ALPCAH: Subspace Learning for Sample-wise Heteroscedastic Data
This addresses a specific issue in data analysis for applications with mixed data quality, offering an incremental improvement over existing heteroscedastic methods.
The paper tackles the problem of dimensionality reduction for heteroscedastic data with sample-wise noise variances, developing ALPCAH and LR-ALPCAH methods that estimate noise variances and improve subspace basis estimation without distributional assumptions or known subspace dimension, showing effectiveness in simulations and real data experiments.
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.