Rank-R Approximation of Tensors: Using Image-as-Matrix Representation

We present a novel multilinear algebra based approach for reduced dimensionality representation of image ensembles. We treat an image as a matrix, instead of a vector as in traditional dimensionality reduction techniques like PCA, and higher-dimensional data as a tensor. This helps exploit spatio-temporal redundancies with less information loss than image-as-vector methods. The challenges lie in the computational and memory requirements for large ensembles. Currently, there exists a rank-R approximation algorithm which, although applicable to any number of dimensions, is efficient for only low-rank approximations. For larger dimensionality reductions, the memory and time costs of this algorithm become prohibitive. We propose a novel algorithm for rank-R approximations of thirdorder tensors, which is efficient for arbitrary R but for the important special case of 2D image ensembles, e.g. video. Both of these algorithms reduce redundancies present in all dimensions. Rank-R tensor approx...

• Type: Conference
• Year: 2005
• Where: CVPR
• Authors: Hongcheng Wang, Narendra Ahuja
• Keywords: Computer Vision, CVPR 2005, Dimensionality Reduction Techniques, Dimensionality Representation, Image Ensembles, Larger Dimensionality Reductions, Rank-r Approximation Algorithm