Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
143 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Weighted Cheeger and Buser Inequalities, with Applications to Clustering and Cutting Probability Densities (2004.09589v3)

Published 20 Apr 2020 in cs.LG, cs.DM, and stat.ML

Abstract: In this paper, we show how sparse or isoperimetric cuts of a probability density function relate to Cheeger cuts of its principal eigenfunction, for appropriate definitions of sparse cut' andprincipal eigenfunction'. We construct these appropriate definitions of sparse cut and principal eigenfunction in the probability density setting. Then, we prove Cheeger and Buser type inequalities similar to those for the normalized graph Laplacian of Alon-Milman. We demonstrate that no such inequalities hold for most prior definitions of sparse cut and principal eigenfunction. We apply this result to generate novel algorithms for cutting probability densities and clustering data, including a principled variant of spectral clustering.

Citations (2)

Summary

We haven't generated a summary for this paper yet.