Additive Tensor Decomposition Considering Structural Data Information

Shancong Mou, Andi Wang, Chuck Zhang, Jianjun Shi

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Tensor data with rich structural information become increasingly important in process modeling, monitoring, and diagnosis in manufacturing medical and other applications. Here structural information is referred to the information of tensor components such as sparsity, smoothness, low-rank, and piecewise constancy. To reveal useful information from tensor data, we propose to decompose the tensor into the summation of multiple components based on their different structural information. In this article, we provide a new definition of structural information in tensor data. We then propose an additive tensor decomposition (ATD) framework to extract useful information from tensor data. This framework specifies a high dimensional optimization problem to obtain the components with distinct structural information. An alternating direction method of multipliers (ADMM) algorithm is proposed to solve it, which is highly parallelable and thus suitable for the proposed optimization problem. Two simulation examples and a real case study in medical image analysis illustrate the versatility and effectiveness of the ATD framework.

Original languageEnglish (US)
JournalIEEE Transactions on Automation Science and Engineering
DOIs
StateAccepted/In press - 2021
Externally publishedYes

Keywords

  • Additives
  • Alternating direction method of multipliers (ADMM) algorithm
  • Computed tomography
  • Image edge detection
  • Matrix decomposition
  • Medical diagnostic imaging
  • Optimization
  • structural information
  • tensor decomposition.
  • Tensors

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Electrical and Electronic Engineering

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