# eRPCA: Robust Principal Component Analysis for Exponential Family Distributions

arXiv: https://arxiv.org/abs/2310.19787 · HTML: https://mlsanity.com/paper/2310.19787/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 46 references that are in the map.
- First posted on arXiv 30 Oct 2023.

## Builds on (most cited first, 9 of 9)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Plug-and-Play ADMM for Image Restoration: Fixed Point Convergence and Applications](https://mlsanity.com/paper/1605.01710/) (2016)
- [Personalized PCA: Decoupling Shared and Unique Features](https://mlsanity.com/paper/2207.08041/) (2022)
- [What Does a One-Bit Quanta Image Sensor Offer?](https://mlsanity.com/paper/2208.10350/) (2022)
- [Poisson Matrix Recovery and Completion](https://mlsanity.com/paper/1504.05229/) (2015)
- [Bayesian Uncertainty Quantification for Low-Rank Matrix Completion](https://mlsanity.com/paper/2101.01299/) (2021)
- [A graphical multi-fidelity Gaussian process model, with application to emulation of heavy-ion collisions](https://mlsanity.com/paper/2108.00306/) (2021)
- [Additive Multi-Index Gaussian process modeling, with application to multi-physics surrogate modeling of the quark-gluon plasma](https://mlsanity.com/paper/2306.07299/) (2023)
- [ePCA: High Dimensional Exponential Family PCA](https://mlsanity.com/paper/1611.05550/) (2016)

## Abstract (arXiv)

Robust Principal Component Analysis (RPCA) is a widely used method for recovering low-rank structure from data matrices corrupted by significant and sparse outliers. These corruptions may arise from occlusions, malicious tampering, or other causes for anomalies, and the joint identification of such corruptions with low-rank background is critical for process monitoring and diagnosis. However, existing RPCA methods and their extensions largely do not account for the underlying probabilistic distribution for the data matrices, which in many applications are known and can be highly non-Gaussian. We thus propose a new method called Robust Principal Component Analysis for Exponential Family distributions (eRPCA), which can perform the desired decomposition into low-rank and sparse matrices when such a distribution falls within the exponential family. We present a novel alternating direction method of multiplier optimization algorithm for efficient eRPCA decomposition. The effectiveness of eRPCA is then demonstrated in two applications: the first for steel sheet defect detection, and the second for crime activity monitoring in the Atlanta metropolitan area.