# Clustering Algorithm with a Greedy Agglomerative Heuristic and Special Distance Measures
## 2 Kohonen Neural Networks for Clustering Problem
### Proposed Algorithms
Moreover, it can be seen that the use of the greedy agglomerative heuristic in batch mode improves the accuracy of batch separation for BVQ algorithm but degrades for SOM algorithm. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Algorithm** &
\begin{tabular}{c} **Initialization** \\ **Method** \\ \end{tabular} & **ChD** & **EuD** & **SEuD** & **MahD** & **ManD** \\ \hline \multirow{3}{*}{BVQ} & average & 0.98 & 1 & 1 & 1 & 1 \\  & k-means & 0.98 & 1 & 1 & 1 & 1 \\  & random & 0.98 & 1 & 1 & 0.62 & 1 \\ \hline \multirow{3}{*}{BVQ-GREEDY(2)} & average & 0.99 & 1 & 1 & 1 & 1 \\  & k-means & 1 & 1 & 1 & 1 & 1 \\  & random & 0.99 & 1 & 1 & 1 & 1 \\ \hline \multirow{3}{*}{BVQ-GREEDY(3)} & average & 1 & 1 & 1 & 1 & 1 \\  & k-means & 1 & 1 & 1 & 1 & 1 \\  & random & 1 & 1 & 1 & 1 & 1 \\ \hline \multirow{3}{*}{SOM-GREEDY(2)} & average & 1 & 1 & 1 & 1 & 1 \\  & k-means & 1 & 1 & 1 & 1 & 1 \\ \hline \multirow{3}{*}{SOM-GREEDY(3)} & average & 1 & 1 & 1 & 1 & 1 \\  & k-means & 1 & 1 & 1 & 1 & 1 \\ \hline \multirow{3}{*}{SOM-GREEDY(2)} & average & 1 & 1 & 1 & 1 & 1 \\  & k-means & 1 & 1 & 1 & 1 & 1 \\ \hline \multirow{3}{*}{SOM-GREEDY(3)} & average & 1 & 1 & 1 & 1 & 1 \\  & k-means & 1 & 1 & 1 & 1 & 1 \\ \cline{1-1}  & random & 1 & 1 & 1 & 0.62 & 1 \\ \hline \multirow{3}{*}{k-means} & random & 0.99 & 0.98 & 0.98 & 0.67 & 0.99 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Accuracy of device clustering for BVQ, SOM, BVQ-GREEDY(2), BVQ-GREEDY(3), SOM-GREEDY(2) and SOM-GREEDY(3) algorithms (two-batch mixed lot). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Algorithm** &
\begin{tabular}{c} **Initialization** \\ **Method** \\ \end{tabular} & **ChD** & **EuD** & **SEuD** & **MahD** & **ManD** \\ \hline \multirow{3}{*}{BVQ} & average & 0.72 & 0.64 & 0.64 & 0.94 & 0.64 \\  & k-means & 0.97 & 0.64 & 0.64 & 0.92 & 0.64 \\  & random & 0.60 & 0.64 & 0.64 & 0.62 & 0.64 \\ \hline \multirow{3}{*}{BVQ-GREEDY(2)} & average & 0.95 & 1 & 1 & 0.95 & 1 \\  & k-means & 0.95 & 1 & 1 & 0.92 & 1 \\  & random & 0.95 & 0.64 & 0.64 & 0.51 & 0.64 \\ \hline \multirow{3}{*}{BVQ-GREEDY(3)} & average & 0.95 & 1 & 1 & 0.95 & 1 \\  & k-means & 0.95 & 0.98 & 1 & 0.94 & 0.98 \\  & random & 0.96 & 0.64 & 0.64 & 0.39 & 0.64 \\ \hline \multirow{3}{*}{SOM-GREEDY(2)} & average & 0.69 & 0.57 & 0.98 & 0.93 & 0.98 \\  & k-means & 0.7 & 0.98 & 0.98 & 0.91 & 0.98 \\  & random & 0.7 & 0.98 & 0.56 & 0.88 & 0.98 \\ \hline \multirow{3}{*}{SOM-GREEDY(2)} & average & 0.96 & 0.64 & 0.64 & 0.94 & 0.64 \\  & k-means & 0.96 & 0.64 & 0.64 & 0.94 & 0.64 \\ \hline \multirow{3}{*}{SOM-GREEDY(3)} & average & 0.96 & 0.64 & 0.64 & 0.94 & 0.64 \\  & k-means & 0.96 & 0.64 & 0.64 & 0.44 & 0.64 \\ \hline \multirow{3}{*}{k-means} & random & 0.62 & 0.63 & 0.66 & 0.49 & 0.63 \\ \cline{1-1}  & \multicolumn{1}{c}{} & & & & & \\ \end{tabular}
\end{table} 
Table 7: Accuracy of device clustering for BVQ, SOM, BVQ-GREEDY(2), BVQ-GREEDY(3), SOM-GREEDY(2) and SOM-GREEDY(3) algorithms (three-batch mixed lot). From Table 6, it can be seen that, for two-batch mixed lot, all presented algorithms exceed k-means in accuracy. However, BVQ, SOM-GREEDY(2), SOM-GREEDY(3) algorithms showed worse results for random initialization with Mahalanobis distance. From Table 7, it can be seen that, for three-batch mixed lot, all presented algorithms were approximately equal to k-means algorithm in accuracy except Chebyshev distance. For BVQ algorithm, its greedy version was more accurate, but, for SOM algorithm, its greedy version was better only for Chebyshev distance. From Table 8, it can be seen that, for four-batch mixed lot, all presented algorithms were approximately equal to k-means algorithm in accuracy except Chebyshev distance. For BVQ algorithm, its greedy version was more accurate. For SOM algorithm, on the contrary, result was generally better than its greedy version. Characteristics of objective function value for batch-type algorithms with various combinations of distance measure and initialization method are given in Tables A1-A15 of Appendix A.