Learning from Hidden Traits: Joint Factor Analysis and Latent Clustering

Bo Yang, Xiao Fu, Nicholas D. Sidiropoulos

Research output: Contribution to journalArticlepeer-review

30 Scopus citations


Dimensionality reduction techniques play an essential role in data analytics, signal processing, and machine learning. Dimensionality reduction is usually performed in a preprocessing stage that is separate from subsequent data analysis, such as clustering or classification. Finding reduced-dimension representations that are well-suited for the intended task is more appealing. This paper proposes a joint factor analysis and latent clustering framework, which aims at learning cluster-aware low-dimensional representations of matrix and tensor data. The proposed approach leverages matrix and tensor factorization models that produce essentially unique latent representations of the data to unravel latent cluster structure-which is otherwise obscured because of the freedom to apply an oblique transformation in latent space. At the same time, latent cluster structure is used as prior information to enhance the performance of factorization. Specific contributions include several custom-built problem formulations, corresponding algorithms, and discussion of associated convergence properties. Besides extensive simulations, real-world datasets such as Reuters document data and MNIST image data are also employed to showcase the effectiveness of the proposed approaches.

Original languageEnglish (US)
Pages (from-to)256-269
Number of pages14
JournalIEEE Transactions on Signal Processing
Issue number1
StatePublished - Jan 1 2017

Bibliographical note

Funding Information:
National Science Foundation under Grant IS-1447788 and Grant IIS-1247632.

Publisher Copyright:
© 1991-2012 IEEE.


  • Factor analysis
  • clustering
  • clustering prior
  • dimensionality reduction
  • factorial K -means
  • identifiability
  • matrix factorization
  • reduced K -means
  • subspace learning
  • tensor factorization


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