Extending T-mode canonical correlation analysis to T-mode pre-filtered canonical correlation analysis: a novel approach to discover shared patterns between two image time series

Abstract

This article introduces T-mode pre-filtered canonical correlation analysis (CCA) as an extension to T-mode CCA for identifying recurring spatial patterns over time shared between two image time series. T-mode pre-filtered CCA does this by first pre-filtering the individual image time series using T-mode PCA and then identifying the joint spatial variability between the principal components of the two series. There are two major advantages of the T-mode pre-filtered CCA over the T-mode CCA. Since the T-mode principal components are orthogonal, estimation of the inverse matrix for CCA becomes possible when the original data sets are highly correlated, which is mostly true in the case of image time series. The second advantage is that reducing the dimensionality of the original data decreases the number of variables substantially (typically from hundreds down to less than 10) compared to the number of observations and thus resolves the statistical requirement for such methods to have substantially more observations than variables. As will be illustrated through a case study, T-mode pre-filtered CCA finds shared relationships between spatially recurring patterns in the different data fields consistent with T-mode CCA.

Acknowledgement

I am greatly indebted to Dr J.R. Eastman for his insightful discussions and comments, and to the two anonymous reviewers whose comments helped me improve the manuscript.