# Clustering Algorithm with a Greedy Agglomerative Heuristic and Special Distance Measures
## 2 Kohonen Neural Networks for Clustering Problem
### Proposed Algorithms
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**BVQ**} & \multirow{2}{*}{**SOM**} & \multicolumn{2}{c}{**BVQ-**} & \multicolumn{2}{c}{**BVQ-**} & \multicolumn{2}{c}{**SOM-**} & \multicolumn{2}{c}{**SOM-**} \\  & & & **GREEDY(2)** & **GREEDY(3)** & **GREEDY(2)** & **GREEDY(3)** \\ \hline \hline \multicolumn{7}{c}{Two-batch mixed lot} \\  & \multicolumn{2}{c}{\(KI=2\)} & \multicolumn{2}{c}{\(KI=4\)} & \multicolumn{2}{c}{\(KI=6\)} & \multicolumn{2}{c}{\(KI=4\)} & \multicolumn{2}{c}{\(KI=6\)} \\ Min & 331.089 & 194.303 & 205.657 & 206.582 & 335.258 & 337.849 \\ Max & 331.107 & 196.693 & 335.401 & 337.849 & 335.401 & 337.849 \\ Mean & 331.106 & 195.717 & 326.716 & 320.358 & 335.387 & 337.849 \\ \(\sigma\) & 0.005 & 0.503 & 33.490 & 46.116 & 0.038 & 0.000 \\ V & 0.001 & 0.257 & 10.251 & 14.395 & 0.011 & 0.000 \\ R & 0.018 & 2.390 & 129.744 & 131.268 & 0.143 & 0.000 \\ \multicolumn{7}{c}{Three-batch mixed lot} \\  & \multicolumn{2}{c}{\(KI=3\)} & \multicolumn{2}{c}{\(KI=6\)} & \multicolumn{2}{c}{\(KI=9\)} & \multicolumn{2}{c}{\(KI=6\)} & \multicolumn{2}{c}{\(KI=9\)} \\ Min & 443.219 & 305.398 & 437.281 & 437.742 & 440.640 & 438.611 \\ Max & 444.607 & 361.336 & 444.378 & 439.538 & 444.607 & 439.598 \\ Mean & 444.133 & 338.766 & 442.954 & 438.906 & 444.084 & 439.413 \\ \(\sigma\) & 0.479 & 15.177 & 2.163 & 0.540 & 1.011 & 0.275 \\ V & 0.108 & 4.480 & 0.488 & 0.123 & 0.228 & 0.063 \\ R & 1.388 & 55.937 & 7.097 & 1.795 & 3.967 & 0.987 \\ \multicolumn{7}{c}{Four-batch mixed lot} \\  & \multicolumn{2}{c}{\(KI=4\)} & \multicolumn{2}{c}{\(KI=8\)} & \multicolumn{2}{c}{\(KI=12\)} & \multicolumn{2}{c}{\(KI=8\)} & \multicolumn{2}{c}{\(KI=12\)} \\ Min & 764.357 & 564.890 & 764.433 & 771.053 & 839.280 & 838.055 \\ Max & 856.541 & 673.446 & 836.222 & 866.897 & 851.622 & 874.529 \\ Mean & 818.674 & 614.438 & 787.136 & 790.511 & 845.713 & 854.250 \\ \(\sigma\) & 45.914 & 27.721 & 31.284 & 37.296 & 3.154 & 13.329 \\ V & 5.608 & 4.512 & 3.974 & 4.718 & 0.373 & 1.560 \\ R & 92.185 & 108.556 & 71.789 & 95.844 & 12.342 & 36.475 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Objective function value summarized after 30 attempts (Mahalanobis distance, initialization by random). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Parameter**} & \multirow{2}{*}{**BVQ**} & \multirow{2}{*}{**SOM**} & \multicolumn{2}{c}{**BVQ-**} & \multicolumn{2}{c}{**BVQ-**} & \multicolumn{2}{c}{**SOM-**} & \multicolumn{2}{c}{**SOM-**} \\  & & & **GREEDY(2)** & **GREEDY(3)** & **GREEDY(2)** & **GREEDY(3)** \\ \hline \hline \multicolumn{7}{c}{Two-batch mixed lot} \\  & \multicolumn{2}{c}{\(KI=2\)} & \multicolumn{2}{c}{\(KI=4\)} & \multicolumn{2}{c}{\(KI=6\)} & \multicolumn{2}{c}{\(KI=4\)} & \multicolumn{2}{c}{\(KI=6\)} \\ Min & 186.160 & 185.934 & 186.346 & 186.372 & 186.346 & 186.372 \\ Max & 186.160 & 186.214 & 335.401 & 337.849 & 335.401 & 337.849 \\ Mean & 186.160 & 186.071 & 226.094 & 297.455 & 236.031 & 266.997 \\ \(\sigma\) & 0.000 & 0.064 & 68.228 & 69.337 & 72.732 & 78.067 \\ V & 0.000 & 0.035 & 30.177 & 23.310 & 30.814 & 29.239 \\ R & 0.000 & 0.281 & 149.055 & 151.477 & 149.055 & 151.477 \\ \multicolumn{7}{c}{Three-batch mixed lot} \\  & \multicolumn{2}{c}{\(KI=3\)} & \multicolumn{2}{c}{\(KI=6\)} & \multicolumn{2}{c}{\(KI=9\)} & \multicolumn{2}{c}{\(KI=6\)} & \multicolumn{2}{c}{\(KI=9\)} \\ Min & 690.643 & 493.044 & 551.927 & 493.236 & 695.985 & 696.331 \\ Max & 700.891 & 555.231 & 706.183 & 705.449 & 711.926 & 892.642 \\ Mean & 692.693 & 508.407 & 645.549 & 633.408 & 705.483 & 714.682 \\ \(\sigma\) & 4.243 & 25.699 & 72.850 & 81.067 & 5.039 & 49.382 \\ V & 0.613 & 5.055 & 11.285 & 12.799 & 0.714 & 6.910 \\ R & 10.247 & 62.187 & 154.257 & 212.213 & 15.941 & 196.311 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Objective function value summarized after 30 attempts (Manhattan distance, initialization by average).