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Splitting Choice and Computational Complexity Analysis of Decision Trees.

Xin Zhao1, Xiaokai Nie2

  • 1School of Mathematics, Southeast University, Nanjing 211189, China.

Entropy (Basel, Switzerland)
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Summary

This study evaluates decision tree algorithms, finding the Gini index less biased than entropy for splitting criteria. It also reveals noise variables can be favored, and computational complexity increases linearly with noise.

Keywords:
computational complexitydecision treenoise variablesplitting biassplitting criteria

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Area of Science:

  • Computer Science
  • Machine Learning
  • Data Mining

Background:

  • Decision trees are widely used for classification and regression tasks.
  • The selection of splitting criteria and handling of missing values and noise variables are critical for decision tree performance.
  • Existing research highlights potential biases in splitting criteria and the impact of noise on computational complexity.

Purpose of the Study:

  • To provide theoretical support for decision tree applications by analyzing key aspects of their construction.
  • To investigate the splitting bias related to missing values and variables with many possible values.
  • To examine the influence of noise variables on variable selection and computational complexity.

Main Methods:

  • Theoretical analysis of decision tree algorithms.
  • Evaluation of different splitting criteria, specifically comparing the Gini index and entropy information.
  • Analysis of the impact of missing values and noise variables on the tree-building process and computational cost.

Main Results:

  • The Gini index demonstrates less bias compared to entropy information when selecting splitting criteria, especially with missing values or variables with many possible values.
  • Noise variables with more missing values have a higher probability of being selected over informative variables.
  • Computational complexity increases linearly with the number of noise variables included in the tree-building process.

Conclusions:

  • The Gini index is a more robust splitting criterion than entropy information in decision tree construction.
  • The presence of noise variables can negatively impact variable selection and significantly increase computational demands.
  • Methods that enhance information decomposition while managing increased dimensionality are viable for practical decision tree applications.