Cover’s theorem on the separability of patterns

E641827

result in statistical learning theory theorem

Cover’s theorem on the separability of patterns is a fundamental result in statistical learning theory stating that complex pattern-classification problems are more likely to be linearly separable when data are mapped into a higher-dimensional feature space.

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Statements (45)

Predicate	Object
instanceOf	result in statistical learning theory ⓘ theorem ⓘ
appliesTo	binary classification ⓘ pattern classification problems ⓘ
assumes	patterns are in general position ⓘ patterns are randomly labeled ⓘ
category	theorem in information theory ⓘ theorem in machine learning ⓘ
clarifies	relationship between dimensionality and classification complexity ⓘ
concerns	random dichotomies of finite point sets ⓘ systems of linear inequalities ⓘ
contrastsWith	curse of dimensionality ⓘ
coreIdea	complex pattern-classification problems are more likely to be linearly separable in higher-dimensional spaces ⓘ
describes	probability of linear separability of patterns ⓘ
field	information theory NERFINISHED ⓘ machine learning ⓘ pattern recognition ⓘ statistical learning theory ⓘ
hasConsequence	linear classifiers can be powerful in suitably chosen feature spaces ⓘ nonlinear decision boundaries in input space can correspond to linear boundaries in feature space ⓘ
implies	high-dimensional embeddings can increase separability of classes ⓘ nonlinear transformations can simplify classification ⓘ
inspired	kernel methods ⓘ support vector machines ⓘ
involves	dimensionality of feature space ⓘ linear separability ⓘ mapping data into higher-dimensional feature spaces ⓘ number of patterns ⓘ randomly placed patterns ⓘ
motivates	use of high-dimensional feature spaces ⓘ use of nonlinear feature mappings ⓘ
namedAfter	Thomas M. Cover NERFINISHED ⓘ
oftenIllustratedBy	mapping data to a higher-dimensional space where a hyperplane can separate classes ⓘ
originalArticleTitle	Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition NERFINISHED ⓘ
provides	formula for probability that random dichotomies of points are linearly separable ⓘ
publishedIn	IEEE Transactions on Electronic Computers NERFINISHED ⓘ
relatedTo	VC dimension NERFINISHED ⓘ capacity of linear classifiers ⓘ kernel trick ⓘ perceptron learning ⓘ
states	for a given number of patterns, the probability of linear separability increases with the dimensionality of the feature space up to a point ⓘ
usedIn	analysis of neural network architectures ⓘ design of pattern classifiers ⓘ feature engineering strategies ⓘ
yearProposed	1965 ⓘ

Referenced by (1)

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Thomas M. Cover → knownFor → Cover’s theorem on the separability of patterns ⓘ