The Laplacian PDF Distance: A Cost Function for Clustering in a Kernel Feature Space
Abstract
A new distance measure between probability density functions (pdfs) is introduced, which we refer to as the Laplacian pdf dis- tance. The Laplacian pdf distance exhibits a remarkable connec- tion 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 dis- tance is shown to measure the cosine of the angle between cluster mean vectors. The Laplacian data matrix, and hence its eigenspec- trum, 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.
Cite
Text
Jenssen et al. "The Laplacian PDF Distance: A Cost Function for Clustering in a Kernel Feature Space." Neural Information Processing Systems, 2004.Markdown
[Jenssen et al. "The Laplacian PDF Distance: A Cost Function for Clustering in a Kernel Feature Space." Neural Information Processing Systems, 2004.](https://mlanthology.org/neurips/2004/jenssen2004neurips-laplacian/)BibTeX
@inproceedings{jenssen2004neurips-laplacian,
title = {{The Laplacian PDF Distance: A Cost Function for Clustering in a Kernel Feature Space}},
author = {Jenssen, Robert and Erdogmus, Deniz and Principe, Jose and Eltoft, Torbjørn},
booktitle = {Neural Information Processing Systems},
year = {2004},
pages = {625-632},
url = {https://mlanthology.org/neurips/2004/jenssen2004neurips-laplacian/}
}