ALPCAHUS: Subspace Clustering for Heteroscedastic Data
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Abstract (arXiv)
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.
Key facts. Cited by 1 paper in the map (data through 14 Oct 2026). Builds on 12 of its 68 references that are in the map. First posted on arXiv 25 May 2025.
Builds on
12 of 68 references.
References · 12
- 2018Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overviewcited by 160
- 2018Heteroskedastic PCA: Algorithm, Optimality, and Applicationscited by 34
- 2013Robust Subspace Clustering via Thresholdingcited by 16
- 2020Doubly Stochastic Subspace Clusteringcited by 14
- 2022Convergence and Recovery Guarantees of the K-Subspaces Method for Subspace Clusteringcited by 9
- 2021HePPCAT: Probabilistic PCA for Data with Heteroscedastic Noisecited by 8
- 2017Subspace Clustering using Ensembles of K-Subspacescited by 7
- 2020Selecting the number of components in PCA via random signflipscited by 6
- 2023ALPCAH: Sample-wise Heteroscedastic PCA with Tail Singular Value Regularizationcited by 2
- 2025ALPCAH: Subspace Learning for Sample-wise Heteroscedastic Datacited by 2
- 2013Spectral Clustering with Imbalanced Datacited by 1
- 2025Smooth optimization using global and local low-rank regularizerscited by 1
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Citing papers per year: 2026: 1.
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