Variable Reduction Schemes Based on Principal Component, Canonical Correlation, and Procrustes Analyses
This paper was concerning with the dimension reduction over data with two multivariable sets of variables. We examined the robustness of four schemes of variable reduction with respect to the degree of information preserved by the reduced data. The proposed schemes were constructed in the framework of principal component, canonical correlation, and Procrustes analyses. Iterative procedures were then developed to subsequently removing variables with less significant contribution to the data variability pertaining to smaller first canonical correlation, smaller coefficient of canonical variable, larger correlation to principal component, and larger Procrustes goodness-of-fit. To assess the effectiveness of the schemes we considered the variable reduction problem of Barents fish data set. It is shown that reduction scheme based direct canonical correlation analysis performs effectively as it can preserve about 90.16 percent information contained by the first canonical correlation after removing 18 variables.
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