ALPCAHUS: Subspace Clustering for Heteroscedastic Data
This addresses the challenge of handling heterogeneous data quality in subspace clustering for applications like signal processing or computer vision, but it is incremental as it builds on existing K-Subspaces and heteroscedastic PCA methods.
The paper tackles the problem of clustering data from multiple subspaces with heteroscedastic noise by developing ALPCAHUS, a method that estimates sample-wise noise variances to improve subspace basis estimation, showing effectiveness in simulations and real-data experiments compared to existing algorithms.
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 come 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-focused 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.