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Efficient Orthogonal Tensor Decomposition, with an Application to Latent Variable Model Learning

Király, FJ; (2013) Efficient Orthogonal Tensor Decomposition, with an Application to Latent Variable Model Learning. arXiv , Article arXiv:1309.3233 [stat.ML]. Green open access

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Abstract

Decomposing tensors into orthogonal factors is a well-known task in statistics, machine learning, and signal processing. We study orthogonal outer product decompositions where the factors in the summands in the decomposition are required to be orthogonal across summands, by relating this orthogonal decomposition to the singular value decompositions of the flattenings. We show that it is a non-trivial assumption for a tensor to have such an orthogonal decomposition, and we show that it is unique (up to natural symmetries) in case it exists, in which case we also demonstrate how it can be efficiently and reliably obtained by a sequence of singular value decompositions. We demonstrate how the factoring algorithm can be applied for parameter identification in latent variable and mixture models.

Type: Article
Title: Efficient Orthogonal Tensor Decomposition, with an Application to Latent Variable Model Learning
Open access status: An open access version is available from UCL Discovery
Publisher version: https://arxiv.org/abs/1309.3233
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Machine Learning (stat.ML); Learning (cs.LG); Statistics Theory (math.ST)
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Statistical Science
URI: https://discovery.ucl.ac.uk/id/eprint/1517409
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