Spectral clustering algorithm for the allometric extension model

TL;DR

This paper analyzes the spectral clustering algorithm's theoretical properties under the allometric extension model, relaxing the restrictive homoscedasticity assumption and establishing error bounds and consistency in high-dimensional data.

Contribution

It introduces a non-asymptotic error bound for spectral clustering under the allometric extension model, extending theoretical understanding beyond traditional assumptions.

Findings

Provides a non-asymptotic error bound for spectral clustering.

Establishes the consistency of spectral clustering in high-dimensional settings.

Relaxes the homoscedasticity assumption in theoretical analysis.

Abstract

The spectral clustering algorithm is often used as a binary clustering method for unclassified data by applying the principal component analysis. To study theoretical properties of the algorithm, the assumption of conditional homoscedasticity is often supposed in existing studies. However, this assumption is restrictive and often unrealistic in practice. Therefore, in this paper, we consider the allometric extension model, that is, the directions of the first eigenvectors of two covariance matrices and the direction of the difference of two mean vectors coincide, and we provide a non-asymptotic bound of the error probability of the spectral clustering algorithm for the allometric extension model. As a byproduct of the result, we obtain the consistency of the clustering method in high-dimensional settings.