Image clustering with tensor representation

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 isom...

• Type: Conference
• Year: 2005
• Where: MM
• Authors: Xiaofei He, Deng Cai, Haifeng Liu, Jiawei Han
• Keywords: Image, MM 2005, Tensor, Tensor Space