Evaluation Criteria Based on Mutual Information for Classifications Including Rejected Class
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摘要: 不同于传统的基于性能为评价指标的机器学习方法, 基于互信息评价准则的学习方法显示出了独到的优越性. 但是, 如何理解互信息概念在分类问题中的具体内涵与应用特点仍然是不明确的. 本文推导了归一化互信息与包括拒识类别分类矩阵的显式表达关系. 给出了归一化互信息在极值情况下的三个相关定理, 以及在二值分类情况下误差敏感度分析方程. 为互信息与传统分类性能指标作出了初步理论方面解释. 通过给出的若干简单实例, 讨论了互信息概念及评价准则在分类问题中的基本应用特点及相关问题.Abstract: Different from the conventional evaluation criteria using performance measures, information theory based criteria present a unique beneficial feature in applications of machine learning. However, we are still far from possessing an in-depth understanding of the ``entropy'' type criteria, say, in relation to the conventional performance-based criteria. This paper studies generic classification problems, which include a rejected, or unknown, class. We present the basic formulas and schematic diagram of classification learning based on information theory. A closed-form equation is derived between the normalized mutual information and the augmented confusion matrix for the generic classification problems. Three theorems and one set of sensitivity equations are given for studying the relations between mutual information and conventional performance indices. We also present numerical examples and several discussions related to advantages and limitations of mutual information criteria in comparison with the conventional criteria.
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Key words:
- Entropy /
- mutual information /
- evaluation criteria /
- classification /
- confusion matrix /
- machine learning
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