A Bregman Proximal ADMM for NMF with Outliers: Estimating features with missing values and outliers: a Bregman-proximal point algorithm for robust Non-negative Matrix Factorization with application to gene expression analysis

TL;DR

This paper introduces a novel Bregman proximal ADMM algorithm to perform robust non-negative matrix factorization, effectively handling missing data and outliers, with applications in gene expression analysis.

Contribution

It extends NMF to robustly handle missing values and outliers using a Bregman proximal ADMM approach, combining denoising, imputation, and outlier detection.

Findings

Effective in denoising and imputing missing data

Successfully detects outliers in gene expression data

Demonstrates improved feature extraction in biological datasets

Abstract

To extract the relevant features in a given dataset is a difficult task, recently resolved in the non-negative data case with the Non-negative Matrix factorization (NMF) method. The objective of this research work is to extend this method to the case of missing and/or corrupted data due to outliers. To do so, data are denoised, missing values are imputed, and outliers are detected while performing a low-rank non-negative matrix factorization of the recovered matrix. To achieve this goal, a mixture of Bregman proximal methods and of the Augmented Lagrangian scheme are used, in a similar way to the so-called Alternating Direction of Multipliers method. An application to the analysis of gene expression data of patients with bladder cancer is finally proposed.