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Revisiting Possibilistic Fuzzy C-Means Clustering Using the Majorization-Minimization Method.

Yuxue Chen1, Shuisheng Zhou1

  • 1School of Mathematics and Statistics, Xidian University, Xi'an 710071, China.

Entropy (Basel, Switzerland)
|August 29, 2024
PubMed
Summary

This study introduces MMPFCM, an improved Possibilistic Fuzzy C-Means (PFCM) clustering algorithm. MMPFCM uses majorization-minimization to overcome PFCM

Keywords:
fuzzy c-meanslocal minimummajorization-minimizationpossibilistic fuzzy c-means

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Area of Science:

  • Data Mining
  • Machine Learning
  • Pattern Recognition

Background:

  • Possibilistic Fuzzy C-Means (PFCM) combines Fuzzy C-Means (FCM) and Possibilistic C-Means (PCM).
  • PFCM offers stability and robustness but can converge to suboptimal solutions.
  • Existing PFCM methods face challenges with local minima, impacting clustering performance.

Purpose of the Study:

  • To rederive Possibilistic Fuzzy C-Means (PFCM) using the majorization-minimization (MM) method.
  • To propose an optimized algorithm, MMPFCM, addressing PFCM's local minimum convergence issue.
  • To enhance the performance and efficiency of hybrid clustering techniques.

Main Methods:

  • Re-derivation of PFCM using the majorization-minimization (MM) technique.
  • Introduction of a novel intermediate variable 's' to simplify the optimization problem.
  • Development of an iterative sub-problem solver based on the MM method for MMPFCM.

Main Results:

  • MMPFCM converges to a superior local minimum compared to standard PFCM.
  • Experimental results validate MMPFCM's improved objective function values and clustering accuracy.
  • MMPFCM maintains the same computational complexity as PFCM but requires less memory per iteration.

Conclusions:

  • MMPFCM offers a more effective optimization approach for PFCM clustering.
  • The MM-based derivation and optimization strategy enhance clustering performance.
  • MMPFCM presents a computationally efficient and memory-sparing alternative for hybrid clustering.