Fast similarity computation in factorized tensors

Authors:
Michael E. Houle;Hisashi Kashima;Michael Nett
Affiliations:
National Institute of Informatics, Tokyo, Japan;University of Tokyo, Tokyo, Japan,Basic Research Programs PRESTO, Synthesis of Knowledge for Information Oriented Society, Japan;National Institute of Informatics, Tokyo, Japan,University of Tokyo, Tokyo, Japan
Venue:
SISAP'12 Proceedings of the 5th international conference on Similarity Search and Applications
Year:
2012

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Abstract

Low-rank factorizations of higher-order tensors have become an invaluable tool for researchers from many scientific disciplines. Tensor factorizations have been successfully applied for moderately sized multimodal data sets involving a small number of modes. However, a significant hindrance to the full realization of the potential of tensor methods is a lack of scalability on the client side: even when low-rank representations are provided by an external agent possessing the necessary computational resources, client applications are quickly rendered infeasible by the space requirements for explicitly storing a (dense) low-rank representation of the input tensor. We consider the problem of efficiently computing common similarity measures between entities expressed by fibers (vectors) or slices (matrices) within a given factorized tensor. We show that after appropriate preprocessing, inner products can be efficiently computed independently of the dimensions of the input tensor.