Proceedings ArticleDOI
Linear image coding for regression and classification using the tensor-rank principle
Amnon Shashua,Anat Levin +1 more
- Vol. 1, pp 42-49
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TLDR
It is found that for regression the tensor-rank coding, as a dimensionality reduction technique, significantly outperforms other techniques like PCA.Abstract:
Given a collection of images (matrices) representing a "class" of objects we present a method for extracting the commonalities of the image space directly from the matrix representations (rather than from the vectorized representation which one would normally do in a PCA approach, for example). The general idea is to consider the collection of matrices as a tensor and to look for an approximation of its tensor-rank. The tensor-rank approximation is designed such that the SVD decomposition emerges in the special case where all the input matrices are the repeatition of a single matrix. We evaluate the coding technique both in terms of regression, i.e., the efficiency of the technique for functional approximation, and classification. We find that for regression the tensor-rank coding, as a dimensionality reduction technique, significantly outperforms other techniques like PCA. As for classification, the tensor-rank coding is at is best when the number of training examples is very small.read more
Citations
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Journal ArticleDOI
Tensor Decompositions and Applications
Tamara G. Kolda,Brett W. Bader +1 more
TL;DR: This survey provides an overview of higher-order tensor decompositions, their applications, and available software.
Book ChapterDOI
Multilinear Analysis of Image Ensembles: TensorFaces
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Patent
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TL;DR: In this article, a forward-facing vision system for a vehicle includes a forwardfacing camera disposed in a windshield electronics module attached at a windshield of the vehicle and viewing through the windshield.
Patent
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Proceedings ArticleDOI
Non-negative tensor factorization with applications to statistics and computer vision
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TL;DR: A "direct" positive-preserving gradient descent algorithm and an alternating scheme based on repeated multiple rank-1 problems are derived and motivate the use of n-NTF in three areas of data analysis.
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