On the Eigenspectrum of the Gram Matrix and Its Relationship to the Operator Eigenspectrum

Abstract. In this paper we analyze the relationships between the eigenvalues of the m × m Gram matrix K for a kernel k(·, ·) corresponding to a sample x1, . . . , xm drawn from a density p(x) and the eigenvalues of the corresponding continuous eigenproblem. We bound the differences between the two spectra and provide a performance bound on kernel PCA.

• Type: Conference
• Year: 2002
• Where: ALT
• Authors: John Shawe-Taylor, Christopher K. I. Williams, Nello Cristianini, Jaz S. Kandola
• Keywords: ALT 2002, Corresponding Continuous Eigenproblem, Kernel PCA, Machine Learning