MrNMF and SrNMF: Recent Development in Robust Non-Negative Matrix Factorization Procedures

• Activity Number: 582
• Type: Invited
• Date/Time: Thursday, August 7, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yifan Xu*+ and Jiayang Sun and Kenneth K. Lopiano and S. Stanley Young
• Companies: Case Western Reserve University and Case Western Reserve University and SAMSI and NISS
• Keywords: Robust non-negative matrix factorization ; Principle component analysis ; Sparsity ; Supervised learning ; Big data

Abstract

PCA is one of the most widely used multivariate analysis techniques, modernized for analyzing large and sparse data. Nonnegative Matrix Factorization (NMF) is a modern alternative to PCA, offering better parts-based decompositions. Both procedures can fail if the noises or outliers in a data set are ignored. In this talk we show our recent development in robust NMF (rNMF) procedure for analyzing large and corrupted data. Our rNMF algorithm solves a penalized trimmed criterion iteratively, with sparsity controls and multiple trimming mechanisms for handling different types of data. The convergence of the algorithm is shown. Its associated sequential plots offer a new way of selecting the critical dimension used in NMF; and facilitates interpretation of the factorization. We compare rNMF with robust PCA/SVD and regular NMF procedures, and demonstrate the power of rNMF and its sibling, MrNMF (that allows semi-supervised intelligence controls) for removing various corruptions, data cleaning, compression, feature selection, and clustering. If time permits, we show an application to ovarian cancer data, and SrNMF, a new variant incorporating a kernel machine for supervised learning.