Directional sparse filtering for blind estimation of under-determined complex-valued mixing matrices

• Main Authors: Nguyen, Anh Hai Trieu, Reju, Vaninirappuputhenpurayil Gopalan, Khong, Andy W. H.
• Other Authors: School of Electrical and Electronic Engineering
• Format: Article
• Language: English
• Published: 2020
• Subjects: Engineering::Electrical and electronic engineering; ICA; Directional Clustering
• Online Access: https://hdl.handle.net/10356/138107
• Institution: Nanyang Technological University

We propose an algorithm that exploits the benefits of sparse filtering and directional clustering when estimating under-determined mixing matrix from mixtures of sufficiently sparse sources. To express the direction of each sample by only a few vectors in which one vector is more dominant than the remaining ones, we propose to minimize the power mean of the magnitude-squared cosine distances between the estimated mixing matrix and the data. For the special case of estimating determined mixing matrix, we derive a stability condition for methods based on the magnitude-squared cosine metric. Our stability condition shows that the proposed approach, K-hyperlines, and sparse filtering can recover the invertible mixing matrix when the sources are i.i.d. super-Gaussian. Simulations using both synthetic data and recorded speech mixtures show that the proposed algorithm outperforms existing algorithms with lower computational complexity.