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

Summary: Rank-R Approximation of Tensors Using Image-as-Matrix
Hongcheng Wang, Narendra Ahuja
Beckman Institute, University of Illinois at Urbana-Champaign, USA
{wanghc,ahuja }@vision.ai.uiuc.edu
We present a novel multilinear algebra based ap-
proach for reduced dimensionality representation of im-
age ensembles. We treat an image as a matrix, in-
stead of a vector as in traditional dimensionality reduc-
tion techniques like PCA, and higher-dimensional data
as a tensor. This helps exploit spatio-temporal redun-
dancies 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 ef-
ficient for only low-rank approximations. For larger
dimensionality reductions, the memory and time costs
of this algorithm become prohibitive. We propose a


Source: Ahuja, Narendra - Department of Electrical and Computer Engineering, University of Illinois at Urbana-Champaign


Collections: Computer Technologies and Information Sciences; Engineering