Adaptive Initialization Method Based on Spatial Local Information for 𝑘-Means Algorithm

Algorithm 3

Determining initial centers from candidates.

Input:  cluster number 𝐾, candidate set 𝐶_cand (obtained by Algorithm 1 or Algorithm 2).

Output:  Initial centers 𝐜⁰₁,…,𝐜⁰_𝐾.

(1) 𝐜⁰₁=𝑥_𝑖, 𝑥_𝑖 is random chosen from 𝐶_cand, set 𝑘=1;

(2) 𝐜⁰₂=argmax_𝑥𝑗𝑥_𝑗−𝐜⁰₁,∀𝑥_𝑗∈𝐶_cand, set 𝑘=2;

(3) if   𝑘<𝐾 do

(4)  set 𝑘=𝑘+1,𝐜⁰_𝑘=argmax_𝑥𝑗min𝑥_𝑗−𝐜⁰_𝑡,∀𝑥_𝑗∈𝐶_cand,𝑡=1,…,𝑘−1;

(5) repeat step (4) until 𝑘=𝐾.