# 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} \hline \hline
**Parameter** & **SCL** & **SCL-GREEDY(2)** & **SCL-GREEDY(3)** \\ \hline  & \multicolumn{3}{c}{Two-batch mixed lot (\(p<0.00001\))} \\  & \(KI=2\) & \(KI=4\) & \(KI=6\) \\ Min & 198.486 & 193.825 & 191.611 \\ Max & 450.382 & 413.390 & 386.087 \\ Mean & 312.271 & 228.919 & **205.969 1**  \\ \(\sigma\) & 100.749 & 74.987 & 47.677 \\ V & 32.263 & 32.757 & 23.148 \\ R & 251.896 & 219.564 & 194.475 \\  & \multicolumn{3}{c}{Three-batch mixed lot (\(p<0.00001\))} \\  & \(KI=3\) & \(KI=6\) & \(KI=9\) \\ Min & 367.557 & 366.012 & 366.085 \\ Max & 372.730 & 370.568 & 369.725 \\ Mean & 372.527 & 369.305 & **368.306** \\ \(\sigma\) & 0.942 & 1.715 & 1.324 \\ V & 0.253 & 0.464 & 0.360 \\ R & 5.173 & 4.556 & 3.640 \\  & \multicolumn{3}{c}{Four-batch mixed lot (\(p=0.02088\))} \\  & \(KI=4\) & \(KI=8\) & \(KI=12\) \\ Min & 952.513 & 939.456 & 914.668 \\ Max & 1142.098 & 1129.014 & 1112.335 \\ Mean & 1097.790 & 1099.933 & **1067.170** \\ \(\sigma\) & 73.902 & 54.806 & 69.570 \\ V & 6.732 & 4.983 & 6.519 \\ R & 189.584 & 189.558 & 197.668 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Objective function value summarized after 30 attempts (squared Euclidean distance). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **SCL** & **SCL-GREEDY(2)** & **SCL-GREEDY(3)** \\ \hline \hline  & \multicolumn{2}{c}{Two-batch mixed lot (\(p\) = 0.06288)} \\  & \(KI=2\) & \(KI=4\) & \(KI=6\) \\ Min & 352.603 & 359.915 & 356.673 \\ Max & 458.955 & 439.944 & 421.191 \\ Mean & 399.825 & 396.924 & 388.449 \\ \(\sigma\) & 24.151 & 21.471 & 15.522 \\ V & 6.040 & 5.409 & 3.996 \\ R & 106.353 & 80.029 & 64.519 \\  & \multicolumn{2}{c}{Three-batch mixed lot (\(p\) = 0.00338)} \\  & \(KI=3\) & \(KI=6\) & \(KI=9\) \\ Min & 462.220 & 455.998 & 451.949 \\ Max & 493.155 & 493.356 & 490.924 \\ Mean & 484.589 & 480.276 & **476.854 1** \\ \(\sigma\) & 7.020 & 8.892 & 8.978 \\ V & 1.449 & 1.851 & 1.883 \\ R & 30.935 & 37.358 & 38.976 \\ \multicolumn{2}{c}{Four-batch mixed lot (\(p\) = 0.00034)} \\  & \(KI=4\) & \(KI=8\) & \(KI=12\) \\ Min & 962.070 & 980.266 & 959.326 \\ Max & 1084.960 & 1129.044 & 1109.918 \\ Mean & 1050.083 & 1044.941 & **996.063** \\ \(\sigma\) & 34.760 & 63.595 & 51.328 \\ V & 3.310 & 6.086 & 5.153 \\ R & 122.890 & 148.778 & 150.592 \\ \hline \end{tabular}

* The best mean values of objective function are given in bold if the difference between SCL algorithm and its greedy version is statistically significant at \(p\leq 0.05\) (statistical significance was tested using the Wilcoxon rank sum test).

\end{table} 
Table 4: Objective function value summarized after 30 attempts (Mahalanobis distance). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **SCL** & **SCL-GREEDY(2)** & **SCL-GREEDY(3)** \\ \hline \hline  & \multicolumn{2}{c}{Two-batch mixed lot (\(p\) = 0.00001)} \\  & \(KI=2\) & \(KI=4\) & \(KI=6\) \\ Min & 198.486 & 193.825 & 191.609 \\ Max & 437.413 & 403.538 & 396.210 \\ Mean & 360.874 & 248.205 & **224.361 1** \\ \(\sigma\) & 87.569 & 88.921 & 72.589 \\ V & 24.266 & 35.826 & 32.354 \\ R & 238.927 & 209.712 & 204.602 \\  & \multicolumn{2}{c}{Three-batch mixed lot (\(p\) < 0.00001)} \\  & \(KI=3\) & \(KI=6\) & \(KI=9\) \\ Min & 372.016 & 366.748 & 365.858 \\ Max & 372.730 & 370.567 & 369.709 \\ Mean & 372.636 & 369.982 & **368.337** \\ \(\sigma\) & 0.179 & 1.256 & 1.271 \\ V & 0.048 & 0.340 & 0.345 \\ R & 0.714 & 3.819 & 3.851 \\  & \multicolumn{2}{c}{Four-batch mixed lot (\(p\) = 0.00096)} \\  & \(KI=4\) & \(KI=8\) & \(KI=12\) \\ Min & 952.637 & 939.453 & 912.548 \\ Max & 1140.960 & 1131.118 & 1109.011 \\ Mean & 1114.074 & 1077.780 & **1062.806** \\ \(\sigma\) & 55.075 & 77.853 & 68.147 \\ V & 4.944 & 7.223 & 6.412 \\ R & 188.324 & 191.665 & 196.463 \\ \hline \end{tabular}

* The best mean values of objective function are given in bold if the difference between SCL algorithm and its greedy version is statistically significant at \(p\leq 0.05\) (statistical significance was tested using the Wilcoxon rank sum test).

\end{table}