Cover’s theorem
E641828
Cover’s theorem is a result in statistical pattern recognition stating that data cast nonlinearly into a higher-dimensional space is more likely to be linearly separable than in a lower-dimensional space.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Cover’s theorem canonical | 1 |
Statements (41)
| Predicate | Object |
|---|---|
| instanceOf |
result in statistical pattern recognition
ⓘ
theorem ⓘ |
| addresses | conditions for linear separability ⓘ |
| appearsIn |
literature on statistical learning theory
ⓘ
textbooks on pattern recognition ⓘ |
| appliesTo |
classification problems
ⓘ
pattern classification ⓘ |
| assumes | random nonlinear embedding of data into higher-dimensional space ⓘ |
| assumption | patterns are in general position ⓘ |
| concerns |
number of dichotomies realizable by hyperplanes
ⓘ
randomly placed points in general position ⓘ |
| conclusion | patterns are more likely to be linearly separable in higher-dimensional spaces ⓘ |
| context |
binary classification
ⓘ
multiclass classification via one-vs-rest schemes ⓘ |
| coreIdea | nonlinear mapping to higher-dimensional spaces increases probability of linear separability ⓘ |
| describes | relationship between dimensionality and linear separability of patterns ⓘ |
| field |
machine learning
ⓘ
pattern recognition ⓘ statistical pattern recognition ⓘ |
| formalizes | probability of linear separability as a function of dimensionality and number of patterns ⓘ |
| implies | increased dimensionality can simplify classification boundaries ⓘ |
| influenced |
development of kernel trick
ⓘ
development of support vector machines ⓘ theory of pattern classification in high dimensions ⓘ |
| mathematicalForm | bound on number of linearly separable labelings of points ⓘ |
| motivates |
use of high-dimensional embeddings in classification
ⓘ
use of nonlinear feature maps ⓘ |
| namedAfter | Thomas M. Cover NERFINISHED ⓘ |
| originallyPublishedIn | IEEE Transactions on Electronic Computers NERFINISHED ⓘ |
| originalTitle | Geometrical and Statistical Properties of Systems of Linear Inequalities with Applications in Pattern Recognition NERFINISHED ⓘ |
| publicationYear | 1965 ⓘ |
| relatedTo |
curse of dimensionality
ⓘ
feature space transformation ⓘ kernel methods ⓘ linear separability ⓘ support vector machines NERFINISHED ⓘ |
| statedBy | Thomas M. Cover NERFINISHED ⓘ |
| states | for a complex pattern-classification problem, a nonlinear transformation to a high-dimensional space is likely to convert it into a linearly separable problem ⓘ |
| typeOf | geometric result in high-dimensional spaces ⓘ |
| usedIn |
analysis of high-dimensional feature mappings
ⓘ
design of kernel-based classifiers ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.