ALPCAH: Subspace Learning for Sample-wise Heteroscedastic Data
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Abstract (arXiv)
Principal component analysis (PCA) is a key tool in the field of data dimensionality reduction. 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 subspace learning method, named ALPCAH, that can estimate the sample-wise noise variances and use this information to improve the estimate of the subspace basis associated with the low-rank structure of the data. Our method makes no distributional assumptions of the low-rank component and does not assume that the noise variances are known. Further, this method uses a soft rank constraint that does not require subspace dimension to be known. Additionally, this paper develops a matrix factorized version of ALPCAH, named LR-ALPCAH, that is much faster and more memory efficient at the cost of requiring subspace dimension to be known or estimated. Simulations and real data experiments show the effectiveness of accounting for data heteroscedasticity compared to existing algorithms. Code available at https://github.com/javiersc1/ALPCAH.
Key facts. Cited by 2 papers in the map (data through 14 Oct 2026). Builds on 11 of its 57 references that are in the map. First posted on arXiv 12 May 2025.
Builds on
11 of 57 references.
References · 11
- 2018Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overviewcited by 160
- 2015Low-rank Solutions of Linear Matrix Equations via Procrustes Flowcited by 97
- 2018Heteroskedastic PCA: Algorithm, Optimality, and Applicationscited by 34
- 2017Robust Subspace Learning: Robust PCA, Robust Subspace Tracking, and Robust Subspace Recoverycited by 25
- 2015Partial Sum Minimization of Singular Values in Robust PCA: Algorithm and Applicationscited by 11
- 2017Permutation methods for factor analysis and PCAcited by 9
- 2021HePPCAT: Probabilistic PCA for Data with Heteroscedastic Noisecited by 8
- 2020Selecting the number of components in PCA via random signflipscited by 6
- 2014Weighted principal component analysis: a weighted covariance eigendecomposition approachcited by 4
- 2023ALPCAH: Sample-wise Heteroscedastic PCA with Tail Singular Value Regularizationcited by 2
- 2023Streaming Heteroscedastic Probabilistic PCA with Missing Datacited by 2
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Citing papers per year: 2025: 1; 2026: 1.
2 papers.