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arXiv 2007.09524stat.MLcs.LGmath.OCq-bio.GN
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稀疏谱聚类的流形近似线性方法及其在单细胞RNA测序数据分析中的应用

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

University of California, Davis（加州大学戴维斯分校）；The Pennsylvania State University（宾夕法尼亚州立大学）；Texas A&M University（得克萨斯农工大学）；Yale University（耶鲁大学）

Zhongruo Wang, Bingyuan Liu, Shixiang Chen, Shiqian Ma, Lingzhou Xue, Hongyu Zhao

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摘要：

谱聚类是一种基本的无监督学习方法，广泛应用于数据分析中。稀疏谱聚类（SSC）赋予谱聚类以稀疏性，提高了模型的可解释性。本文考虑了一个广泛采用的SSC模型，它可以表示为Stiefel流形上的非光滑和非凸目标的优化问题。这样的优化问题非常具有挑战性。现有的方法通常解决其凸松弛或需要使用某些光滑技术来光滑其非光滑部分。在本文中，我们提出了一个流形近似线性方法（ManPL），解决了原来的SSC制定。我们还将该算法扩展到求解多核SSC问题，并提出了一种交替ManPL算法。收敛性和迭代复杂性的结果所提出的方法。我们通过单细胞RNA测序数据分析证明了我们提出的方法相对于现有方法的优势。

英文摘要：

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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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