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What is fuzzy c-means?

hard

Answer

  • Each point has a membership degree uiju_{\mathrm{ij}} ∈ [0,1] for every cluster (rows sum to 1).
  • Centroids weighted by uijmu_{\mathrm{ij}}^{m} for a fuzzifier m > 1 (m=2 typical).
  • Update alternates between soft assignments and weighted means.
  • Use when clusters overlap naturally and hard assignment loses information.
  • Sits between k-means (m→1: hard) and uniform (m→∞).
Check yourself — multiple choice
  • Hard assignment
  • Soft membership uiju_{\mathrm{ij}} ∈ [0,1] with fuzzifier m>1; centroids weighted by umu^{m}; sits between k-means (m→1) and uniform (m→∞)
  • Random
  • Only supervised

Fuzzy c-means: soft memberships with fuzzifier m; useful for overlapping clusters.

#clustering

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