# ALPCAHUS: Subspace Clustering for Heteroscedastic Data

arXiv: https://arxiv.org/abs/2505.18918 · HTML: https://mlsanity.com/paper/2505.18918/

## Key facts

- Cited by 1 papers 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 (most cited first, 12 of 12)

- [Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview](https://mlsanity.com/paper/1809.09573/) (2018)
- [Heteroskedastic PCA: Algorithm, Optimality, and Applications](https://mlsanity.com/paper/1810.08316/) (2018)
- [Robust Subspace Clustering via Thresholding](https://mlsanity.com/paper/1307.4891/) (2013)
- [Doubly Stochastic Subspace Clustering](https://mlsanity.com/paper/2011.14859/) (2020)
- [Convergence and Recovery Guarantees of the K-Subspaces Method for Subspace Clustering](https://mlsanity.com/paper/2206.05553/) (2022)
- [HePPCAT: Probabilistic PCA for Data with Heteroscedastic Noise](https://mlsanity.com/paper/2101.03468/) (2021)
- [Subspace Clustering using Ensembles of K-Subspaces](https://mlsanity.com/paper/1709.04744/) (2017)
- [Selecting the number of components in PCA via random signflips](https://mlsanity.com/paper/2012.02985/) (2020)
- [ALPCAH: Sample-wise Heteroscedastic PCA with Tail Singular Value Regularization](https://mlsanity.com/paper/2307.02745/) (2023)
- [ALPCAH: Subspace Learning for Sample-wise Heteroscedastic Data](https://mlsanity.com/paper/2505.07272/) (2025)
- [Spectral Clustering with Imbalanced Data](https://mlsanity.com/paper/1309.2303/) (2013)
- [Smooth optimization using global and local low-rank regularizers](https://mlsanity.com/paper/2505.06073/) (2025)

## Built on by (most cited first, 1 of 1)

- [PET-TURTLE: Deep Unsupervised Support Vector Machines for Imbalanced Data Clusters](https://mlsanity.com/paper/2601.03237/) (2026)

## 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.