勷勤数学•专家报告

题      目：A Provably-Correct and Robust Convex Model for Smooth Separable NMF

报  告  人： 潘珺珺 助理教授  (邀请人：黎稳)

                                          香港浸会大学

时      间： 3月12日  16：00-17:00

地     点：数科院东楼302

报告人简介:

        潘珺珺博士现为香港浸会大学研究助理教授，其研究兴趣主要集中在数值算法及其在数据科学中的应用，在SIMAX、SISC、SIIMS、TPAMI、Neural Networks等期刊上发表过论文。

摘      要：

       Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for nonnegative data, with applications such as hyperspectral unmixing and topic modeling. NMF is a difficult problem in general (NP-hard), and its solutions are typically not unique. To address these two issues, additional constraints or assumptions are often used. In particular, separability assumes that the basis vectors in the NMF are equal to some columns of the input matrix. In that case, the problem is referred to as separable NMF (SNMF) and can be solved in polynomial-time with robustness guarantees, while identifying a unique solution. However, in real-world scenarios, due to noise or variability, multiple data points may lie near the basis vectors, which SNMF does not leverage. In this work, we rely on the smooth separability assumption, which assumes that each basis vector is close to multiple data points. We explore the properties of the corresponding problem, referred to as smooth SNMF (SSNMF), and examine how it relates to SNMF and orthogonal NMF. We then propose a convex model for SSNMF and show that it provably recovers the sought-after factors, even in the presence of noise. We finally adapt an existing fast gradient method to solve this con vex model for SSNMF, and show that it compares favorably with state-of-the-art methods on both synthetic and hyperspectral datasets.

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