M. Namba and Y. Ishida (Japan)
Signal Analysis, PCA, Overcomplete Representation
The purpose of this paper is to show the effectiveness of the overcomplete representations in the estimate of principal components and present a method. Our work differs from a similar work of Chen et al. [6] in the respect that the basis is not a static dictionary but is learned by an iterative algorithm proposed by Lewicki et al. [8, 9], besides overcomplete. This paper carries this idea one step further; the signal data matrix is decomposed into the overcomplete basis and its gain matrix. Then the gain matrix is once again analyzed in the SVD subspace to yield the principal components of the signal itself. The purpose of this paper is to show the effectiveness of the overcomplete representations in the estimate of principal components and present a method. The simulation results using a periodic rectangular and a speech signals show that the first few principal components estimated by the proposed scheme can better represent the signal, in comparison with the conventional principal component analysis.
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