Estimating the mixing matrix in Sparse Component Analysis (SCA) based on partial k-dimensional subspace clustering

One of the major problems in underdetermined Sparse Component Analysis (SCA) in the field of (semi) Blind Source Separation (BSS) is the appropriate estimation of the mixing matrix, AA, in the linear model X=ASX=AS, especially where more than one source is active at each instant of time. Most existing algorithms require the restriction that at each instant (i.e. in each column of the source matrix S), there is at most one single dominant component. Moreover, these algorithms require that the number of sources must be determined in advance. In this paper, we proposed a new algorithm for estimating the matrix AA, which does not require the restriction of single dominant source at each instant. Moreover, it is not necessary that the exact number of sources be known a priori.