Keywords: Multiway data, optimization, sparsity
Canonical correlation analysis (CCA) is a popular multivariate analysis technique that finds the linear relationship between two data sets. Recent technologies such as neuroimaging and remote sensing generate data in form of multi-dimensional arrays or tensors. Classic CCA is insufficient for dealing with tensor data due to the multi-dimensional structure and ultra high-dimensionality. We present tensor CCA, a technique that discovers linear relationship between two tensor data sets while respecting the spatial information. We delineate various population models and propose efficient and scalable estimation algorithms that have global convergence guarantees. Simulation studies illustrate the performance of our method.