Local spectral clustering for heterogeneous clustering structures

2026-07-31

AI Summary

Traditional clustering methods struggle with high-dimensional data where different subsets of features correspond to distinct cluster structures and some features are uninformative. This work proposes a local spectral clustering framework that formulates local clustering as a “clustering of clusterings” problem. It groups features via a label-invariant clustering matrix and constructs feature-specific Gaussian kernel similarity matrices based on a heterogeneous sub-Gaussian mixture model. The approach jointly identifies homogeneous feature groups and their corresponding sample partitions without requiring explicit likelihood evaluation or Bayesian inference. Experiments demonstrate that the method effectively uncovers complex heterogeneous clustering structures in both synthetic and real-world datasets, exhibiting superior performance and practical utility.

Abstract

Classical clustering methods typically assume that all informative features support a single latent partition of the observations. This assumption can be overly restrictive for modern high-dimensional data, where different subsets of features may encode distinct notions of similarity and induce heterogeneous sample partitions, while some features may contain no meaningful clustering information. We develop a frequentist framework for local clustering that simultaneously identifies feature groups and estimates the sample clustering structure associated with each group. Our approach represents each sample partition by a label-invariant clustering matrix and groups features according to their shared clustering structures, thereby reformulating local clustering as a feature-grouping, or clustering-of-clusterings, problem. Under a heterogeneous sub-Gaussian mixture model, we construct feature-specific Gaussian-kernel similarity matrices and propose a local spectral clustering procedure based on a clustering-matrix optimization criterion. The proposed method avoids explicit likelihood specification and Bayesian posterior computation, accommodates heterogeneous feature distributions, and permits the presence of non-informative features. Extensive simulations and applications further demonstrate the practical utility and superiority of the proposed approach.

Problem

• heterogeneous clustering
• local spectral clustering
• feature grouping
• non-informative features
• clustering-of-clusterings

Innovation

• local spectral clustering
• heterogeneous clustering
• feature grouping
• clustering-of-clusterings
• sub-Gaussian mixture model