An Algebraic Algorithm for Joint Independent Subspace Analysis

In this work, we propose an algebraic algorithm called coupled exact joint block decomposition (CE-JBD) for joint independent subspace analysis (JISA), an extension to joint blind source separation. In JISA, tensors admitting coupled rank-\((L_m,L_n,\cdot )\) Block Term Decomposition (BTD) can be constructed using second order statistics of non-stationary signals. And the loading matrices to be estimated will be computed from these tensors via coupled rank-\((L_m,L_n,\cdot )\) BTD based algorithms. However, most of the existing algorithms resort to iterative techniques. They heavily rely on a good starting point. Capable of providing such a point, our proposed CE-JBD, based on coupled rank-\((L_m,L_n,\cdot )\) BTD, achieves JISA only by employing generalized eigenvalue decomposition followed by a clustering step and singular value decomposition. To validate its efficacy, as well as its ability to serve its iterative counterparts, we present some experiment results in the end.