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Robust Canonical Correlation Analysis for Asymmetric Distributions: Method Development and Evaluation

Bekesuoyeibo, Rebecca, Emmanuel O. Biu

Abstract

Canonical Correlation Analysis is an effective way of investigating the association between two sets of variables. Its utility, however, may be impaired in the presence of non- normal, skewed or heavy-tailed distributions of data that is often present in real-world data sets. The present study can build and test a better model of CCA, known as Enhanced CCA, which will aim at solving these shortcomings. We test the performance of Enhanced CCA on simulated data with normal, heavy-tailed (t-distribution) and skewness CCA log-normal distributions against four CCA algorithms: Pearson, Kendall, Spearman and Sparse CCA. The findings reveal that Enhanced CCA is the most reliable and accurate estimator of canonical correlations when evaluated by the mean squared error , and the smallest overall. Enhanced CCA method also expresses better performance in the form of trace and Rho values of Pillai, most of the distributions have the highest correlation (1.00000) which is evidence of strength. On the other hand, Kendall CCA was always poor particularly when skewed and heavy tails are taken. Although Pearson, Spearman and Sparse CCA methods yielded the same results, Enhanced CCA was better than them in precision and stability. These results indicate that Enhanced CCA can be used effectively to work with complex and non-normal data distributions and emphasize that it may better provide more robust and precise results when multivariate analysis is performed. The paper concludes that it is a better approach to the canonical correlation analysis through Enhanced CCA, especially in demanding data settings where the conventional approaches fail.

References

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