Structured Sparse Non-negative Matrix Factorization with L20-Norm for scRNA-seq Data Analysis

TL;DR

This paper introduces a novel sparse NMF model with an $ ext{l}_{2,0}$-norm constraint for improved feature selection and clustering in high-dimensional scRNA-seq data, supported by efficient algorithms and theoretical guarantees.

Contribution

It proposes the first $ ext{l}_{2,0}$-norm constrained NMF model with provable properties and develops algorithms for sparse, orthogonal NMF tailored for biological data analysis.

Findings

The proposed methods outperform existing approaches in numerical experiments.

The algorithms effectively handle high-dimensional scRNA-seq data.

The $ ext{l}_{2,0}$-norm constraint enhances feature selection and clustering accuracy.

Abstract

Non-negative matrix factorization (NMF) is a powerful tool for dimensionality reduction and clustering. Unfortunately, the interpretation of the clustering results from NMF is difficult, especially for the high-dimensional biological data without effective feature selection. In this paper, we first introduce a row-sparse NMF with $\ell_{2,0}$-norm constraint (NMF_$\ell_{20}$), where the basis matrix $W$ is constrained by the $\ell_{2,0}$-norm, such that $W$ has a row-sparsity pattern with feature selection. It is a challenge to solve the model, because the $\ell_{2,0}$-norm is non-convex and non-smooth. Fortunately, we prove that the $\ell_{2,0}$-norm satisfies the Kurdyka-\L{ojasiewicz} property. Based on the finding, we present a proximal alternating linearized minimization algorithm and its monotone accelerated version to solve the NMF_$\ell_{20}$ model. In addition, we also present a orthogonal NMF with $\ell_{2,0}$-norm constraint (ONMF_$\ell_{20}$) to enhance the clustering performance by using a non-negative orthogonal constraint. We propose an efficient algorithm to solve ONMF_$\ell_{20}$ by transforming it into a series of constrained and penalized matrix factorization problems. The results on numerical and scRNA-seq datasets demonstrate the efficiency of our methods in comparison with existing methods.