Fast DTT - A Near Linear Algorithm for Decomposing a Tensor into Factor Tensors

author: Xiaomin Fang, Sun Yat-Sen University
published: Oct. 7, 2014,   recorded: August 2014,   views: 2153


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As tensors provide a natural representation for the higher-order relations, tensor factorization techniques such as Tucker decomposition and CANDECOMP/PARAFAC decomposition have been applied to many fields. Tucker decomposition has strong capacity of expression, but the time complexity is unpractical for the large-scale real problems. On the other hand, CANDECOMP/PARAFAC decomposition is linear in the feature dimensionality, but the assumption is so strong that it abandons some important information. Besides, both of TD and CP decompose a tensor into several factor matrices. However, the factor matrices are not natural for the representation of the higher-order relations. To overcome these problems, we propose a near linear tensor factorization approach, which decompose a tensor into factor tensors in order to model the higher-order relations, without loss of important information. In addition, to reduce the time complexity and the number of the parameters, we decompose each slice of the factor tensors into two smaller matrices. We conduct experiments on both synthetic datasets and real datasets. The experimental results on the synthetic datasets validate that our model has strong capacity of expression. The results on the real datasets show that our approach outperforms the state-of-the-art tensor factorization methods.

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