NEW ICA ALGORITHMS BASED ON SPECIAL LINEAR GROUP

Abstract

Unlike the traditional independent component analysis (ICA) algorithms and some recently emerging linear ICA algorithms that search for solutions in the space of general matrices or orthogonal matrices, in this paper we propose two new methods which only search for solutions in the space of the matrices with unitary determinant and without whitening. The new algorithms are based on the special linear group SL(n). In order to achieve our target, we first provide a representation theory for any matrix in SL(n), which only simply uses the product of multiple exponentials of traceless matrices. Based on the matrix representation theory, two novel ICA algorithms are developed along with simple analysis on their equilibrium points. Moreover, we apply our methods to the classical problem of signal separation. The experimental results indicate that the superior convergence of our proposed algorithms, which can be expected as two viable alternatives to the ICA algorithms available in publications.