Empirical Evaluation of Four Tensor Decomposition Algorithms

Turney, Peter D. (2007) Empirical Evaluation of Four Tensor Decomposition Algorithms. [Departmental Technical Report] (Unpublished)

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Higher-order tensor decompositions are analogous to the familiar Singular Value Decomposition (SVD), but they transcend the limitations of matrices (second-order tensors). SVD is a powerful tool that has achieved impressive results in information retrieval, collaborative filtering, computational linguistics, computational vision, and other fields. However, SVD is limited to two-dimensional arrays of data (two modes), and many potential applications have three or more modes, which require higher-order tensor decompositions. This paper evaluates four algorithms for higher-order tensor decomposition: Higher-Order Singular Value Decomposition (HO-SVD), Higher-Order Orthogonal Iteration (HOOI), Slice Projection (SP), and Multislice Projection (MP). We measure the time (elapsed run time), space (RAM and disk space requirements), and fit (tensor reconstruction accuracy) of the four algorithms, under a variety of conditions. We find that standard implementations of HO-SVD and HOOI do not scale up to larger tensors, due to increasing RAM requirements. We recommend HOOI for tensors that are small enough for the available RAM and MP for larger tensors.

Item Type:Departmental Technical Report
Keywords:tensors, singular value decomposition, Tucker decomposition, tensor decomposition, latent semantic analysis
Subjects:Computer Science > Language
Computer Science > Statistical Models
Linguistics > Computational Linguistics
Computer Science > Machine Learning
Computer Science > Artificial Intelligence
ID Code:5841
Deposited By: Turney, Peter
Deposited On:22 Nov 2007 21:41
Last Modified:11 Mar 2011 08:57

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