Decentralized Canonical Correlation Analysis for Large Data-sets

Canonical Correlation Analysis (CCA) is a widely used statistical tool for finding correlation structures in multivariate data-sets. In this paper, we deal with a main application of CCA - Alternate Least Squares (ALS), and we introduce a decentralized approach to apply the algorithm on huge distributed data-sets. We propose to solve CCA using local processors, which apply ALS locally, and a central processor, which optimize a consensus problem, in order to find the first canonical order of CCA. We show that with this approach, CCA can be computed efficiently and feasibly on rank deficient data matrices. We demonstrate its performance by synthesized numerical simulations and real data-sets experiments.