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

## Abstract

データの統計的特徴を考慮した距離構造を学習する方法論としてメトリックラーニングが知られており，そのための様々な手法が提案されている．メトリックラーニングはマハラノビス距離におけるマハラノビス行列（以下，計量行列）を学習するための手法であるが，パラメータ数が入力データの次元数の2乗に比例することが知られている．加えて，学習に要するデータの数も同様に増加してしまうため，高次元データを用いた場合には非常に多くのデータを用意する必要がある．本研究では，計量行列のパラメータ数を減少させるための方法として<i>l</i><sub>1</sub>正則化に基づくアプローチを採用し，ADMM (Alternating Direction Method of Multiplier) を用いた最適な計量行列の導出方法を示す．提案手法を高次元，スパースなデータセット，ならびに低次元，密なデータセットそれぞれについて適用し，その有効性について示す．

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 <i>l</i><sub>1</sub> 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.

## Journal

• Journal of Japan Industrial Management Association

Journal of Japan Industrial Management Association 66(3), 230-239, 2015

Japan Industrial Management Association

## Codes

• NII Article ID (NAID)
130005107068
• NII NACSIS-CAT ID (NCID)
AN10561806
• Text Lang
JPN
• ISSN
1342-2618
• NDL Article ID
026816796
• NDL Call No.
Z4-298
• Data Source
NDL  J-STAGE

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