Logdet Divergence Based Sparse Non-Negative Matrix Factorization for Stable Representation
- 1 November 2015
- conference paper
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE) in 2015 IEEE International Conference on Data Mining
- p. 871-876
- https://doi.org/10.1109/icdm.2015.52
Abstract
Non-negative matrix factorization (NMF) decomposes any non-negative matrix into the product of two low dimensional non-negative matrices. Since NMF learns effective parts-based representation, it has been widely applied in computer vision and data mining. However, traditional NMF has the riskrisk learning rank-deficient basis learning rank-deficient basis on high-dimensional dataset with few examples especially when some examples are heavily corrupted by outliers. In this paper, we propose a Logdet divergence based sparse NMF method (LDS-NMF) to deal with the rank-deficiency problem. In particular, LDS-NMF reduces the risk of rank deficiency by minimizing the Logdet divergence between the product of basis matrix with its transpose and the identity matrix, meanwhile penalizing the density of the coefficients. Since the objective function of LDS-NMF is nonconvex, it is difficult to optimize. In this paper, we develop a multiplicative update rule to optimize LDS-NMF in the frame of block coordinate descent, and theoretically prove its convergence. Experimental results on popular datasets show that LDS-NMF can learn more stable representations than those learned by representative NMF methods.Keywords
This publication has 21 references indexed in Scilit:
- Visualizing Rank Deficient Models: A Row Equation Geometry of Rank Deficient Matrices and Constrained-RegressionPLOS ONE, 2012
- Matrix Nearness Problems with Bregman DivergencesSIAM Journal on Matrix Analysis and Applications, 2008
- From few to many: illumination cone models for face recognition under variable lighting and poseIEEE Transactions on Pattern Analysis and Machine Intelligence, 2001
- An overlap invariant entropy measure of 3D medical image alignmentPattern Recognition, 1999
- Visual Object RecognitionAnnual Review of Neuroscience, 1996
- Recognition of Objects and Their Component Parts: Responses of Single Units in the Temporal Cortex of the MacaqueCerebral Cortex, 1994
- Principal component analysisChemometrics and Intelligent Laboratory Systems, 1987
- On rank-deficient pseudoinversesLinear Algebra and its Applications, 1980
- Hierarchical structure in perceptual representationCognitive Psychology, 1977
- The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programmingUSSR Computational Mathematics and Mathematical Physics, 1967