TY - GEN

T1 - System evaluation of ternary error-correcting output codes for multiclass classification problems

AU - Hirasawa, Shigeichi

AU - Kumoi, Gendo

AU - Yagi, Hideki

AU - Kobayashi, Manabu

AU - Goto, Masayuki

AU - Sakai, Tetsuya

AU - Inazumi, Hiroshige

N1 - Funding Information:
*Research leading to this paper was partially supported by the Ministry of Education, Science, Sports and Culture Grant-in-Aids for Scientific Research (C) 19K04914, (B) 19H01721, and (C) 18K11585.
Publisher Copyright:
© 2019 IEEE.

PY - 2019/10

Y1 - 2019/10

N2 - To solve multiple classification problems with M (geq 3) categories, many studies have been devoted using N (geq lceillog-{2}Mrceil) binary ({0, 1}) classifiers, where these systems are known as binary Error-Correcting Output Codes (binary ECOC). As an extended version of the binary ECOC, the ternary ({0,∗1}) ECOC have also been discussed, where ternary classifiers classify data into positive examples when the element is 1, into negative examples when the element is 0, and no classification when the element is. In this paper, we discuss the ternary ECOC system from the view point of the system evaluation model based on rate-distortion function. First, we discuss a table of M code words with length N which is given by a ternary matrix W of M rows and N columns. Next, by leveraging the benchmark data for multiclass document classification which is widely used in Japan, the relationships between the probability of classification error Pe and the number of the ternary classifiers N for a given M are experimentally investigated. In addition, by assuming the M-dimensional Normal distribution for a classification data model, the relationship between Pe and N for a given M is also examined. Finally, we show by the system evaluation model that the ternary ECOC systems have desirable properties such as 'Flexible', 'Elastic', and 'Effective Elastic', when M becomes large.

AB - To solve multiple classification problems with M (geq 3) categories, many studies have been devoted using N (geq lceillog-{2}Mrceil) binary ({0, 1}) classifiers, where these systems are known as binary Error-Correcting Output Codes (binary ECOC). As an extended version of the binary ECOC, the ternary ({0,∗1}) ECOC have also been discussed, where ternary classifiers classify data into positive examples when the element is 1, into negative examples when the element is 0, and no classification when the element is. In this paper, we discuss the ternary ECOC system from the view point of the system evaluation model based on rate-distortion function. First, we discuss a table of M code words with length N which is given by a ternary matrix W of M rows and N columns. Next, by leveraging the benchmark data for multiclass document classification which is widely used in Japan, the relationships between the probability of classification error Pe and the number of the ternary classifiers N for a given M are experimentally investigated. In addition, by assuming the M-dimensional Normal distribution for a classification data model, the relationship between Pe and N for a given M is also examined. Finally, we show by the system evaluation model that the ternary ECOC systems have desirable properties such as 'Flexible', 'Elastic', and 'Effective Elastic', when M becomes large.

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U2 - 10.1109/SMC.2019.8914295

DO - 10.1109/SMC.2019.8914295

M3 - Conference contribution

AN - SCOPUS:85076755223

T3 - Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics

SP - 2893

EP - 2898

BT - 2019 IEEE International Conference on Systems, Man and Cybernetics, SMC 2019

PB - Institute of Electrical and Electronics Engineers Inc.

T2 - 2019 IEEE International Conference on Systems, Man and Cybernetics, SMC 2019

Y2 - 6 October 2019 through 9 October 2019

ER -