In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind...In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level k (r 1,r 2,…,r k) circulant matrices are derived,and it is also proved that the sort of matrices are diagonalizable.展开更多
In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of th...In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level-k circulant matrices are derived,and it is also proved that the sort matrices are unitarily diagonalizable.展开更多
Recently,sparse component analysis (SCA) has become a hot spot in BSS re-search. Instead of independent component analysis (ICA),SCA can be used to solve underdetermined mixture efficiently. Two-step approach (TSA) is...Recently,sparse component analysis (SCA) has become a hot spot in BSS re-search. Instead of independent component analysis (ICA),SCA can be used to solve underdetermined mixture efficiently. Two-step approach (TSA) is one of the typical methods to solve SCA based BSS problems. It estimates the mixing matrix before the separation of the sources. K-means clustering is often used to estimate the mixing matrix. It relies on the prior knowledge of the source number strongly. However,the estimation of the source number is an obstacle. In this paper,a fuzzy clustering method is proposed to estimate the source number and mixing matrix simultaneously. After that,the sources are recovered by the shortest path method (SPM). Simulations show the availability and robustness of the proposed method.展开更多
文摘In this paper,we give the explicit expressions of level k (r 1,r 2,…,r k) circulant matrices of order n 1n 2…n k,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level k (r 1,r 2,…,r k) circulant matrices are derived,and it is also proved that the sort of matrices are diagonalizable.
文摘In this paper, we give the explicit expressions of level-k circulant matrices of type (n1,n2,…nk) and of order n1n2…nk,and the explicit expressions for the eigenvalues,the determinants and the inverse matrices of the kind level-k circulant matrices are derived,and it is also proved that the sort matrices are unitarily diagonalizable.
基金Key Program of the National Natural Science Foundation of China (Grant No.U0635001)the National Natural Science Foundation of China (Grant Nos.60674033 and 60774094)
文摘Recently,sparse component analysis (SCA) has become a hot spot in BSS re-search. Instead of independent component analysis (ICA),SCA can be used to solve underdetermined mixture efficiently. Two-step approach (TSA) is one of the typical methods to solve SCA based BSS problems. It estimates the mixing matrix before the separation of the sources. K-means clustering is often used to estimate the mixing matrix. It relies on the prior knowledge of the source number strongly. However,the estimation of the source number is an obstacle. In this paper,a fuzzy clustering method is proposed to estimate the source number and mixing matrix simultaneously. After that,the sources are recovered by the shortest path method (SPM). Simulations show the availability and robustness of the proposed method.
