Overlapping Clusterwise Simultaneous Component Analysis

When confronted with multivariate multiblock data (i.e., data in which the observations are nested within different data blocks that have the variables in common), it can be useful to synthesize the available information in terms of components and to inspect between-block similarities and differences in component structure. To this end, the clusterwise simultaneous component analysis (C-SCA) framework was developed across a series of papers: C-SCA partitions the data blocks into a limited number of mutually exclusive groups and performs separate SCA's per cluster. In this paper, we present a more general version of C-SCA. The key difference with the existing C-SCA methods is that the new method does not impose that the clusters are mutually exclusive, but allows for overlapping clusters. Therefore, the new method is called Overlapping Clusterwise Simultaneous Component Analysis (OC-SCA). Each of these clusters corresponds to a single component, such that all the data blocks that are assigned to a particular cluster have the associated component in common. Moreover, the more clusters a specific data block belongs to, the more complex the underlying component structure. A simulation study and an empirical application to emotion data are included in the paper.