TY - GEN

T1 - Image clustering with tensor representation

AU - He, Xiaofei

AU - Cai, Deng

AU - Liu, Haifeng

AU - Han, Jiawei

PY - 2005

Y1 - 2005

N2 - 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.

AB - 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.

KW - Dimensionality reduction

KW - Graph

KW - Image clustering

KW - Image representation

KW - Locality preserving projection

KW - Manifold

KW - Subspace learning

KW - Tensor

UR - http://www.scopus.com/inward/record.url?scp=84883126925&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84883126925&partnerID=8YFLogxK

U2 - 10.1145/1101149.1101169

DO - 10.1145/1101149.1101169

M3 - Conference contribution

AN - SCOPUS:84883126925

SN - 1595930442

SN - 9781595930446

T3 - Proceedings of the 13th ACM International Conference on Multimedia, MM 2005

SP - 132

EP - 140

BT - Proceedings of the 13th ACM International Conference on Multimedia, MM 2005

T2 - 13th ACM International Conference on Multimedia, MM 2005

Y2 - 6 November 2005 through 11 November 2005

ER -