A convex model for nonnegative matrix factorization and dimensionality reduction on physical space.
A collaborative convex framework for factoring a data matrix X into a nonnegative product AS , with a sparse coefficient matrix S, is proposed. We restrict the columns of the dictionary matrix A to coincide with certain columns of the data matrix X, thereby guaranteeing a physically meaningful dictionary and dimensionality reduction. We use l(1, ∞) regularization to select the dictionary from the data and show that this leads to an exact convex relaxation of l(0) in the case of distinct noise-free data. We also show how to relax the restriction-to- X constraint by initializing an alternating minimization approach with the solution of the convex model, obtaining a dictionary close to but not necessarily in X. We focus on applications of the proposed framework to hyperspectral endmember and abundance identification and also show an application to blind source separation of nuclear magnetic resonance data.
Duke Scholars
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- Artificial Intelligence & Image Processing
- 4607 Graphics, augmented reality and games
- 4603 Computer vision and multimedia computation
- 1702 Cognitive Sciences
- 0906 Electrical and Electronic Engineering
- 0801 Artificial Intelligence and Image Processing
Citation
Published In
DOI
EISSN
ISSN
Publication Date
Volume
Issue
Start / End Page
Related Subject Headings
- Artificial Intelligence & Image Processing
- 4607 Graphics, augmented reality and games
- 4603 Computer vision and multimedia computation
- 1702 Cognitive Sciences
- 0906 Electrical and Electronic Engineering
- 0801 Artificial Intelligence and Image Processing