ALPCAHUS: Subspace Clustering for Heteroscedastic Data

2025/05/25 by Javier Salazar Cavazos, Jeffrey A. Fessler, Cavazos, Javier Salazar +3
Computer Science · #Advanced Clustering Algorithms Research #FOS: Computer and information sciences #FOS: Electrical engineering #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Signal Processing (eess.SP) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.2505.18918

openalex publication_date 2025/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Convergence and Recovery Guarantees of the K-Subspaces Method for Subspace Clustering
• Selecting the number of components in PCA via random signflips
• Doubly Stochastic Subspace Clustering
• Optimally Weighted PCA for High-Dimensional Heteroscedastic Data
• Heteroskedastic PCA: Algorithm, Optimality, and Applications
• Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview
• Subspace Clustering using Ensembles of K-Subspaces
• Spectral Clustering with Imbalanced Data
• Robust Subspace Clustering via Thresholding
• Sparse Subspace Clustering: Algorithm, Theory, and Applications
• The 16th Data Release of the Sloan Digital Sky Surveys: First Release from the APOGEE-2 Southern Survey and Full Release of eBOSS Spectra

Related

• Principal component analysis based clustering for high-dimension, low-sample-size data
• Improved Distributed Principal Component Analysis
• Subspace clustering of high-dimensional data: a predictive approach
• Heteroskedastic PCA: Algorithm, Optimality, and Applications
• Scalable Iterative Algorithm for Robust Subspace Clustering