Tensor Canonical Correlation Analysis on Graphs

Thummaluru Siddartha Reddy, Sundeep Prabhakar Chepuri

Abstract: In this work, we focus on canonical correlation analysis (CCA) for tensor dataset pairs. To handle tensor datasets, traditional CCA requires vectorization of the tensor data. By doing so, we lose the intrinsic structure in the data. Vectorization also leads to a significant increase in the dataset size and thereby increasing the computational complexity. The low-dimensional representations of the data often have a structure that a graph can conveniently capture. This paper proposes tensor graph CCA (TGCCA) that generalizes CCA to handle tensor data while incorporating a graph structure in the canonical variates through a graph regularizer. We present an alternating minimization solver to learn the canonical subspaces, where we learn the canonical subspaces corresponding to a mode of the tensor using a partial singular value decomposition as in the classical CCA, while keeping the other canonical subspaces fixed. Through experiments on real datasets for correspondence learning, we demonstrate the benefit of leveraging the graph structure of the canonical variates and directly working with tensor data.