Correlation Clustering for Learning Mixtures of Canonical Correlation Models

This paper addresses the task of analyzing the correlation between two related domains X and Y. Our research is motivated by an Earth Science task that studies the relationship between vegetation and precipitation. A standard statistical technique for such problems is Canonical Correlation Analysis (CCA). A critical limitation of CCA is that it can only detect linear correlation between the two domains that is globally valid throughout both data sets. Our approach addresses this limitation by constructing a mixture of local. linear CCA. models through a process we name correlation clustering. In correlation clustering, both data sets are clustered simultaneously according to the data's correlation structure such that, within a cluster, domain X and domain Y are linearly correlated in the same way. Each cluster is then analyzed using the traditional CCA to construct local linear correlation models. We present results on both artificial data sets and Earth Science data sets to demonstrate that the proposed approach can detect useful correlation patterns, which traditional CCA fails to discover.