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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All labels observed (2)

Label	Occurrences
Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition	2
Cover’s theorem on the separability of patterns canonical	1

How this entity was disambiguated

This entity first appeared as the object of triple T7115739 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Cover’s theorem on the separability of patterns
Context triple: [Thomas M. Cover, knownFor, Cover’s theorem on the separability of patterns]

A. Blum complexity measures
Blum complexity measures are a formal framework in computational complexity theory that rigorously define and compare the resource usage (such as time or space) of algorithms via axiomatic conditions.
B. Probably Approximately Correct learning (PAC learning)
Probably Approximately Correct (PAC) learning is a foundational framework in computational learning theory that formalizes what it means for an algorithm to efficiently learn a concept from examples with high probability and small error.
C. Wozencraft ensemble in coding theory
The Wozencraft ensemble in coding theory is a family of randomly constructed linear codes introduced by John Wozencraft that plays a key role in analyzing the performance limits of coding schemes, particularly for achieving capacity on noisy channels.
D. P, NP, and NP-Completeness: The Basics of Complexity Theory
"P, NP, and NP-Completeness: The Basics of Complexity Theory" is a foundational textbook by Oded Goldreich that introduces the core concepts, problems, and techniques of computational complexity theory, with a focus on the classes P, NP, and NP-complete problems.
E. Cascade-Correlation learning architecture
Cascade-Correlation learning architecture is a neural network training method that incrementally builds its own topology by adding new hidden units during learning to improve performance.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Cover’s theorem on the separability of patterns
Target entity description: 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.

A. Blum complexity measures
Blum complexity measures are a formal framework in computational complexity theory that rigorously define and compare the resource usage (such as time or space) of algorithms via axiomatic conditions.
B. Probably Approximately Correct learning (PAC learning)
Probably Approximately Correct (PAC) learning is a foundational framework in computational learning theory that formalizes what it means for an algorithm to efficiently learn a concept from examples with high probability and small error.
C. Wozencraft ensemble in coding theory
The Wozencraft ensemble in coding theory is a family of randomly constructed linear codes introduced by John Wozencraft that plays a key role in analyzing the performance limits of coding schemes, particularly for achieving capacity on noisy channels.
D. P, NP, and NP-Completeness: The Basics of Complexity Theory
"P, NP, and NP-Completeness: The Basics of Complexity Theory" is a foundational textbook by Oded Goldreich that introduces the core concepts, problems, and techniques of computational complexity theory, with a focus on the classes P, NP, and NP-complete problems.
E. Cascade-Correlation learning architecture
Cascade-Correlation learning architecture is a neural network training method that incrementally builds its own topology by adding new hidden units during learning to improve performance.
F. None of above. chosen

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 ⓘ 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 ⓘ
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 ⓘ linked to: Cover’s theorem on the separability of patterns
provides	formula for probability that random dichotomies of points are linearly separable ⓘ
publishedIn	IEEE Transactions on Electronic Computers ⓘ linked to: IEEE Transactions on Computers
relatedTo	VC dimension ⓘ 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 ⓘ

How these facts were elicited

Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

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

Cover’s theorem on the separability of patterns → originalArticleTitle → Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition ⓘ

linked to: Cover’s theorem on the separability of patterns

Cover’s theorem → originalTitle → Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition ⓘ