Computing Absolute Maximum Correlation

Optimizing correlations between sets of variables is an important task in many areas of applications. There are plenty of algorithms for computing the maximum correlation. Most disappointedly, however, these methods typically cannot guarantee attaining the absolute maximum correlation which would have significant impact on practical applications. This paper makes two contributions. Firstly, some distinctive traits of the absolute maximum correlation are characterized. By exploiting these attributes, it is possible to propose an effective starting point strategy that significantly increases the likelihood of attaining the absolute maximum correlation. Numerical testing of the classical Horst algorithm with the starting point strategy seems to evince the potency of this approach. Secondly, the Horst algorithm is but one aggregated Jacobi-type power method. Following the innate iterative structure, a generalization to the Gauss-Seidel formulation is proposed as a natural improvement on the power method. Monotone convergence of the Gauss-Seidel algorithm is proved. When combined with the starting point strategy, the newer Gauss-Seidel approach leads to faster computation of the absolute maximum correlation.