A bilinear algorithm for sparse representations

Authors:
Pando Georgiev;Panos Pardalos;Fabian Theis
Affiliations:
ECECS Department, University of Cincinnati, Cincinnati, USA 45221 and Sofia University "St. Kliment Ohridski", Sofia, Bulgaria 1126;Center for Applied Optimization, University of Florida, Gainesville, FL, USA;Institute of Biophysics, University of Regensburg, Regensburg, Germany 93040
Venue:
Computational Optimization and Applications
Year:
2007

Citing 6
Cited 0

Optimal control

Optimal control
Atomic Decomposition by Basis Pursuit

SIAM Journal on Scientific Computing
k-Plane Clustering

Journal of Global Optimization
Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications

Adaptive Blind Signal and Image Processing: Learning Algorithms and Applications
Blind Source Separation by Sparse Decomposition in a Signal Dictionary

Neural Computation
Sparse component analysis and blind source separation of underdetermined mixtures

IEEE Transactions on Neural Networks

Quantified Score

Hi-index	0.00

Visualization

Abstract

We consider the following sparse representation problem: represent a given matrix X驴驴 m脳N as a multiplication X=AS of two matrices A驴驴 m脳n (m驴nN) and S驴驴 n脳N , under requirements that all m脳m submatrices of A are nonsingular, and S is sparse in sense that each column of S has at least n驴m+1 zero elements. It is known that under some mild additional assumptions, such representation is unique, up to scaling and permutation of the rows of S. We show that finding A (which is the most difficult part of such representation) can be reduced to a hyperplane clustering problem. We present a bilinear algorithm for such clustering, which is robust to outliers. A computer simulation example is presented showing the robustness of our algorithm.