Robust Volume Minimization-Based Matrix Factorization for Remote Sensing and Document Clustering

摘要

This paper considers \emph{volume minimization} (VolMin)-based structuredmatrix factorization (SMF). VolMin is a factorization criterion that decomposesa given data matrix into a basis matrix times a structured coefficient matrixvia finding the minimum-volume simplex that encloses all the columns of thedata matrix. Recent work showed that VolMin guarantees the identifiability ofthe factor matrices under mild conditions that are realistic in a wide varietyof applications. This paper focuses on both theoretical and practical aspectsof VolMin. On the theory side, exact equivalence of two independently developedsufficient conditions for VolMin identifiability is proven here, therebyproviding a more comprehensive understanding of this aspect of VolMin. On thealgorithm side, computational complexity and sensitivity to outliers are twokey challenges associated with real-world applications of VolMin. These areaddressed here via a new VolMin algorithm that handles volume regularization ina computationally simple way, and automatically detects and {iterativelydownweights} outliers, simultaneously. Simulations and real-data experimentsusing a remotely sensed hyperspectral image and the Reuters document corpus areemployed to showcase the effectiveness of the proposed algorithm.