Cumulant Tensors in Partitioned Independent Component Analysis

In this talk, we introduce the concept of Partitioned Independent Component Analysis (PICA), an extension of the classical Independent Component Analysis technique. ICA traditionally aims at separating a mixture of signals into its independent components by determining a mixing matrix. Our work focuses on the conditions under which this mixing matrix can be identified when the assumption of mutual independence among signals is relaxed. Building on recent work of Mesters and Zwiernik, we explore the cases where only subsets of source signals are required to be mutually independent, in other words PICA. Utilizing algebraic techniques similar to previous work, we investigate the identifiability of the mixing matrix in such cases. In this talk, we discuss our findings that reveal that the conditions for identifiability can be generalized, hence broadening the use of ICA in practical cases where traditional independence assumptions may not hold.