A Study of Learning a Sparse Metric Matrix using <i>l</i><sub>1</sub> Regularization Based on Supervised Learning

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  • MIKAWA Kenta
    Department of Industrial and Management Systems Engineering, School of Creative Science and Engineering, Waseda University
  • KOBAYASHI Manabu
    Department Information Management Science, Shonan Institute of Technology
  • GOTO Masayuki
    Department of Industrial and Management Systems Engineering, School of Creative Science and Engineering, Waseda University

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Other Title
  • 教師あり学習に基づく<i>l</i><sub>1</sub>正則化を用いた計量行列の学習法に関する一考察
  • 教師あり学習に基づくl₁正則化を用いた計量行列の学習法に関する一考察
  • キョウシ アリ ガクシュウ ニ モトズク l ₁ セイソクカ オ モチイタ ケイリョウ ギョウレツ ノ ガクシュウホウ ニ カンスル イチ コウサツ

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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.

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