Grouping Scheme Discriminant Canonical Correlation Analysis for Time-Dependent Multivariate Data Structure

Abstract

One popular covariance analysis methodology, canonical correlation analysis, is not primarily intended for multivariate multiple time-dependent data structures that may be appropriately divided into two response and predictor variables groups. This means that conventional canonical correlation analysis does not yield practical results for such data problems. This study, therefore, designs and implements a grouping scheme discriminant canonical correlation analysis to handle this problem so that the time effect is adequately captured in the computation of the correlation coefficient between the two sets of variables. We also show how multiple discriminant analyses obtain the ideal value. This process is known as grouping scheme discriminant canonical correlation analysis in this study. Therefore, the grouping scheme discriminant canonical correlation analysis is a method designed to handle time-dependent multivariate data efficiently by integrating the time effect into the canonical correlation through discriminant analysis. Based on data on six weather conditions, the demonstrations show that the correlation coefficient between heating and cooling sets of weather conditions varies at different time points, and that the overall correlations are higher than that obtained from data assumed to be time-independent. The detection techniques for multiple discriminant analysis and the currently used canonical correlation analysis are compared in this paper. The results are validated through simulation and real performance review. According to the findings, determining the genuine correlation between the two sets of variables with time-dependent structure is significantly improved by seven-group discriminant analysis. Furthermore, seven-group discriminant analysis yielded the best results for the combination method based on multiple discriminant analysis and conventional canonical correlation analysis. It has been noted that the time impact is successfully incorporated into the calculation of the canonical correlation when the grouping scheme is used in discriminant canonical correlation analysis. The results finally show that incorporating the time effect into canonical correlation analysis achieves a more reasonable relationship between subset variables within the data.