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Abstract:
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When studying two three-mode three-way data sets, we are often interested in two factors. The first indicates the uniqueness of the data sets, which can be obtained by maximizing the variance in subspace whereas the second factor shows the relationship between the data sets by using correlation as a measure of relationship. To interpret these two factors, canonical covariance analysis by using Tucker2 model (CCAT2) is often applied to the data. However, CCAT2 has the following two problems: the dimension of subspace of two data sets needs to the same and any canonical variables are connected with at least one canonical variable among others. Therefore, CCAT2 could not adequately represent the uniqueness of the data. To overcome these problems, we propose constrained canonical covariance analysis by using Tucker2 model (CCCAT2.) By constraining the number of connections, CCCAT2 allows for a different number of dimensions between two data sets and can represents the uniqueness.
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