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Example: Let cluster feature be C1: “digital camera” & “lense” C2: “computer”

• Fuzzy clustering:
• k fuzzy clusters C1, …, Ck, represented as a partition matrix M = [wij]
• P1: For each object oi and cluster Cj, 0 ≤ wij ≤ 1(fuzzy set)
• P2: For each object oi,
  \[\sum_{i=1}^{k} w_{ij}=1\]
  (equal participation in clustering)
• P3: For each cluster Cj,
  \[0<\sum_{i=1}^{n} w_{ij}
  (ensure no empty cluster)
• Let c1, …, ck as the centers of k clusters
• For each object oi, sum of square error SSE, p is a parameter:

\[SSE(C_{j})=\sum_{i=1}^{n} w_{ij}^{p}dist(o_{i},c_{j})^2\]

\[SSE(o_{j})=\sum_{j=1}^{k} w_{ij}^{p}dist(o_{i},c_{j})^2\]

• For each cluster C, sum of square error: