K-Means

Context

Algorithm Details & Recommendations

  • The K-Means algorithm is based on the classical K-Means data clustering algorithm but uses only one dimension, which is the to-be-discretized variable.

  • K-Means returns a discretization that directly depends on the Probability Density Function of the variable.

  • More specifically, it employs the Expectation-Maximization algorithm with the following steps:

    1. Initialization: random creation of K centers

    2. Expectation: each point is associated with the closest center

    3. Maximization: each center position is computed as the barycenter of its associated points

  • Steps 2 and 3 are repeated until convergence is reached.

  • Based on the centers K, the discretization thresholds are defined as:

  • The following figure illustrates how the algorithm works with K=3.

  • For example, applying a three-bin K-Means Discretization to a normally distributed variable would create a central bin representing 50% of the data points and one bin of 25% each for the distribution's tails.

  • Without a Target variable, or if little else is known about the variation domain and distribution of the Continuous variables, K-Means is recommended as the default method.

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