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Reducing Multiclass to Binary: A Unifying Approach for Margin Classifiers (2000)

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by Erin L. Allwein , Robert E. Schapire , Yoram Singer
Venue:JOURNAL OF MACHINE LEARNING RESEARCH
Citations:561 - 20 self
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BibTeX

@ARTICLE{Allwein00reducingmulticlass,
    author = {Erin L. Allwein and Robert E. Schapire and Yoram Singer},
    title = {Reducing Multiclass to Binary: A Unifying Approach for Margin Classifiers},
    journal = {JOURNAL OF MACHINE LEARNING RESEARCH},
    year = {2000},
    volume = {1},
    pages = {113--141}
}

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Abstract

We present a unifying framework for studying the solution of multiclass categorization problems by reducing them to multiple binary problems that are then solved using a margin-based binary learning algorithm. The proposed framework unifies some of the most popular approaches in which each class is compared against all others, or in which all pairs of classes are compared to each other, or in which output codes with error-correcting properties are used. We propose a general method for combining the classifiers generated on the binary problems, and we prove a general empirical multiclass loss bound given the empirical loss of the individual binary learning algorithms. The scheme and the corresponding bounds apply to many popular classification learning algorithms including support-vector machines, AdaBoost, regression, logistic regression and decision-tree algorithms. We also give a multiclass generalization error analysis for general output codes with AdaBoost as the binary learner. Experimental results with SVM and AdaBoost show that our scheme provides a viable alternative to the most commonly used multiclass algorithms.

Keyphrases

margin classifier    unifying approach    binary problem    multiclass categorization problem    empirical loss    viable alternative    general method    individual binary learning algorithm    multiclass generalization error analysis    binary learner    popular approach    logistic regression    many popular classification    experimental result    error-correcting property    unifying framework    corresponding bound    output code    margin-based binary learning algorithm    general empirical multiclass loss bound    decision-tree algorithm    used multiclass algorithm    general output code    support-vector machine   

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