## 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 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.

Original language | American English |
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Pages (from-to) | I42-I49 |

Journal | Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition |

Volume | 1 |

State | Published - 2001 |

Event | 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Kauai, HI, United States Duration: 8 Dec 2001 → 14 Dec 2001 |