# Sparse outlier-robust PCA for multi-source data

arXiv: https://arxiv.org/abs/2407.16299 · HTML: https://mlsanity.com/paper/2407.16299/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 52 references that are in the map.
- First posted on arXiv 23 Jul 2024.

## Builds on (most cited first, 10 of 10)

- [Optimal parameter selection for the alternating direction method of multipliers (ADMM): quadratic problems](https://mlsanity.com/paper/1306.2454/) (2013)
- [Integrated Principal Components Analysis](https://mlsanity.com/paper/1810.00832/) (2018)
- [Sparse PCA: a Geometric Approach](https://mlsanity.com/paper/2210.06590/) (2022)
- [The Minimum Regularized Covariance Determinant estimator](https://mlsanity.com/paper/1701.07086/) (2017)
- [Estimating Multiple Precision Matrices with Cluster Fusion Regularization](https://mlsanity.com/paper/2003.00371/) (2020)
- [Tree-based Node Aggregation in Sparse Graphical Models](https://mlsanity.com/paper/2101.12503/) (2021)
- [Generalized Spherical Principal Component Analysis](https://mlsanity.com/paper/2303.05836/) (2023)
- [A Cluster Elastic Net for Multivariate Regression](https://mlsanity.com/paper/1707.03530/) (2017)
- [Cauchy robust principal component analysis with applications to high-deimensional data sets](https://mlsanity.com/paper/2211.03181/) (2022)
- [Spatially smoothed robust covariance estimation for local outlier detection](https://mlsanity.com/paper/2305.05371/) (2023)

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

- [Worst-case low-rank approximations](https://mlsanity.com/paper/2603.11304/) (2026)

## Abstract (arXiv)

Sparse and outlier-robust Principal Component Analysis (PCA) has been a very active field of research recently. Yet, most existing methods apply PCA to a single dataset whereas multi-source data-i.e. multiple related datasets requiring joint analysis-arise across many scientific areas. We introduce a novel PCA methodology that simultaneously (i) selects important features, (ii) allows for the detection of global sparse patterns across multiple data sources as well as local source-specific patterns, and (iii) is resistant to outliers. To this end, we develop a regularization problem with a penalty that accommodates global-local structured sparsity patterns, and where the ssMRCD estimator is used as plug-in to permit joint outlier-robust analysis across multiple data sources. We provide an efficient implementation of our proposal via the Alternating Direction Method of Multiplier and illustrate its practical advantages in simulation and in applications.