Individualized Multilayer Tensor Learning With an Application in Imaging Analysis

Xiwei Tang, Xuan Bi, Annie Qu

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)836-851
Number of pages16
JournalJournal of the American Statistical Association
Issue number530
StatePublished - Apr 2 2020


  • Cancer imaging
  • Dimension reduction
  • Heterogeneous modeling
  • High-order tensor decomposition
  • Multimodality integration
  • Spatial information

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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