Title: Functional canonical correlation analysis for multivariate stochastic processes
Authors: Michio Yamamoto - Osaka University / RIKEN AIP (Japan) [presenting]
Yoshikazu Terada - Osaka University; RIKEN (Japan)
Abstract: The aim is to study the extension of canonical correlation analysis from pairs of random functions to the case where a data sample consists of multivariate square integrable stochastic processes. We refer to this extension as the generalized functional canonical correlation analysis (GFCCA). In functional data analysis, the data space is essentially infinite. Thus, unlike the generalized canonical correlation analysis (GCCA) for multivariate data, the well-definedness of GFCCA cannot be ensured in general. To address this issue, we provide sufficient conditions under which GFCCA has a meaningful solution. In addition, we develop the functional version of homogeneity analysis, which is another formulation of GCCA for multivariate data. Interestingly, we show that, unlike in the case of finite-dimensional space, the functional homogeneity analysis is not necessarily equivalent to GFCCA.