Data spectroscopy
Tao Shi, Mikhail Belkin, Bin Yu · 2008
In this paper we develop a spectral framework for estimating mixture distributions, specifically Gaussian mixture models. In physics, spectroscopy is often used for the identification of substances through their spectrum. Treating a kernel function K(x, y) as "light" and the sampled data as "substance", the spectrum of their interaction (eigenvalues and eigenvectors of the kernel matrix K) unveils certain aspects of the underlying parametric distribution p, such as the parameters of a Gaussian mixture. Our approach extends the intuitions and analyses underlying the existing spectral techniques, such as spectral clustering and Kernel Principal Components Analysis (KPCA).