Algorithm 1 Node Clustering

Input:$P$, $K^{\prime }$, $K$, $N$, $\sigma$ Output:$C_1,\cdots ,C_K$ /* Constructs adjacency matrix$W$ */ for each$i\in \{1,\cdots ,N\}$do for each$j\in \{1,\cdots ,N\}$do $w_{ij}=\exp \left(-{\Vert p_i-p_j\Vert }_2^2/2{\sigma }^2\right)$ end for end for $W={(w_{ij})}_{N\times N}$ /* Constructs degree matrixd */ for each$i\in \{1,\cdots ,N\}$do $d_i={\displaystyle {\sum }_{j=1}^N{w}_{ij}}$ end for $D=\mathrm{diag}(d_1,d_2,\cdots ,d_N)$ $L=D-W$ $\{f_1,\cdots ,f_{K^{\prime }}\}=Eigenvector(D^{-1/2}L{D}^{-1/2},K^{\prime })$ $F=(f_1,\cdots ,f_{K^{\prime }})$ /* Standardizes$F$by row and generates$F^{\ast }$ */ for each$i\in \{1,\cdots ,N\}$do for each$j\in \{1,\cdots ,K^{\prime }\}$do $f_{ij}^{\ast }=f_{ij}/\sqrt{{\displaystyle {\sum }_{k^{\prime }=1}^{K^{\prime }}{f}_{i{k}^{\prime }}^2}}$ end for end for $F^{\ast }={(f_{ij}^{\ast })}_{N\times K^{\prime }}$ /* Constructs new samples after reducing dimensionality */ for each$i\in \{1,\cdots ,N\}$do ${p^{\prime }}_i={(f_{i1}^{\ast },\cdots ,f_{i{K}^{\prime }}^{\ast })}^{\mathrm{T}}$ end for $P^{\prime }=\{{p^{\prime }}_1,\cdots ,{p^{\prime }}_N\}$ $\{C_1,\cdots ,C_K\}=Kmeans(P^{\prime },K)$ return$C_1,\cdots ,C_K$