Multivariate Maximal Correlation Analysis

Correlation analysis is one of the key elements of statistics, and has various applications in data analysis. Whereas most existing measures can only detect pairwise correlations between two dimensions, modern analysis aims at detecting correlations in multi-dimensional spaces. We propose MAC, a novel multivariate correlation measure designed for discovering multidimensional patterns. It belongs to the powerful class of maximal correlation analysis, for which we propose a generalization to multivariate domains. We highlight the limitations of current methods in this class, and address these with MAC. Our experiments show that MAC outperforms existing solutions, is robust to noise, and discovers interesting and useful patterns.