Multi-view data are increasingly prevalent in practice. It is often relevant to analyze the relationships between pairs of views by multi-view component analysis techniques such as Canonical Correlation Analysis (CCA). However, data may easily exhibit nonlinear relations, which CCA cannot reveal. We aim to investigate the usefulness of nonlinear multi-view relations to characterize multi-view data in an explainable manner. To address this challenge, we propose a method to characterize globally nonlinear multi-view relationships as a mixture of linear relationships. A clustering method, it identifies partitions of observations that exhibit the same relationships and learns those relationships simultaneously. It defines cluster variables by multi-view rather than spatial relationships, unlike almost all other clustering methods. Furthermore, we introduce a supervised classification method that builds on our clustering method by employing multi-view relationships as discriminative factors. The value of these methods resides in their capability to find useful structure in the data that single-view or current multi-view methods may struggle to find. We demonstrate the potential utility of the proposed approach using an application in clinical informatics to detect and characterize slow bleeding in patients whose central venous pressure (CVP) is monitored at the bedside. Presently, CVP is considered an insensitive measure of a subjects intravascular volume status or its change. However, we reason that features of CVP during inspiration and expiration should be informative in early identification of emerging changes of patient status. We empirically show how the proposed method can help discover and analyze multiple-to-multiple correlations, which could be nonlinear or vary throughout the population, by finding explainable structure of operational interest to practitioners.
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