Matrix-variate and higher-order probabilistic projections

Shipeng Yu, Jinbo Bi, Jieping Ye

Research output: Contribution to journalArticlepeer-review

15 Scopus citations


Feature extraction from two-dimensional or higher-order data, such as face images and surveillance videos, have recently been an active research area. There have been several 2D or higher-order PCA-style dimensionality reduction algorithms, but they mostly lack probabilistic interpretations and are difficult to applywith, e.g., incomplete data. It is also hard to extend these algorithms for applications where a certain region of the data point needs special focus in the dimensionality reduction process (e.g., the facial region in a face image). In this paper we propose a probabilistic dimensionality reduction framework for 2D and higher-order data. It specifies a particular generative process for this type of data, and leads to better understanding of some 2D and higher-order PCA-style algorithms. In particular, we show it actually takes several existing algorithms as its (non-probabilistic) special cases. We develop efficient iterative learning algorithms within this framework and study the theoretical properties of the stationary points. The model can be easily extended to handle special regions in the high-order data. Empirical studies on several benchmark data and real-world cardiac ultrasound images demonstrate the strength of this framework.

Original languageEnglish (US)
Pages (from-to)372-392
Number of pages21
JournalData Mining and Knowledge Discovery
Issue number3
StatePublished - May 2011


  • Dimensionality reduction
  • Higher-order principle component analysis
  • Low-rank matrix factorization
  • Probabilistic projection

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Computer Networks and Communications


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