Robust Non-Negative Matrix Factorization Procedures for Analyzing Tumor and Face Image Data

• Activity Number: 120
• Type: Topic Contributed
• Date/Time: Monday, August 5, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Jiayang Sun*+ and Kenneth Lopiano and S. Stanley Young
• Companies: Case Western Reserve University and SAMSI and National Institute of Statistical Sciences
• Keywords: Large, sparse data ; Nongenative matrix factorization, NMF ; Robustness ; Data mining, Dimension Reduction ; Image Cleaning ; SVD, Compression

Abstract

In this paper we introduce a set of robust non-negative factorization (rNMF) algorithms for analyzing large and corrupted data. The central idea is to introduce a penalized criterion that incorporates a trimming component, so that the rNMF procedure is flexible enough to handle different types of noise that may arise in a data source, and simultaneously control the sparsity of the decomposition. Multiple algorithms are developed by varying the way that outliers are determined and subsequently handled. The resulting algorithms work well when compared to existing NMF algorithms commonly used in practice and an existing robust NMF procedure. The rNMF algorithms developed here include fully automatic controls and semi-supervised controls to address more difficult areas that an unsupervised algorithm cannot properly handle. We illustrate the proposed methodology using simulated tumor image data and images of faces subject to different types of corruptions.