A study of learning a sparse metric matrix using l1 regularization based on supervised learning

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In this paper, we focus on classification problems based on the vector space model. As one of the methods, distance metric learning which estimates an appropriate metric matrix for classification by using the iterative optimization procedure is known as an effective method. However, the distance metric learning for high dimensional data tends to cause the problems of overfitting to a training dataset and longer computational time. In addition, the number of parameters that need to be estimated is in proportion to the square of the input data dimension. Therefore, if the dimension of input data becomes high, the number of training data to acquire a metric matrix with enough accuracy becomes enormous. Especially, these problems are caused when analyzing the document data and purchase history data stored in the EC site with high dimensional and sparse structure. To avoid these problems, we propose the method of l1 regularized distance metric learning by introducing the alternating direction method of multiplier (ADMM) algorithm. The effectiveness of our proposed method is clarified by classification experiments using a newspaper article that has a highly dimensional and sparse structure and the UCI machine learning repository, which has a low and dense structure.

Original languageEnglish
Pages (from-to)230-239
Number of pages10
JournalJournal of Japan Industrial Management Association
Issue number3
Publication statusPublished - 2015


  • ADMM
  • Distance metric learning
  • Document classification
  • L regularization
  • Vector space model

ASJC Scopus subject areas

  • Strategy and Management
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics


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