Georgiev, P. and Pardalos, P. and Theis, Fabian J. (2005) A bilinear algorithm for sparse representations. Computational optimization and applications.
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We consider the following sparse representation problem: represent a given matrix X∈ℝ m×N as a multiplication X=AS of two matrices A∈ℝ m×n (m≤n<N) and S∈ℝ n×N , under requirements that all m×m submatrices of A are nonsingular, and S is sparse in sense that each column of S has at least n−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.
|Institutions:||Biology, Preclinical Medicine > Institut für Biophysik und physikalische Biochemie > Prof. Dr. Elmar Lang|
|Keywords:||Sparse component analysis; Blind source separation; Underdetermined mixtures|
|Subjects:||500 Science > 570 Life sciences|
|Created at the University of Regensburg:||Unknown|
|Deposited On:||14 Oct 2010 06:07|
|Last Modified:||31 Jan 2014 06:58|