Individualized Multilayer Tensor Learning With an Application in Imaging Analysis
Individualized Multilayer Tensor Learning With an Application in Imaging Analysis
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DOI：
10.1080/01621459.2019.1585254
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发表时间：
2019-03
影响因子：
3.7
通讯作者：
Xiwei Tang;Xuan Bi;A. Qu
中科院分区：
文献类型：
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作者：
Xiwei Tang;Xuan Bi;A. Qu
摘要这项工作是由多模式乳腺癌成像数据推动的，这是一个相当具有挑战性的问题，因为离散的肿瘤相关微泡的信号是随机分布的，具有不同的模式。这对传统的基于同质特征结构的图像回归和降维模型提出了很大的挑战。我们开发了一种创新的多层张量学习方法，将异质性融入到高阶张量分解中，并通过利用受试者的成像特征和多模信息有效地预测疾病状态。具体地说，我们构造了一个多层分解，它除了利用特定于形态的张量结构之外，还利用了个性化的成像层。该方法的一个主要优点是能够有效地捕捉信号中不具有种群结构特征的异质空间特征，并能够同时集成多模式信息。为了实现可伸缩计算，我们提出了一种新的两级块改进算法。在理论上，我们研究了预测模型估计的算法收敛性质、张量信号恢复误差界和渐近相合性。我们还将提出的方法应用于模拟的乳腺癌成像数据和人类乳腺癌的成像数据。数值结果表明，该方法的性能优于现有的其他竞争方法。这篇文章的补充材料可以在网上找到。
Abstract This work is motivated by multimodality breast cancer imaging data, which is quite challenging in that the signals of discrete tumor-associated microvesicles 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. Supplementary materials for this article are available online.