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Title: Canonical dependency analysis by using chi-square matrix Authors:  Jun Tsuchida - Tokyo University of Science (Japan) [presenting]
Hiroshi Yadohisa - Doshisha University (Japan)
Abstract: Canonical correlation analysis(CCA) is a popular method for investigating the relationship between datasets. CCA assumes that the relationship is represented as linear function. Therefore, it is not suitable to apply CCA to datasets whose relationship are non-linear. To achieve this problem, canonical dependency analysis(CDA) has been proposed by researchers. Many canonical dependency analyses adopt K-L divergence and kernel-based method as measure of dependency. Although these measures are useful for CDA, calculation cost is higher. Moreover, canonical variables maximize dependency between canonical variables. Thus, it is not as if the result of CDA is a summary of dependency between datasets. To overcome this problem, we propose CDA by using chi-square matrix. Chi-square matrix is calculated from datasets as similar manner of correlation matrix. Hence, using chi-square matrix, the proposed method summarizes dependency relationships between datasets. In addition, the calculation cost is not so high, because chi-square statistic is simple. As result of the numerical example, the proposed method has the best results in the sense of estimation accuracy of loadings matrix.