# Clustering Algorithm with a Greedy Agglomerative Heuristic and Special Distance Measures
## 2 Kohonen Neural Networks for Clustering Problem
### Proposed Algorithms

Table 5: Objective function value summarized after 30 attempts (Manhattan distance). Statistical significance of difference in the objective function values given by SCL algorithm and best of its greedy version were tested with Wilcoxon rank sum test. The best (minimal) mean values of objective function are given in bold if the precedence is statistically significant at \(p\leq 0.05\). For Chebyshev distance, the best objective function value was achieved with SCL-GREEDY(3) algorithm for two and three batches in a mixed lot. For four batches, the difference between algorithms was insignificant. The coefficient of variation and span factor have minimal values with SCL algorithm for two-batch mixed lot and four-batch mixed lot. For three-batch mixed lot, the coefficient of variation and span factor show best result with SCL-GREEDY(3). For Euclidean distance, the best objective function value was achieved with SCL-GREEDY(3) algorithm for two and four batches, and with SCL-GREEDY(2) for three batches. The coefficient of variation and span factor have minimal values with SCL-GREEDY(3) algorithm for almost all mixed lots. For the four-batch mixed lot, the coefficient of variation shows best result with SCL algorithm. For squared Euclidean distance, for all mixed lots, SCL-GREEDY(3) gives the best value of objective function. Besides, SCL-GREEDY(3) algorithm gives minimal values of the coefficient of variation and span factor for the two-batch mixed lot and minimal value of the span factor for the three-batch mixed lot. SCL-GREEDY(2) algorithm gives minimal values of the coefficient of variation and span factor for the four-batch mixed lot. SCL algorithm for the three-batch mixed lot gives minimal value of the coefficient of variation. For Mahalanobis distance, the difference between objective function values was insignificant for two-batch mixed lot. For three-batch and four-batch mixed lots, the minimal objective function value was achieved with SCL-GREEDY(3) algorithm. The coefficient of variation and span factor have minimal values with SCL-GREEDY(3) for the two-batch mixed lot. For the three-batch and four-batch mixed lots, the coefficient of variation and span factor show best result with SCL algorithm. For Manhattan distance, the precedence of SCL-GREEDY(3) algorithm in objective function value was observed for all mixed lots. The coefficient of variation and span factor have minimal values with SCL algorithm for almost all mixed lots. For the two-batch mixed lot, the span factor shows best result with SCL-GREEDY(3) algorithm. From Figure 2, it can be seen that the coefficient of variation is minimum with Chebyshev distance and Mahalanobis distance for mixed two-batch lot. For mixed three-batch lot, the coefficient of variation is minimum with square Euclidean distance and Manhattan distance. The worst (maximum) value it shows with Chebyshev distance for four-batch lot; other distances are similar to each other in this case. The span factor shows the best result with Chebyshev distance and Mahalanobis distance for mixed two-batch lot. For mixed three-batch lot and four-batch lot, the span factor is the best with square Euclidean distance and Manhattan distance. ### Experiments in Batch Mode

In this section, we compare the results of the experiment performed with modifications of BVQ and SOM algorithms. Experiment with initial number of neurons \(KI\) coinciding with a given number of clusters is marked as BVQ and SOM; experiments with the initial number of neurons exceeding the specified number of clusters by two (\(K=2\times KI\)) and three (\(K=3\times KI\)) times are marked as BVQ-GREEDY(2), BVQ-GREEDY(3), SOM-GREEDY(2) and SOM-GREEDY(3). We used different methods for initializing the weight coefficients: by average, by random and with preliminary clustering by the k-means algorithm. Experiments showed that, like in online mode, clustering accuracy decreases with increasing number of homogeneous batches in a mixed lot (Tables 6-8).