A Simple Multivariable Maximum Covariance Analysis Method

Abstract

This paper proposes a new simple method of multivariable maximum covariance analysis (MMCA) for extracting common variability from multiple (more than two) datasets that expands the singular value decomposition analysis method. The method is based on iteration of a recurrence equation derived by a dual relationship between pattern vectors and time coefficients. Two approaches of the method are proposed, one using the extreme of a summation of covariances (sum MMCA) and the other using the product of covariances (product MMCA). Both approaches are demonstrated by successfully extracting the variability related to the Arctic Oscillation from three monthly-mean meteorological datasets. The method is useful because it is easily programmed and is computationally inexpensive. The method can be applied to an arbitrary number of datasets, although a complete set of the product MMCA method cannot be applied to an even number of datasets.