known as a linear predictor function and has the following general form score x i k β k x i displaystyle operatorname score mathbf x _ i k boldsymbol beta _ k cdot mathbf x _ i where x i is the feature vector for instance i β k is the vector of weights corresponding to category k and score x i k is the score associated with assigning instance i to category k in discrete choice theory where instances represent people and categories represent choices the score is considered the utility associated with person i choosing category k algorithms with this basic setup are known as linear classifiers what distinguishes them is the procedure for determining training the optimal weights coefficients and the way that the score is interpreted examples of such algorithms include logistic regression statistical model for a binary dependent variable multinomial logistic regression regression for more than two discrete outcomes probit regression statistical regression where the dependent variable can take only two values pages displaying short descriptions of redirect targets the perceptron algorithm support vector machine set of methods for supervised statistical learning linear discriminant analysis method used in statistics pattern recognition and other fields algorithms edit since no single form of classification is appropriate for all data sets a large toolkit of classification algorithms has been developed the most commonly used include 9 artificial neural networks computational model used in machine learning pages displaying short descriptions of redirect targets boosting machine learning ensemble learning method random forest tree based ensemble machine learning methods genetic programming evolving computer programs with techniques analogous to natural genetic processes gene expression programming evolutionary algorithm multi expression programming linear genetic programming kernel estimation concept in statistics pages displaying short descriptions of redirect targets k nearest neighbor non parametric classification method pages displaying short descriptions of redirect targets learning vector quantization linear classifier statistical classification in machine learning fisher s linear discriminant method used in statistics pattern recognition and other fields pages displaying short descriptions of redirect targets logistic regression statistical model for a binary dependent variable naive bayes classifier probabilistic classification algorithm perceptron algorithm for supervised learning of binary classifiers quadratic classifier statistical classifier in machine learning support vector machine set of methods for supervised statistical learning least squares support vector machine choices between different possible algorithms are frequently made on the basis of quantitative evaluation of accuracy application domains edit see also cluster analysis applications classification has many applications in some of these it is employed as a data mining procedure while in others more detailed statistical modeling is undertaken biological classification the science of identifying describing defining and naming groups of biological organisms biometric metrics related to human characteristics pages displaying short descriptions of redirect targets identification computer vision computerized information extraction from images medical image analysis and medical imaging technique and process of creating visual representations of the interior of a body optical character recognition computer recognition of visual text video tracking locating a moving object by analyzing frames of a video credit scoring numerical expression representing a person s creditworthiness pages displaying short descriptions of redirect targets document classification process of categorizing documents drug discovery and development process of bringing a new pharmaceutical drug to the market toxicogenomics branch of toxicology and genomics quantitative structure activity relationship predictive chemical model pages displaying short descriptions of redirect targets geostatistics branch of statistics focusing on spatial data sets handwriting recognition ability of a computer to receive and interpret intelligible handwritten input internet search engines micro array classification pattern recognition automated recognition of patterns and regularities in data recommender system system to predict users preferences speech recognition automatic conversion of spoken language into text statistical natural language processing processing of natural language by a computer pages displaying short descriptions of redirect targets this article includes a list of general references but lacks sufficient corresponding inline citations please help improve this article by introducing more precise citations january 2010 learn how and when to remove this message see also edit mathematics portal artificial intelligence intelligence in machines binary classification dividing things between two categories multiclass classification problem in machine learning and statistical classification class membership probabilities machine learning problem pages displaying short descriptions of redirect targets classification rule compound term processing confusion matrix table layout for visualizing performance also called an error matrix data mining process of analyzing large data sets data warehouse centralized storage of knowledge fuzzy logic system for reasoning about vagueness information retrieval finding information for an information need list of datasets for machine learning research machine learning subset of artificial intelligence recommender system system to predict users preferences references edit wikimedia commons has media related to statistical classification fisher r a 1936 the use of multiple measurements in taxonomic problems annals of eugenics 7 2 179 188 doi 10 1111 j 1469 1809 1936 tb02137 x hdl 2440 15227 fisher r a 1938 the statistical utilization of multiple measurements annals of eugenics 8 4 376 386 doi 10 1111 j 1469 1809 1938 tb02189 x hdl 2440 15232 1 2 gnanadesikan r 1977 methods for statistical data analysis of multivariate observations wiley isbn 0 471 30845 5 p 83 86 rao c r 1952 advanced statistical methods in multivariate analysis wiley section 9c anderson t w 1958 an introduction to multivariate statistical analysis wiley binder d a 1978 bayesian cluster analysis biometrika 65 31 38 doi 10 1093 biomet 65 1 31 binder david a 1981 approximations to bayesian clustering rules biometrika 68 275 285 doi 10 1093 biomet 68 1 275 har peled s roth d zimak d 2003 constraint classification for multiclass classification and ranking in becker b thrun s obermayer k eds advances in neural information processing systems 15 proceedings of the 2002 conference mit press isbn 0 262 02550 7 a tour of the top 10 algorithms for machine learning newbies built in 2018 01 20 retrieved 2019 06 10 v t e statistics outline index descriptive statistics continuous data center mean arithmetic arithmetic geometric contraharmonic cubic generalized power geometric harmonic heronian heinz lehmer median mode dispersion average absolute deviation coefficient of variation interquartile range percentile range standard deviation variance shape central limit theorem moments kurtosis l moments skewness count data index of dispersion summary tables contingency table frequency distribution grouped data dependence partial correlation pearson product moment correlation rank correlation kendall s τ spearman s ρ scatter plot graphics bar chart biplot box plot control chart correlogram fan chart forest plot histogram pie chart q q plot radar chart run chart scatter plot stem and leaf display violin plot heatmap scatter plot matrix ecdf plot line chart statistical data processing transformations data transformation log transformation power transform box cox transformation yeo johnson transformation variance stabilizing transformation anscombe transform fisher transformation scaling and normalization feature scaling normalization standardization z score min max normalization unit vector normalization data cleaning data cleaning outlier winsorizing truncation missing data data reduction dimensionality reduction principal component analysis factor analysis time series preprocessing differencing detrending seasonal adjustment stationarity transformation data collection study design effect size mis...
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