Three Discretization Methods

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本文详细阐述了如何使用熵作为指导，选择最优的二元离散化边界来离散化特征，该过程可以递归应用于生成多个区间。熵作为监督方法的核心，在划分数据集时考虑了类标签信息。同时，介绍了等频区间和等宽区间划分两种无监督离散化方法，它们不依赖于类标签。

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If we are given a set of instances S, a feature A, and a partition boundary T, the class information entropy of the partition induced by T, denoted E(A,T,S) is given by:

For a given feature A, the boundary Tmin which minimizes the entropy function over all possible partition boundaries is selected as a binary discretization boundary. This method can then be applied recursively to both of the partitions induced by Tmin until some stopping condition is achieved, thus creating multiple intervals on the feature A.

Discretization based on entropy is supervised method because it needs the class lables of instances.

Equal frequency Intervals, divides a continuous variable into k bins where (given m instances) each bin contains m/k (possibly duplicated) adjacent values.