Cellwise robust and sparse principal component analysis

TL;DR

This paper introduces SCRAMBLE, a scalable, cellwise robust, and sparse PCA method that improves robustness and flexibility in high-dimensional data analysis, outperforming existing approaches in simulations and real-world applications.

Contribution

It presents the first sparse, cellwise robust PCA method using a robust loss and sparsity penalties, with a scalable Riemannian stochastic gradient descent algorithm.

Findings

SCRAMBLE outperforms established methods in robustness tests.

The method is scalable to high-dimensional data.

Applications demonstrate practical advantages in tribology.

Abstract

A first proposal of a sparse and cellwise robust PCA method is presented. Robustness to single outlying cells in the data matrix is achieved by substituting the squared loss function for the approximation error by a robust version. The integration of a sparsity-inducing $L_1$ or elastic net penalty offers additional modeling flexibility. For the resulting challenging optimization problem, an algorithm based on Riemannian stochastic gradient descent is developed, with the advantage of being scalable to high-dimensional data, both in terms of many variables as well as observations. The resulting method is called SCRAMBLE (Sparse Cellwise Robust Algorithm for Manifold-based Learning and Estimation). Simulations reveal the superiority of this approach in comparison to established methods, both in the casewise and cellwise robustness paradigms. Two applications from the field of tribology underline the advantages of a cellwise robust and sparse PCA method.