The Laplacian PDF Distance: A Cost Function for Clustering in a Kernel Feature Space

A new distance measure between probability density functions (pdfs) is introduced, which we refer to as the Laplacian pdf distance. The Laplacian pdf distance exhibits a remarkable connection to Mercer kernel based learning theory via the Parzen window technique for density estimation. In a kernel feature space defined by the eigenspectrum of the Laplacian data matrix, this pdf distance is shown to measure the cosine of the angle between cluster mean vectors. The Laplacian data matrix, and hence its eigenspectrum, can be obtained automatically based on the data at hand, by optimal Parzen window selection. We show that the Laplacian pdf distance has an interesting interpretation as a risk function connected to the probability of error.

• Type: Conference
• Year: 2004
• Where: NIPS
• Authors: Robert Jenssen, Deniz Erdogmus, José Carlos Príncipe, Torbjørn Eltoft
• Keywords: Laplacian Data Matrix, Laplacian Pdf Distance, NIPS 2004, NIPS 2007, Parzen Window