TY - JOUR

T1 - Linear image coding for regression and classification using the tensor-rank principle

AU - Shashua, Amnon

AU - Levin, Anat

PY - 2001

Y1 - 2001

N2 - 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 repetition 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.

AB - 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 repetition 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.

UR - http://www.scopus.com/inward/record.url?scp=0035683732&partnerID=8YFLogxK

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AN - SCOPUS:0035683732

SN - 1063-6919

VL - 1

SP - I42-I49

JO - Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition

JF - Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition

T2 - 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition

Y2 - 8 December 2001 through 14 December 2001

ER -