Abstract
Construction methods for multi-valued classification (multi-class) systems using binary classifiers are discussed and evaluated by a trade-off model for system evaluation based on rate-distortion theory. Suppose the multi-class systems consisted of \(M (\ge 3)\) categories and \(N (\ge M-1)\) binary classifiers, then they can be represented by a matrix W, where the matrix W is given by a table of M code words with length N, called a code word table. For a document classification task, the relationship between the probability of classification error \(P_e\) and the number of binary classifiers N for given M is investigated, and we show that our constructed systems satisfy desirable properties such as “Flexible”, and “Elastic”. In particular, modified Reed Muller codes perform well: they are shown to be “Effective elastic”. As a second application we consider a hand-written character recognition task, and we show that the desirable properties are also satisfied.
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- 1.
For the purpose of comparison, we use “modified one vs. the rest” method by removing the column vector \((0, 0, \cdots , 0, 1)^\mathrm{T}\) of “one vs. the rest” method.
- 2.
The column vectors are randomly chosen, when the number of \(\left( {\begin{array}{c}N_\mathrm{max}\\ N\end{array}}\right) \) combinations is large , e.g. \(N_{\mathrm{max}}=127,\,\,N=63\), \(\left( {\begin{array}{c}N_\mathrm{max}\\ N\end{array}}\right) \fallingdotseq 1.20 \times 10^{37}\).
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Acknowledgment
One of the authors S. H. would like to thank Professor Shin’ ichi Oishi of Waseda University for giving a chance to study this work. The research leading to this paper was partially supported by MEXT Kakenhi under Grant-in Aids for Scientific Research (B) No. 26282090 and (C) No. 16K00491.
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Hirasawa, S., Kumoi, G., Kobayashi, M., Goto, M., Inazumi, H. (2018). System Evaluation of Construction Methods for Multi-class Problems Using Binary Classifiers. In: Rocha, Á., Adeli, H., Reis, L., Costanzo, S. (eds) Trends and Advances in Information Systems and Technologies. WorldCIST'18 2018. Advances in Intelligent Systems and Computing, vol 746. Springer, Cham. https://doi.org/10.1007/978-3-319-77712-2_86
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