Correlation Tensor Decomposition and Its Application in Spatial Imaging Data

Multi-dimensional tensor data have gained increasing attention in the recent years, especially in biomedical imaging analyses. However, the most existing tensor models are only based on the mean information of imaging pixels. Motivated by multimodal optical imaging data in a breast cancer study, we develop a new tensor learning approach to use pixel-wise correlation information, which is represented through the higher order correlation tensor. We proposed a novel semi-symmetric correlation tensor decomposition method which effectively captures the informative spatial patterns of pixel-wise correlations to facilitate cancer diagnosis. We establish the theoretical properties for recovering structure and for classification consistency. In addition, we develop an efficient algorithm to achieve computational scalability. Our simulation studies and an application on breast cancer imaging data all indicate that the proposed method outperforms other competing methods in terms of pattern recognition and prediction accuracy.