A Flexible and Efficient Algorithmic Framework for Constrained Matrix and Tensor Factorization

Kejun Huang, Nicholas D. Sidiropoulos, Athanasios P. Liavas

Research output: Contribution to journalArticlepeer-review

103 Scopus citations


We propose a general algorithmic framework for constrained matrix and tensor factorization, which is widely used in signal processing and machine learning. The new framework is a hybrid between alternating optimization (AO) and the alternating direction method of multipliers (ADMM): each matrix factor is updated in turn, using ADMM, hence the name AO-ADMM. This combination can naturally accommodate a great variety of constraints on the factor matrices, and almost all possible loss measures for the fitting. Computation caching and warm start strategies are used to ensure that each update is evaluated efficiently, while the outer AO framework exploits recent developments in block coordinate descent (BCD)-type methods which help ensure that every limit point is a stationary point, as well as faster and more robust convergence in practice. Three special cases are studied in detail: non-negative matrix/tensor factorization, constrained matrix/tensor completion, and dictionary learning. Extensive simulations and experiments with real data are used to showcase the effectiveness and broad applicability of the proposed framework.

Original languageEnglish (US)
Article number7484753
Pages (from-to)5052-5065
Number of pages14
JournalIEEE Transactions on Signal Processing
Issue number19
StatePublished - Oct 1 2016

Bibliographical note

Funding Information:
Their work was supported in part by NSF IIS-1247632, IIS-1447788, and a UM Informatics Institute fellowship.

Publisher Copyright:
© 2016 IEEE.


  • Constrained matrix/tensor factorization
  • alternating direction method of multipliers
  • alternating optimization
  • canonical polyadic decomposition
  • dictionary learning
  • matrix/tensor completion
  • non-negative matrix/tensor factorization


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