Similarity learning with a collection of matrices and tensors

Clément Grimal 1 Gilles Bisson 1, *
* Auteur correspondant
Abstract : In data analysis domain, data are often described by a single matrix in which the rows describe objects and the columns describe features of these objects. Nevertheless, in many real world applications, data are said to be multi-dimensional, meaning that they cannot be fully described by only one matrix, but rather by a collection of matrices, or even as a tensor. Typically, we can nd these kind of data in the social networks where several entities (people, documents, etc) can have multiple relationship. In the framework of the co-clustering problem (or two-way clustering) we already proposed (Bisson et al. 2008; Hussain et al. 2010) an algorithm, named chisim, to compute simultaneously the similarity measures between rows and columns. This approach allows to discover high order similarities between objects and features, and we experimentally shown that our method achieves better results than the state of the art co-clustering systems such as LSA, ITCC, etc. In this paper, we propose to go a step further by extending the chisim method in two directions. First, we introduce di erent architectures in order to combine the similarity matrices obtained by applying chisim to a collection of matrices. We show that some of these architectures improve the quality of the co-clustering. Second, we propose a natural generalization of chisim in order to directly tackle tensors. Here a major concern is time and space complexity of this new method and thus we analyze some trade-o allowing the problem to become tractable for medium size datasets.
Type de document :
Communication dans un congrès
GfKl 2011 - Joint Conference of the German Classification Society, Aug 2011, Frankfurt, Germany. pp.82, 2011
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https://hal.archives-ouvertes.fr/hal-00742207
Contributeur : Gilles Bisson <>
Soumis le : mardi 16 octobre 2012 - 11:14:10
Dernière modification le : mardi 28 octobre 2014 - 18:34:57

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  • HAL Id : hal-00742207, version 1

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Clément Grimal, Gilles Bisson. Similarity learning with a collection of matrices and tensors. GfKl 2011 - Joint Conference of the German Classification Society, Aug 2011, Frankfurt, Germany. pp.82, 2011. <hal-00742207>

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