Image clustering with tensor representation

Xiaofei He, Deng Cai, Haifeng Liu, Jiawei Han

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We consider the problem of image representation and clustering. Traditionally, an n1 × n2 image is represented by a vector in the Euclidean space Rn1×n2. Some learning algorithms are then applied to these vectors in such a high dimensional space for dimensionality reduction, classification, and clustering. However, an image is intrinsically a matrix, or the second order tensor. The vector representation of the images ignores the spatial relationships between the pixels in an image. In this paper, we introduce a tensor framework for image analysis. We represent the images as points in the tensor space Rn1 ⊗ Rn2 which is a tensor product of two vector spaces. Based on the tensor representation, we propose a novel image representation and clustering algorithm which explicitly considers the manifold structure of the tensor space. By preserving the local structure of the data manifold, we can obtain a tensor subspace which is optimal for data representation in the sense of local isometry. We call it TensorImage approach. Traditional clustering algorithm such as K-means is then applied in the tensor sub-space. Our algorithm shares many of the data representation and clustering properties of other techniques such as Locality Preserving Projections, Laplacian Eigenmaps, and spectral clustering, yet our algorithm is much more computationally efficient. Experimental results show the efficiency and effectiveness of our algorithm.

Original languageEnglish (US)
Title of host publicationProceedings of the 13th ACM International Conference on Multimedia, MM 2005
Number of pages9
StatePublished - 2005
Event13th ACM International Conference on Multimedia, MM 2005 - Singapore, Singapore
Duration: Nov 6 2005Nov 11 2005

Publication series

NameProceedings of the 13th ACM International Conference on Multimedia, MM 2005


Other13th ACM International Conference on Multimedia, MM 2005


  • Dimensionality reduction
  • Graph
  • Image clustering
  • Image representation
  • Locality preserving projection
  • Manifold
  • Subspace learning
  • Tensor

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Computer Vision and Pattern Recognition
  • Human-Computer Interaction
  • Software


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