Machine Learning and Data Mining in Pattern Recognition

The paper is centered on an algebraic approach to the notion of entropy and of several related concepts (conditional entropy, gain, metrics on sets of partitions produced by entropic approaches). Partitions are naturally associated with major data mining problems such as classification, clustering, data quality evaluations, and data preparation. This areas benefit from an algebraic and geometric study of metric structures defined on partitions. We discuss data mining techniques that use metrics defined on sets of partitions of finite sets such as decision tree induction, feature selection, and data discretization.

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