Hierarchical Clustering Algorithm

Input: HRRP average range profile sample set $\mathrm{S}=\left\{{\mathsf{\mu }}_1{,\mathsf{\mu }}_2,\cdots {,\mathsf{\mu }}_{\mathrm{m}}\right\}$;             distance metric ${\mathrm{d}}_{\mathrm{avg}}\left({\mathrm{C}}_{\mathrm{i}}{,\mathrm{C}}_{\mathrm{j}}\right)=\frac{1}{\left|{\mathrm{C}}_{\mathrm{i}}\right|\left|{\mathrm{C}}_{\mathrm{j}}\right|}{\displaystyle \sum }_{{\mathsf{\mu }}_{\mathrm{i}}\in {\mathrm{C}}_{\mathrm{i}}}{\displaystyle \sum }_{{\mathsf{\mu }}_{\mathrm{j}}\in {\mathrm{C}}_{\mathrm{j}}}\mathrm{d}\left({\mathsf{\mu }}_{\mathrm{i}}{,\mathsf{\mu }}_{\mathrm{j}}\right)$;             cluster number $\mathrm{k}$.

Process: for$\mathrm{j}=1,2,\cdots ,\mathrm{m}$do                      ${\mathrm{C}}_{\mathrm{j}}=\left\{{\mathsf{\mu }}_{\mathrm{j}}\right\}$                 end for                 for $\mathrm{i}=1,2,\cdots ,\mathrm{m}$ do                      for $\mathrm{j}=\mathrm{i}+1,\cdots ,\mathrm{m}$ do                           $\mathrm{M}\left(\mathrm{i},\mathrm{j}\right){=\mathrm{d}}_{\mathrm{avg}}\left({\mathrm{C}}_{\mathrm{i}}{,\mathrm{C}}_{\mathrm{j}}\right)$;                           $\mathrm{M}\left(\mathrm{j},\mathrm{i}\right)=\mathrm{M}\left(\mathrm{i},\mathrm{j}\right)$                      end for                 end for                 set the number of current clusters: $\mathrm{q}=\mathrm{m}$                 while $\mathrm{q}>\mathrm{k}$ do                      find the two nearest cluster ${\mathrm{C}}_{\mathrm{i}*}$ and ${\mathrm{C}}_{\mathrm{j}*}$;                      merge ${\mathrm{C}}_{\mathrm{i}*}$ and ${\mathrm{C}}_{\mathrm{j}*}$: ${\mathrm{C}}_{\mathrm{i}*}{=\mathrm{C}}_{\mathrm{i}*}\cup {\mathrm{C}}_{\mathrm{j}*}$;                      for ${\mathrm{j}=\mathrm{j}}^{*}{+1,\mathrm{j}}^{*}+2,\cdots ,\mathrm{q}$ do                           renumber cluster ${\mathrm{C}}_{\mathrm{j}}$ as ${\mathrm{C}}_{\mathrm{j}-1}$                      end for                      delete line ${\mathrm{j}}^{*}$ and column ${\mathrm{j}}^{*}$ of matrix $\mathrm{M}$                      for $\mathrm{j}=\mathrm{i}+1,\cdots ,\mathrm{q}-1$ do                           $\mathrm{M}\left({\mathrm{i}}^{*},\mathrm{j}\right){=\mathrm{d}}_{\mathrm{avg}}\left({\mathrm{C}}_{\mathrm{i}*}{,\mathrm{C}}_{\mathrm{j}}\right)$;                           $\mathrm{M}\left({\mathrm{j},\mathrm{i}}^{*}\right)=\mathrm{M}\left({\mathrm{i}}^{*},\mathrm{j}\right)$                      end for                      $\mathrm{q}=\mathrm{q}-1$                  end while

Output: clusters $\mathrm{C}=\left\{{\mathrm{C}}_1{,\mathrm{C}}_2,\cdots {,\mathrm{C}}_{\mathrm{k}}\right\}$