Supervised Canonical Correlation Analysis of Data on Symmetric Positive Definite Manifolds by Riemannian Dimensionality Reduction

Most computer vision problems entail data that reside on Riemannian manifolds. Canonical correlation analysis (CCA) is a powerful method that captures correlations between any two sets of matrices. In this paper, we propose a framework for a supervised CCA of manifold-based data. This framework aims to find the optimal dimensionality reduction maps that maximize the discriminative power of any classifier in the reduced dimensional space and the correlation between the projected sets. This allows to incorporate the CCA into a classifier that analyzes multichannel or multimodal data on separate manifolds. The proposed method is evaluated on the challenging task of segmenting cardiac adipose tissues on fat-water (2-channel) magnetic resonance images.