Dictionary learning based on M‐PCA‐N for audio signal sparse representation

Abstract

The current popular dictionary learning algorithms for sparse representation of signals are K-means Singular Value Decomposition (K-SVD) and K-SVD-extended. Only rank-1 approximation is used to update one atom at a time and it is unable to cope with large dictionary efficiently. In order to tackle these two problems, this study proposes M-Principal Component Analysis-N (M-PCA-N), which is an algorithm for dictionary learning and sparse representation. First, M-Principal Component Analysis (M-PCA) utilised information from the top M ranks of SVD decomposition to update M atoms at a time. Then, in order to further utilise the information from remaining ranks, M-PCA-N is proposed on the basis of M-PCA, by transforming information from the following N non-principal ranks onto the top M principal ranks. The mathematic formula indicates that M-PCA may be seen as a generalisation of K-SVD. Experimental results on the BBC Sound Effects Library show that M-PCA-N not only lowers the MSE between original signal and approximation signal in audio signal sparse representation, but also obtains higher audio signal classification precision than K-SVD.