Communication P Systems on Simplicial Complexes with Applications in Cluster Analysis

Algorithm 1

A self-joining clustering algorithm.

Inputs:  Ω={𝑥₁,𝑥₂,…,𝑥_𝑁}, 𝛿₀: similarity threshold value, 𝒩_𝑖={𝑦∣𝑦,𝑥_𝑖 are incident}

Outputs:  𝒞={𝐶₁,𝐶₂,…,𝐶_𝑡}: set of clusters, 𝑡: number of clusters, Ω₀: outliers

Begin

Set Ω₁=Ω₀=∅, 𝐶₁=∅, 𝑡=1.

for 𝑖=1  to 𝑁

  If 𝒩_𝑖=∅, then add 𝑥_𝑖 into set Ω₀. Otherwise add 𝑥_𝑖 into set Ω₁. For each 𝑥_𝑗∈𝒩_𝑖,𝑗>𝑖, calculate

  the similarity measure 𝑓(𝑥_𝑖,𝑦). If 𝑓(𝑥_𝑖,𝑦)>𝛿₀, then set the edge 𝜎(𝑥_𝑖𝑦) as active. In this case, set

  𝐶₁={𝑥_𝑖} if 𝐶₁ is still an empty set.

end

while  Ω₁≠∅  do

   (1) For each 𝑥∈Ω₁ if there exists an active edge 𝜎(𝑥𝑦) with 𝑥≠𝑦, 𝑦∈𝐶_𝑡, then add 𝑥 into 𝐶_𝑡 and

  remove 𝑥 from Ω₁.

   (2) 𝑡=𝑡+1.

end

End