Correlation Tensor Decomposition and Its Application in Spatial Imaging Data
针对现有张量模型仅利用像素均值信息的局限，提出一种基于像素间相关信息的半对称相关张量分解方法，用于捕捉空间模式以辅助癌症诊断，并在乳腺癌成像数据中验证了其优于其他方法。
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.