2024/02/15 by Marina Garrote-López, Garrote-López, Marina, Monroe Stephenson +1 · 1 citation
Computer Science · Mathematics · #15A69 #62H25 #62R01 #Blind Source Separation Techniques #Computational Physics and Python Applications #FOS: Mathematics #Statistics Theory (math.ST) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2402.10089
openalex publication_date 2024/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
In this work, we explore Partitioned Independent Component Analysis (PICA), an extension of the well-established Independent Component Analysis (ICA) framework. Traditionally, ICA focuses on extracting a vector of independent source signals from a linear combination of them defined by a mixing matrix. We aim to provide a comprehensive understanding of the identifiability of this mixing matrix in ICA. Significant to our investigation, recent developments by Mesters and Zwiernik relax these strict independence requirements, studying the identifiability of the mixing matrix from zero restrictions on cumulant tensors. In this paper, we assume alternative independence conditions, in particular, the PICA case, where only partitions of the sources are mutually independent. We study this case from an algebraic perspective, and our primary result generalizes previous results on the identifiability of the mixing matrix.