IEEE transactions on information theory, 2005-07, Vol.51 (7), p.2510-2522
2005
Details
- Autor(en) / Beteiligte
- Titel
- On the eigenspectrum of the gram matrix and the generalization error of kernel-PCA
- Ist Teil von
- IEEE transactions on information theory, 2005-07, Vol.51 (7), p.2510-2522
- Ort / Verlag
- New York, NY: IEEE
- Erscheinungsjahr
- 2005
- Link zum Volltext
- Quelle
- IEEE Xplore
- Beschreibungen/Notizen
- In this paper, the relationships between the eigenvalues of the m/spl times/m Gram matrix K for a kernel /spl kappa/(/spl middot/,/spl middot/) corresponding to a sample x/sub 1/,...,x/sub m/ drawn from a density p(x) and the eigenvalues of the corresponding continuous eigenproblem is analyzed. The differences between the two spectra are bounded and a performance bound on kernel principal component analysis (PCA) is provided showing that good performance can be expected even in very-high-dimensional feature spaces provided the sample eigenvalues fall sufficiently quickly.
- Sprache
- Englisch
- Identifikatoren
- ISSN: 0018-9448eISSN: 1557-9654DOI: 10.1109/TIT.2005.850052Titel-ID: cdi_ieee_primary_1459055
- Format
- –
- Schlagworte
- Algorithm design and analysis, Algorithms, Applied sciences, Computer science, Concentration bounds, Density, Detection, estimation, filtering, equalization, prediction, Eigen values, Eigenvalues, Eigenvalues and eigenfunctions, Errors, Exact sciences and technology, Gaussian processes, Gram matrices, Information theory, Information, signal and communications theory, Kernel, kernel methods, Kernels, Machine learning, Principal component analysis, Principal components analysis, principal components analysis (PCA), Rademacher complexity, Signal and communications theory, Signal, noise, Spectra, spectra of random matrices, Statistical learning, statistical learning theory, Support vector machines, Symmetric matrices, Telecommunications and information theory