Algebraic independent component analysis: an approach for separation of overcomplete speech mixtures

We propose a novel algorithm for blind separation of sparse overcomplete sources called algebraic independent component analysis (AICA). The proposed AICA algorithm is computationally more efficient in estimating blindly the mixing matrix as compared to earlier proposed geometric ICA (geo-ICA) algorithms. AICA is based entirely on algebraic operations and vector-distance measures. Firstly, these choices lead to considerable reduction in the computational cost of the AICA algorithm. Secondly, the robustness of the algebraic operations against the inherent permutation and scaling in ICA simplifies the performance evaluation of the ICA algorithms using the proposed algebraic measure. Thirdly, the algebraic framework is directly extendable to any dimensional ICA problems exhibiting only a linear increase in complexity. The stability of similar algorithms has been comprehensively studied in the realm of geo-ICA. The algorithm has been extensively tested for overcomplete, undercomplete and "quadratic" ICA using unimodal sparse distributions such as the laplacian and gamma distribution for speech. Illustrative blind source separation simulation examples for overcomplete speech mixtures are also presented.