Data Spectroscopy: Learning Mixture Models using Eigenspaces of Convolution Operators
published: Aug. 1, 2008, recorded: July 2008, views: 462
Report a problem or upload filesIf you have found a problem with this lecture or would like to send us extra material, articles, exercises, etc., please use our ticket system to describe your request and upload the data.
Enter your e-mail into the 'Cc' field, and we will keep you updated with your request's status.
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). We construct algorithms to estimate parameters of Gaussian mixture models, including the number of mixture components, their means and covariance matrices, which are important in many practical applications. We provide a theoretical framework and show encouraging experimental results.
Link this pageWould you like to put a link to this lecture on your homepage?
Go ahead! Copy the HTML snippet !