Name
Abstract | ||
|---|---|---|
Motivated by statistical learning theoretic treatment of principal component analysis, we are concerned with the set of points in ℝd that are within a certain distance from a k-dimensional affine subspace. We prove that the VC dimension of the class of such sets is within a constant factor of (k+1)(d−k+1), and then discuss the distribution of eigenvalues of a data covariance matrix by using our bounds of the VC dimensions and Vapnik’s statistical learning theory. In the course of the upper bound proof, we provide a simple proof of Warren’s bound of the number of sign sequences of real polynomials. |
Year | DOI | Venue |
|---|---|---|
2010 | 10.1007/s00454-009-9236-5 | Discrete & Computational Geometry |
Keywords | Field | DocType |
VC dimensions,Principal component analysis,Warren’s bound | Statistical learning theory,Discrete mathematics,VC dimension,Combinatorics,Affine space,Polynomial,Upper and lower bounds,Statistical learning,Mathematics,Eigenvalues and eigenvectors,Principal component analysis | Journal |
Volume | Issue | ISSN |
44 | 3 | 0179-5376 |
Citations | PageRank | References |
2 | 0.51 | 2 |
Authors | ||
4 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Yohji Akama | 1 | 79 | 12.89 |
| Kei Irie | 2 | 6 | 1.08 |
| Akitoshi Kawamura | 3 | 102 | 15.84 |
| Yasutaka Uwano | 4 | 2 | 0.51 |