A Manifold Proximal Linear Method for Sparse Spectral Clustering with Application to Single-Cell RNA Sequencing Data Analysis

• URL: http://arxiv.org/abs/2007.09524v2
• Date: Fri, 30 Oct 2020 22:28:39 GMT
• Title: A Manifold Proximal Linear Method for Sparse Spectral Clustering with Application to Single-Cell RNA Sequencing Data Analysis
• Authors: Zhongruo Wang, Bingyuan Liu, Shixiang Chen, Shiqian Ma, Lingzhou Xue, Hongyu Zhao
• Abstract summary: This paper considers the widely adopted SSC model as an optimization model with nonsmooth and non objective. We propose a new method (ManPL) that solves the original SSC problem. Results of the proposed methods are established.
• Score: 9.643152256249884
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Spectral clustering is one of the fundamental unsupervised learning methods widely used in data analysis. Sparse spectral clustering (SSC) imposes sparsity to the spectral clustering and it improves the interpretability of the model. This paper considers a widely adopted model for SSC, which can be formulated as an optimization problem over the Stiefel manifold with nonsmooth and nonconvex objective. Such an optimization problem is very challenging to solve. Existing methods usually solve its convex relaxation or need to smooth its nonsmooth part using certain smoothing techniques. In this paper, we propose a manifold proximal linear method (ManPL) that solves the original SSC formulation. We also extend the algorithm to solve the multiple-kernel SSC problems, for which an alternating ManPL algorithm is proposed. Convergence and iteration complexity results of the proposed methods are established. We demonstrate the advantage of our proposed methods over existing methods via the single-cell RNA sequencing data analysis.

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