Algorithm 1 K-means Clustering Algorithm

Input:$D=\left\{d_1, d_2, \dots , d_n\right\}$ /* set of data to be clustered */

$K$ /* number of clusters */

$M$ /* limit of iterations */

Output:$C=\left\{c_1, c_2, \dots , c_K\right\}$ /* set of cluster centroids */

$L=\left\{l\left(d_i\right)|i=1, \dots ,n\right\}$ /* set of cluster labels of D */

begin

$C$ initialized by K-means++;

for each $d_i\in D$ do

$l\left(d_i\right)\leftarrow {\mathrm{argmin}}_{j\in \left\{1,\dots ,K\right\}}d\left(d_i, c_j\right)$;

end

$chagned\leftarrow false$;

$iter\leftarrow 0$;

repeat

for each $c_i\in C$ do

UpdateCluster($c_i$);

end

for each $d_i\in D$ do

$minDist\leftarrow {\mathrm{argmin}}_{j\in \left\{1,\dots ,K\right\}}d\left(d_i, c_j\right)$;

if $minDist\ne l\left(d_i\right)$ then

$l\left(d_i\right)\leftarrow minDist$;

$changed\leftarrow true$;

end

end

$iter\leftarrow iter+1$;

until $changed=true$ and $iter\le M$;

end