# 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}{\(K1=2\)} & \multicolumn{2}{c}{\(K1=4\)} & \multicolumn{2}{c}{\(K1=6\)} & \multicolumn{2}{c}{\(K1=4\)} & \multicolumn{2}{c}{\(K1=6\)} \\ Min & 186.160 & 185.962 & 186.346 & 186.372 & 186.346 & 186.372 \\ Max & 186.160 & 186.233 & 186.346 & 186.372 & 186.346 & 186.372 \\ Mean & 186.160 & 186.092 & 186.346 & 186.372 & 186.346 & 186.372 \\ \(\sigma\) & 0.000 & 0.070 & 0.000 & 0.000 & 0.000 & 0.000 \\ V & 0.000 & 0.038 & 0.000 & 0.000 & 0.000 & 0.000 \\ R & 0.000 & 0.271 & 0.000 & 0.000 & 0.000 & 0.000 \\ \multicolumn{7}{c}{Three-batch mixed lot} \\  & \multicolumn{2}{c}{\(K1=3\)} & \multicolumn{2}{c}{\(K1=6\)} & \multicolumn{2}{c}{\(K1=9\)} & \multicolumn{2}{c}{\(K1=6\)} & \multicolumn{2}{c}{\(K1=9\)} \\ Min & 314.924 & 241.673 & 241.731 & 241.795 & 314.924 & 310.298 \\ Max & 314.924 & 312.911 & 241.731 & 241.795 & 314.924 & 310.298 \\ Mean & 314.924 & 265.496 & 241.731 & 241.795 & 314.924 & 310.298 \\ \(\sigma\) & 0.000 & 33.876 & 0.000 & 0.000 & 0.000 & 0.000 \\ V & 0.000 & 12.759 & 0.000 & 0.000 & 0.000 & 0.000 \\ R & 0.000 & 71.238 & 0.000 & 0.000 & 0.000 & 0.000 \\ \multicolumn{7}{c}{Four-batch mixed lot} \\  & \multicolumn{2}{c}{\(K1=4\)} & \multicolumn{2}{c}{\(K1=8\)} & \multicolumn{2}{c}{\(K1=12\)} & \multicolumn{2}{c}{\(K1=8\)} & \multicolumn{2}{c}{\(K1=12\)} \\ Min & 546.596 & 492.541 & 549.130 & 492.903 & 552.883 & 548.802 \\ Max & 546.596 & 544.710 & 549.751 & 492.903 & 552.883 & 559.135 \\ Mean & 546.596 & 509.981 & 549.586 & 492.903 & 552.883 & 550.164 \\ \(\sigma\) & 0.000 & 24.249 & 0.284 & 0.000 & 0.000 & 2.840 \\ V & 0.000 & 4.755 & 0.052 & 0.000 & 0.000 & 0.516 \\ R & 0.000 & 52.169 & 0.621 & 0.000 & 0.000 & 10.333 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Objective function value summarized after 30 attempts (squared Euclidean distance, initialization by k-means). \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 & 201.387 & 194.572 & 205.657 & 206.582 & 205.657 & 206.582 \\ Max & 201.387 & 197.145 & 205.657 & 206.582 & 205.657 & 206.582 \\ Mean & 201.387 & 195.929 & 205.657 & 206.582 & 205.657 & 206.582 \\ \(\sigma\) & 0.000 & 0.568 & 0.000 & 0.000 & 0.000 & 0.000 \\ V & 0.000 & 0.290 & 0.000 & 0.000 & 0.000 & 0.000 \\ R & 0.000 & 2.573 & 0.000 & 0.000 & 0.000 & 0.000 \\ \multicolumn{6}{c}{Three-batch mixed lot} \\  & \multicolumn{2}{c}{\(KI=4\)} & \multicolumn{2}{c}{\(KI=8\)} & \(KI=12\) & \(KI=8\) & \(KI=12\) \\ Min & 758.068 & 572.730 & 728.875 & 696.210 & 757.097 & 756.752 \\ Max & 758.068 & 663.835 & 730.771 & 722.998 & 757.734 & 757.838 \\ Mean & 758.068 & 619.269 & 730.508 & 709.527 & 757.375 & 757.390 \\ \(\sigma\) & 0.000 & 29.509 & 0.663 & 11.950 & 0.269 & 0.344 \\ V & 0.000 & 4.765 & 0.091 & 1.684 & 0.036 & 0.045 \\ R & 0.000 & 91.104 & 1.896 & 26.788 & 0.638 & 1.086 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Objective function value summarized after 30 attempts (Mahalanobis distance, initialization by average).