TY - GEN

T1 - On the boosting algorithm for multiclass functions based on information-theoretic criterion for approximation

AU - Takimoto, Eiji

AU - Maruoka, Akira

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1998.

PY - 1998

Y1 - 1998

N2 - We consider the boosting technique that can be directly applied to the classification problem for multiclass functions. Although many boosting algorithms have been proposed so far, all of them are essentially developed for binary classification problems, and in order to handle multiclass classification problems, they need the problems reduced somehow to binary ones. In order to avoid such reductions, we introduce a notion of the pseudo-entropy function G that gives an information-theoretic criterion, called the conditional G-entropy, for measuring the loss of hypotheses. The conditional G-entropy turns out to be useful for defining the weakness of hypotheses that approximate, in some way, to a multiclass function in general, so that we can consider the boosting problem without reduction. We show that the top-down decision tree learning algorithm using G as its splitting criterion is an efficient boosting algorithm based on the conditional G-entropy. Namely, the algorithm intends to minimize the conditional G-entropy, rather than the classification error. In the binary case, our algorithm is identical to the error-based boosting algorithm proposed by Kearns and Mansour, and our analysis gives a simpler proof of their results.

AB - We consider the boosting technique that can be directly applied to the classification problem for multiclass functions. Although many boosting algorithms have been proposed so far, all of them are essentially developed for binary classification problems, and in order to handle multiclass classification problems, they need the problems reduced somehow to binary ones. In order to avoid such reductions, we introduce a notion of the pseudo-entropy function G that gives an information-theoretic criterion, called the conditional G-entropy, for measuring the loss of hypotheses. The conditional G-entropy turns out to be useful for defining the weakness of hypotheses that approximate, in some way, to a multiclass function in general, so that we can consider the boosting problem without reduction. We show that the top-down decision tree learning algorithm using G as its splitting criterion is an efficient boosting algorithm based on the conditional G-entropy. Namely, the algorithm intends to minimize the conditional G-entropy, rather than the classification error. In the binary case, our algorithm is identical to the error-based boosting algorithm proposed by Kearns and Mansour, and our analysis gives a simpler proof of their results.

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U2 - 10.1007/3-540-49292-5_23

DO - 10.1007/3-540-49292-5_23

M3 - Conference contribution

AN - SCOPUS:84949210605

SN - 3540653902

SN - 9783540653905

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 256

EP - 267

BT - Discovery Science - 1st International Conference, DS 1998, Proceedings

A2 - Arikawa, Setsuo

A2 - Motoda, Hiroshi

PB - Springer Verlag

T2 - 1st International Conference on Discovery Science, DS 1998

Y2 - 14 December 1998 through 16 December 1998

ER -