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Non-negative matrix factorization (NMF) is a powerful tool for dimensionalityreduction and clustering. Unfortunately, the interpretation of the clusteringresults from NMF is difficult, especially for the high-dimensional biologicaldata without effective feature selection. In this paper, we first introduce arow-sparse NMF with $\ell_{2,0}$-norm constraint (NMF_$\ell_{20}$), where thebasis matrix $W$ is constrained by the $\ell_{2,0}$-norm, such that $W$ has arow-sparsity pattern with feature selection. It is a challenge to solve themodel, 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 linearizedminimization algorithm and its monotone accelerated version to solve theNMF_$\ell_{20}$ model. In addition, we also present a orthogonal NMF with$\ell_{2,0}$-norm constraint (ONMF_$\ell_{20}$) to enhance the clusteringperformance by using a non-negative orthogonal constraint. We propose anefficient algorithm to solve ONMF_$\ell_{20}$ by transforming it into a seriesof constrained and penalized matrix factorization problems. The results onnumerical and scRNA-seq datasets demonstrate the efficiency of our methods incomparison with existing methods.

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