Reconstruction and recognition of tensor-based objects with concurrent subspaces analysis

Dong Xu, Shuicheng Yan, Lei Zhang, Stephen Lin, Hong Jiang Zhang, Thomas S. Huang

Research output: Contribution to journalArticlepeer-review


Principal components analysis (PCA) has traditionally been utilized with data expressed in the form of 1-D vectors, but there exists much data such as gray-level images, video sequences, Gabor-filtered images and so on, that are intrinsically in the form of second or higher order tensors. For representations of image objects in their intrinsic form and order rather than concatenating all the object data into a single vector, we propose in this paper a new optimal object reconstruction criterion with which the information of a high-dimensional tensor is represented as a much lower dimensional tensor computed from projections to multiple concurrent subspaces. In each of these subspaces, correlations with respect to one of the tensor dimensions are reduced, enabling better object reconstruction performance. Concurrent subspaces analysis (CSA) is presented to efficiently learn these subspaces in an iterative manner. In contrast to techniques such as PCA which vectorize tensor data, CSA's direct use of data in tensor form brings an enhanced ability to learn a representative subspace and an increased number of available projection directions. These properties enable CSA to outperform traditional algorithms in the common case of small sample sizes, where CSA can be effective even with only a single sample per class. Extensive experiments on images of faces and digital numbers encoded as second or third order tensors demonstrate that the proposed CSA outperforms PCA-based algorithms in object reconstruction and object recognition.

Original languageEnglish (US)
Article number4358655
Pages (from-to)36-47
Number of pages12
JournalIEEE Transactions on Circuits and Systems for Video Technology
Issue number1
StatePublished - Jan 2008


  • Concurrent subspaces analysis (CSA)
  • Dimensionality Reduction
  • Dimensionality reduction
  • Object Reconstruction
  • Object Representation
  • Object reconstruction
  • Object representation
  • Principal Components Analysis
  • Principal components analysis (PCA)

ASJC Scopus subject areas

  • Media Technology
  • Electrical and Electronic Engineering


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