Individualized Multilayer Tensor Learning with An Application in Imaging Analysis

This work is motivated by multimodality breast cancer imaging data, which is quite challenging in that the signals of discrete tumor-associated microvesicles (TMVs) are randomly distributed with heterogeneous patterns. This imposes a significant challenge for conventional imaging regression and dimension reduction models assuming a homogeneous feature structure. We develop an innovative multilayer tensor learning method to incorporate heterogeneity to a higher-order tensor decomposition and predict disease status effectively through utilizing subject-wise imaging features and multimodality information. Specifically, we construct a multilayer decomposition which leverages an individualized imaging layer in addition to a modality-specific tensor structure. One major advantage of our approach is that we are able to efficiently capture the heterogeneous spatial features of signals that are not characterized by a population structure as well as integrating multimodality information simultaneously. To achieve scalable computing, we develop a new bi-level block improvement algorithm. In theory, we investigate both the algorithm convergence property, tensor signal recovery error bound and asymptotic consistency for prediction model estimation. We also apply the proposed method for simulated and human breast cancer imaging data. Numerical results demonstrate that the proposed method outperforms other existing competing methods.

本研究以多模态（multimodality）乳腺癌成像数据为出发点，该类数据存在显著挑战：离散的肿瘤相关微囊泡（tumor-associated microvesicles, TMVs）信号呈随机分布且具有异质性分布模式。这对假设特征结构均一的传统成像回归与降维模型构成了显著挑战。为此，我们提出一种创新性多层张量（tensor）学习方法，将异质性融入高阶张量（tensor）分解，并通过利用受试者水平成像特征与多模态信息，有效预测疾病状态。具体而言，我们构建了多层分解框架，在模态特异性张量结构的基础上引入个体成像层。本方法的核心优势在于，能够高效捕捉无法通过总体特征结构表征的信号异质性空间特征，同时实现多模态信息的融合。为实现可扩展计算，我们提出了一种新型双层块改进算法。理论层面，我们对算法收敛性、张量信号恢复误差界以及预测模型估计的渐近一致性进行了系统性分析。此外，我们将所提方法应用于模拟乳腺癌成像数据与临床人体乳腺癌成像数据。数值实验结果表明，所提方法的性能优于其他现有同类对比方法。