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多値分類問題におけるECOC法の最適性に関する一考察

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  • A Study on the Optimization of the ECOC Method for Multi-label Classification Problems

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Abstract

与えられた二値判分類器を組み合わせて用いる多値分類器の構成法の1つに,符号理論の枠組みを導入した誤り訂正符号に基づく多値分類法(Error-Correcting Output Coding:ECOC法)がある.この手法が実データに対して良い性能を示すことは実験的に知られているが,ECOC法に対する分類精度について,理論的な最適性については明らかになっていない.そこで本研究では最大事後確率分類を可能とする二値分類器を仮定した場合,ECOC法が最適な多値分類法になる十分条件を示す.この結果,同様の仮定のもとでn-vs-allおよびExhaustive符号が最適な多値分類法になることが示せる.これは種々のECOC法に対する最適性の議論の方向性の1つを示唆している.

One of the methods for constructing a multi-valued classifier that uses a combination of given two-valued classifiers is the Error-Correcting Output Coding (ECOC) method, which is based on error-correcting codes introducing a code theory framework. Although it is experimentally known that this method performs well on real data, the theoretical optimality of the classification accuracy for the ECOC method has not been clarified. In this study, we show sufficient conditions for the ECOC method to be an optimal multi-valued classification method under the assumption that binary classifiers achieve maximum posterior probability classification. As a result, we can show that n-vs-all and Exhaustive signs are the best multi-valued classification method under the same assumptions. This suggests one of the directions of the optimization debate for various ECOC methods.

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