Star-Graph Multimodal Matching Component Analysis for Data Fusion and Transfer Learning

The matching component analysis (MCA) technique for transfer learning [1] finds two maps - one from each of two data domains to a lower-dimensional, common domain - using only a small number of matched data pairs, where each matched data pair is comprised of one point from each data domain. These maps minimize the expected distance between mapped data pairs within the common domain, subject to an identity matrix covariance constraint and an affine linear structure. Learning techniques can then be applied to matched data points after they are mapped to the common domain, where each such point is encoded with information from both data domains via its respective optimal affine linear transformation. In [2], the covariance-generalized MCA (CGMCA) technique was developed in order to allow for the encoding of additional statistical information into the MCA maps. This was done by generalizing the identity matrix covariance constraint of MCA to accommodate any covariance matrix (compare Figures 1a and 1b). We are interested in extending the application space of CGMCA to accommodate three or more data domains simultaneously.