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

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2 Author(s)
Shashua, A. ; Sch. of Comput. Sci. & Eng., Hebrew Univ., Jerusalem, Israel ; Levin, A.

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.

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Computer Vision and Pattern Recognition, 2001. CVPR 2001. Proceedings of the 2001 IEEE Computer Society Conference on  (Volume:1 )

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