Tensor factorization using auxiliary information

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• 作者：Atsuhiro Narita (1) atsuhiro_narita@mist.i.u-tokyo.ac.jp
  Kohei Hayashi (1) kohei_hayashi@mist.i.u-tokyo.ac.jp
  Ryota Tomioka (1) tomioka@mist.i.u-tokyo.ac.jp
  Hisashi Kashima (12) kashima@mist.i.u-tokyo.ac.jp
• 关键词：Tensors &#8211 ; Multi ; way arrays &#8211 ; CP ; decomposition &#8211 ; Tucker decomposition &#8211 ; Side information
• 刊名：Data Mining and Knowledge Discovery
• 出版年：2012
• 出版时间：September 2012
• 年：2012
• 卷：25
• 期：2
• 页码：298-324
• 全文大小：1.1 MB
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• 作者单位：1. Department of Mathematical Informatics, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656 Japan2. Basic Research Programs PRESTO, Synthesis of Knowledge for Information Oriented Society, Tokyo, Japan
• ISSN：1573-756X

文摘

Most of the existing analysis methods for tensors (or multi-way arrays) only assume that tensors to be completed are of low rank. However, for example, when they are applied to tensor completion problems, their prediction accuracy tends to be significantly worse when only a limited number of entries are observed. In this paper, we propose to use relationships among data as auxiliary information in addition to the low-rank assumption to improve the quality of tensor decomposition. We introduce two regularization approaches using graph Laplacians induced from the relationships, one for moderately sparse cases and the other for extremely sparse cases. We also give present two kinds of iterative algorithms for approximate solutions: one based on an EM-like algorithms which is stable but not so scalable, and the other based on gradient-based optimization which is applicable to large scale datasets. Numerical experiments on tensor completion using synthetic and benchmark datasets show that the use of auxiliary information improves completion accuracy over the existing methods based only on the low-rank assumption, especially when observations are sparse.