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Normalized mutual information is a biased measure for classification and community detection.

Maximilian Jerdee1,2, Alec Kirkley3,4,5, Mark Newman6,7

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Normalized mutual information (NMI) is biased in clustering and classification evaluations. This study introduces a modified NMI to correct these biases, significantly impacting conclusions on algorithm performance, especially for network community detection.

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Area of Science:

  • Computer Science
  • Information Theory
  • Data Mining

Background:

  • Normalized mutual information (NMI) is a standard metric for evaluating clustering and classification algorithms.
  • Existing NMI calculations contain biases stemming from ignoring information content and symmetric normalization.

Purpose of the Study:

  • To address the limitations of traditional NMI.
  • To introduce a modified, unbiased mutual information measure.
  • To demonstrate the impact of NMI bias on algorithm performance conclusions.

Main Methods:

  • Developed a modified mutual information calculation.
  • Conducted extensive numerical tests on network community detection algorithms.
  • Compared results using traditional NMI versus the modified measure.

Main Results:

  • Identified two key biases in traditional NMI: ignoring contingency table information and spurious dependence from symmetric normalization.
  • The modified mutual information measure corrects these identified shortcomings.
  • Conclusions regarding the best-performing algorithms for network community detection are significantly altered by using the unbiased measure.

Conclusions:

  • Traditional NMI introduces significant biases in performance evaluation.
  • The proposed modified mutual information offers a more accurate and reliable similarity measure.
  • Employing an unbiased measure is crucial for drawing correct conclusions in algorithm comparison studies, particularly in network community detection.