TY - JOUR
AU - Amari, Shun-ichi
AB - In this letter, we analyze a two-stage cluster-then- l 1 -optimization approach for sparse representation of a data matrix, which is also a promising approach for blind source separation (BSS) in which fewer sensors than sources are present. First, sparse representation (factorization) of a data matrix is discussed. For a given overcomplete basis matrix, the corresponding sparse solution (coefficient matrix) with minimum l 1 norm is unique with probability one, which can be obtained using a standard linear programming algorithm. The equivalence of the l 1 —norm solution and the l 0 —norm solution is also analyzed according to a probabilistic framework. If the obtained l 1 —norm solution is sufficiently sparse, then it is equal to the l 0 —norm solution with a high probability. Furthermore, the l 1 —norm solution is robust to noise, but the l 0—norm solution is not, showing that the l 1 —norm is a good sparsity measure. These results can be used as a recoverability analysis of BSS, as discussed. The basis matrix in this article is estimated using a clustering algorithm followed by normalization, in which the matrix columns are the cluster centers of normalized data column vectors. Zibulevsky, Pearlmutter, Boll, and Kisilev (2000) used this kind of two-stage approach in underdetermined BSS. Our recoverability analysis shows that this approach can deal with the situation in which the sources are overlapped to some degree in the analyzed
TI - Analysis of Sparse Representation and Blind Source Separation
JF - Neural Computation
DO - 10.1162/089976604773717586
DA - 2004-06-01
UR - https://www.deepdyve.com/lp/mit-press/analysis-of-sparse-representation-and-blind-source-separation-dovAs1W0xC
SP - 1193
EP - 1234
VL - 16
IS - 6
DP - DeepDyve
ER -