## 4 Results
### Algorithms Comparison
The graphs of J, MIA, CDI, WCBCR, SI and IAI display decreasing tendency while the number of clusters is increasing. The most efficient algorithm should lead to lower values of these indicators. This is also the case for DBI, SMI, SMI2 and MDI; these indicators display an unstable curve. In the IEI and CH the algorithm that wins the competition results in higher values. The J indicator expresses the sum of Euclidean distances among the patterns and the centroids. It is a measure of clusters' compactness. The minCEntropy leads to lower errors followed by Modified Kmeans#1, K-medoids and K-means_B. Like the J indicator, MIA is a measure of compactness. Here the IWFA K-means is the most efficient followed by Modified Kmeans#2, minCEntropy and k-medoids. \begin{table}
\begin{tabular}{c c} \hline \hline
**Algorithm** & **Parameter** \\ \hline WPGMA & - \\ WPGMC & - \\ UPGMC & - \\ MVM & - \\ FCM & - \\ IFCM & - \\ SOM & - \\ AVQ & - \\ Hopfield & - \\ FDL & Parameter \(\rho\) \\ CLA & - \\ IRC & Parameter \(\rho\) \\ BCEC1 & - \\ BCEC2 & - \\ CSC & - \\ SVC & 1. Minimum distance \\  & 2. Cluster formation threshold \\  & 1. Maximum number of clusters \\  & 2. Maximum number of clusters for merging \\  & 3. Maximum number of iterations \\ ISODATA & 4. Threshold of number of patterns in a cluster \\  & 5. Threshold of distance for cluster merging \\  & 6. Threshold of standard deviation for cluster split \\  & 7.Minimum distance between patterns and centroid \\ \hline \hline \end{tabular}
\end{table} 
Table 7: _Cont._Figure 1: Comparison of the partitional algorithms using: (**a**) J, (**b**) MIA, (**c**) CDI, (**d**) WCBCR, (**e**) SMI, (**f**) SMI2. The CDI and WCBCR both measure the compactness and separation. For the CDI, the ranking is minCEntropy, Modified K-means#2, K-medoids \(\kappa\alpha\)t Modified K-means#1. For the WCBCR, is Modified K-means#1, Modified K-means#2, IWFA K-means and minCEntropy. For the SMI and SMI2, the most robust are the Modified K-means#1, IWFA K-means, K-medoids and minCEntropy. The K-medoids and IWFA K-means win the competition according to DBI and MDI, respectively. Figure 2: Comparison of the partitional algorithms using: (**a**) DBI, (**b**) MDI, (**c**) IAI, (**d**) IEI, (**e**) CH, (**f**) SI. IAI is a modification of the J indicator; the same conclusions with J apply. Considering IEI, the algorithms ranking is IWFA K-means, Modified K-means#1, Modified K-means#2 and K-medoids. The CH indicator is the ratio of IAI and IEI. Therefore, it measures compactness and separation. Here the Modified K-means#1 is superior followed by the IWFA K-means, Modified K-means#1 and minCEntropy. Finally, SI measures the compactness of clusters. The algorithms ranking is the same with CH. After the comparison of the partitional algorithms, in general terms Modified K-means#1 and IWFA K-means are the most robust algorithms. Next, minCEntropy and K-medoids reach into the 3 rd and 4 th place in algorithms ranking. Figure 3: Comparison of the hierarchical algorithms using: (**a**) J, (**b**) MIA, (**c**) CDI, (**d**) WCBCR, (**e**) SMI, (**f**) SMI2. Hierarchical agglomerative algorithms are characterized by the simplicity of their operation. The user should define the merging stopping criterion, which is actually the height that the dendrogram is cut. In respect to the algorithms of other categories, hierarchical clustering does not lead to clusters with zero number of members, i.e., empty clusters. Different executions always produce the same cluster. There is no need for a series of successive executions corresponding to different initializations. Figure 4: Comparison of the hierarchical algorithms using: (**a**) DBI, (**b**) MDI, (**c**) IAI, (**d**) IEI, (**e**) CH, (**f**) SI. The MVM is more efficient according to J and IAI followed by CL, WPGMA and UPGMA. In MIA indicator the ranking is SL, UPGMC, UPGMA and WPGMC, while in CDI it is MVM, WPGMA, UPGMA and UPGMC. This comparison shows that MVM leads to lower errors in 6 indicators, namely at J, CDI, SMI, SMI2, MDI, IAI and CH.