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

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 ℓ2,0-norm constraint (NMF_ℓ20), where the basis matrix W is constrained by the ℓ2,0-norm, such that W has a row-sparsity pattern with feature selection. It is a challenge to solve the model, because the ℓ2,0-norm is non-convex and non-smooth. Fortunately, we prove that the ℓ2,0-norm satisfies the Kurdyka-Lojasiewicz property. Based on the finding, we present a proximal alternating linearized minimization algorithm and its monotone accelerated version to solve the NMF_ℓ20 model. In addition, we also present a orthogonal NMF with ℓ2,0-norm constraint (ONMF_ℓ20) to enhance the clustering performance by using a non-negative orthogonal constraint. We propose an efficient algorithm to solve ONMF_ℓ20 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.