ALPCAHUS: Subspace Clustering for Heteroscedastic Data

TL;DR

ALPCAHUS is a novel subspace clustering method that accounts for heteroscedastic noise in data, improving clustering accuracy by estimating sample-specific noise variances, demonstrated through simulations and real data.

Contribution

It extends heteroscedastic PCA to subspace clustering, enabling estimation of sample-wise noise variances to enhance clustering in heterogeneous data.

Findings

Outperforms existing clustering algorithms on heteroscedastic data

Effectively estimates sample-specific noise variances

Improves subspace basis estimation accuracy

Abstract

Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction. Various methods have been proposed to extend PCA to the union of subspace (UoS) setting for clustering data that comes from multiple subspaces like K-Subspaces (KSS). However, some applications involve heterogeneous data that vary in quality due to noise characteristics associated with each data sample. Heteroscedastic methods aim to deal with such mixed data quality. This paper develops a heteroscedastic-based subspace clustering method, named ALPCAHUS, that can estimate the sample-wise noise variances and use this information to improve the estimate of the subspace bases associated with the low-rank structure of the data. This clustering algorithm builds on K-Subspaces (KSS) principles by extending the recently proposed heteroscedastic PCA method, named LR-ALPCAH, for clusters with heteroscedastic noise in the UoS setting. Simulations and real-data experiments show the effectiveness of accounting for data heteroscedasticity compared to existing clustering algorithms. Code available at https://github.com/javiersc1/ALPCAHUS.