Individual-heterogeneous sub-Gaussian Mixture Models

TL;DR

This paper introduces a flexible mixture model that accounts for individual heterogeneity in data, and proposes a spectral clustering method that achieves exact recovery even in high-dimensional, heterogeneous settings.

Contribution

The paper develops the individual-heterogeneous sub-Gaussian mixture model and a spectral method that guarantees exact clustering under mild conditions.

Findings

Spectral method achieves exact recovery of cluster labels.

Method outperforms existing clustering algorithms on synthetic and real data.

Effective in high-dimensional settings with heterogeneity.

Abstract

The classical Gaussian mixture model assumes homogeneity within clusters, an assumption that often fails in real-world data where observations naturally exhibit varying scales or intensities. To address this, we introduce the individual-heterogeneous sub-Gaussian mixture model, a flexible framework that assigns each observation its own heterogeneity parameter, thereby explicitly capturing the heterogeneity inherent in practical applications. Built upon this model, we propose an efficient spectral method that provably achieves exact recovery of the true cluster labels under mild separation conditions, even in high-dimensional settings where the number of features far exceeds the number of samples. Numerical experiments on both synthetic and real data demonstrate that our method consistently outperforms existing clustering algorithms, including those designed for classical Gaussian mixture models.