Abstract

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.

摘要

近年来，多维张量数据越来越受到关注，特别是在生物医学成像分析中。然而，大多数现有的张量模型仅基于成像像素的平均信息。受乳腺癌研究中多模态光学成像数据的启发，我们开发了一种新的张量学习方法来使用像素相关信息，该信息通过高阶相关张量表示。我们提出了一种新的半对称相关张量分解方法，该方法可以有效地捕获像素相关的信息空间模式，以促进癌症诊断。我们建立了恢复结构和分类一致性的理论属性。此外，我们开发了一种有效的算法来实现计算可扩展性。