# 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 \multicolumn{6}{c}{Two-batch mixed lot} \\  & \multicolumn{2}{c}{\(KI=2\)} & \multicolumn{2}{c}{\(KI=4\)} & \(KI=6\) & \(KI=4\) & \(KI=6\) \\ Min & 186.160 & 185.969 & 186.346 & 186.372 & 186.346 & 186.372 \\ Max & 186.160 & 186.183 & 186.346 & 186.372 & 186.346 & 186.372 \\ Mean & 186.160 & 186.088 & 186.346 & 186.372 & 186.346 & 186.372 \\ \(\sigma\) & 0.000 & 0.048 & 0.000 & 0.000 & 0.000 & 0.000 \\ V & 0.000 & 0.026 & 0.000 & 0.000 & 0.000 & 0.000 \\ R & 0.000 & 0.214 & 0.000 & 0.000 & 0.000 & 0.000 \\ \multicolumn{6}{c}{Three-batch mixed lot} \\  & \multicolumn{2}{c}{\(KI=3\)} & \multicolumn{2}{c}{\(KI=6\)} & \(KI=9\) & \(KI=6\) & \(KI=9\) \\ Min & 314.924 & 241.651 & 314.924 & 310.298 & 314.924 & 310.298 \\ Max & 325.737 & 315.550 & 325.737 & 320.973 & 325.737 & 320.973 \\ Mean & 315.645 & 272.613 & 316.366 & 315.280 & 315.645 & 311.010 \\ \(\sigma\) & 2.792 & 35.746 & 3.805 & 5.513 & 2.792 & 2.756 \\ V & 0.885 & 13.112 & 1.203 & 1.748 & 0.885 & 0.886 \\ R & 10.813 & 73.899 & 10.813 & 10.675 & 10.813 & 10.675 \\ \multicolumn{6}{c}{Four-batch mixed lot} \\  & \multicolumn{2}{c}{\(KI=4\)} & \multicolumn{2}{c}{\(KI=8\)} & \(KI=12\) & \(KI=8\) & \(KI=12\) \\ Min & 703.485 & 492.663 & 562.352 & 561.616 & 711.909 & 707.793 \\ Max & 703.485 & 550.840 & 711.945 & 707.793 & 711.945 & 707.793 \\ Mean & 703.485 & 523.502 & 701.972 & 697.952 & 711.942 & 707.793 \\ \(\sigma\) & 0.000 & 26.008 & 38.625 & 37.718 & 0.009 & 0.000 \\ V & 0.000 & 4.968 & 5.502 & 5.404 & 0.001 & 0.000 \\ R & 0.000 & 58.177 & 149.592 & 146.177 & 0.035 & 0.000 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Objective function value summarized after 30 attempts (squared Euclidean 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 & 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 & 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 11: Objective function value summarized after 30 attempts (Mahalanobis distance, initialization by k-means).