Cover’s theorem on the separability of patterns
E641827
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| 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]
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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.
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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.
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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
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 ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Cover’s theorem on the separability of patterns Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.