On spectral clustering under non-isotropic Gaussian mixture models

TL;DR

This paper analyzes the effectiveness of spectral clustering on Gaussian mixture models with complex covariance structures, demonstrating its consistency in high-dimensional settings.

Contribution

It provides a theoretical evaluation of spectral clustering's misclustering probability under non-isotropic Gaussian mixtures, extending understanding of its performance.

Findings

Spectral clustering's misclustering probability is characterized under general covariance structures.

The clustering method is shown to be consistent in high-dimensional regimes.

The analysis applies to Gaussian mixtures with non-isotropic covariances.

Abstract

We evaluate the misclustering probability of a spectral clustering algorithm under a Gaussian mixture model with a general covariance structure. The algorithm partitions the data into two groups based on the sign of the first principal component score. As a corollary of the main result, the clustering procedure is shown to be consistent in a high-dimensional regime.