Generalized canonical correlation analysis for labeled data

Abstract

Multi-view learning is a method that is used to extract standard features from different information sources in various fields such as medical data analysis, computer vision, and web data analysis. Canonical correlation analysis (CCA), a dimensionality reduction method used for the data acquired in multi-view learning, can extract a low-dimensional space where the correlation between two multivariate data is high. However, CCA has the following problems. First, it is difficult to perform dimensionality reduction while taking advantage of the label information attached to the data. Second, CCA is an analysis method for two sets of data; it cannot be directly applied when we have three or more datasets. Discriminative canonical correlation analysis (DCCA) can be used to solve the first problem. It enables the dimensionality reduction of two datasets while reflecting the label information. Further, generalized canonical correlation analysis (GCCA) can be used to solve the second problem. It calculates canonical correlation variables, which are the products of parameters and data, for three or more datasets, and assumes that all datasets aggregate to a piece of shared information so that the parameters aggregate the information of each data. However, DCCA and GCCA do not simultaneously solve the problems of CCA. Therefore, in this study, we extend DCCA and propose a dimensionality reduction method using the label information for three or more datasets. We validate the usefulness of the proposed method through a simulation study.