## 4 Results
### Algorithms Comparison
Next, the SL wins the competition according to MIA, WCBCR, DBI, IEI and SI. Apart from these algorithms, robust performance is displayed by UPGMC and UPGMA. Figure 5: Comparison of the fuzzy algorithms using: (**a**) J, (**b**) MIA, (**c**) CDI, (**d**) WCBCR, (**e**) SMI, (**f**) SMI2. Fuzzy algorithms are iterative and their operation present similarities with the K-means. The difference lies in the fact that they assign the patterns to all clusters. The fuzziness parameter defines the clusters' composition. The increment of fuzziness parameter leads to more crisp clustering. After a parametric analysis, it is set to \(q=2.70\). The maximum number of iterations (i.e., epochs) of both the FCM and IFCM is set to 500. Also, the same number of iterations is set for the K-means that is used for the initialization of the IFCM. The IFCM results in lower errors according to J, MIA, CDI, WCBCR, DBI, MDI, IAI, IEI, CH and SI. In the cases of SMI and SMI2, the fuzzy algorithms have comparative performance. Figure 6: Comparison of the fuzzy algorithms using: (**a**) DBI, (**b**) MDI, (**c**) IAI, (**d**) IEI, (**e**) CH, (**f**) SI. Neural network-based algorithms need a proper parameter calibration analysis. For the AVQ, these are the initial learning rate \(\eta_{o}\) and maximum number of iterations \(T_{\max}\). The following ranges of values are considered: \(\eta_{o}=\{0.05,0.01,0.15,...,0.90\}\) and \(T_{\max}=\{100,200,300,400,500\}\). After a set of experiments for the AVQ, the optimal values are drawn. For the J, MIA, CDI, WCBCR, SMI, SMI2, DBI, MDI, IAI, IEI, CH and SI indicators the optimal values are: \(\{0.65,100\}\), \(\{0.90,200\}\), \(\{0.90,100\}\), \(\{0.90,100\}\), \(\{0.10,300\}\), \(\{0.60,300\}\), \(\{0.60,100\}\), \(\{0.65,100\}\), \(\{0.40,100\}\), \(\{0.10,400\}\) and \(\{0.90,400\}\), respectively. Figure 7: Comparison of the neural network-based algorithms using: (**a**) J, (**b**) MIA, (**c**) CDI, (**d**) WCBCR, (**e**) SMI, (**f**) SMI2. The number of iterations for the Hopfield ANN is set to 50. According to results presented in Figures 7 and 8, the Hopfield ANN leads to lower errors in MIA, WCBCR, DBI, IEI, SI, SMI and SMI2. In the cases of DBI and IEI, the difference among the algorithms is more visible. In the SI, for large number of clusters, SOM approaches the performance of Hopfield. In SMI and SMI2 for number of clusters above 18, the AVQ and Hopfield present similar behaviour. The SOM wins the competition in J and CDI. As for the MDI, special attention is needed to reach into safe conclusions for the algorithms comparison. Figure 8: Comparison of the neural network-based algorithms using: (**a**) DBI, (**b**) MDI, (**c**) IAI, (**d**) IEI, (**e**) CH, (**f**) SI. For CLA, 3 different normalization techniques are considered, namely N1, N2 and N3. The N1 performs a random selection of \(k\) patterns from the smallest hyper-rectangular that contains all vectors of \(Y\). In the N2, a random selection of \(k\) patterns is held. Finally, in N3 the \(k\) most dissimilar patterns are selected. After a parametric analysis, the learning rates are set to \(\eta=0.70\) and \(\eta_{l}=0.00025\) for all validity indicators. The maximum number of iterations is set to 500. The same number is set both for IRC and FDL. Figure 9: Comparison of the rest algorithms using: (**a**) J, (**b**) MIA, (**c**) CDI, (**d**) WCBCR, (**e**) SMI, (**f**) SMI2. For the SVC, the parameters are set to \(C=1\) and \(q=1\). For the ISODATA, the following values are selected: Threshold of number of patterns in a cluster is equal to 15, the threshold of distance for cluster merging equals 10 and the maximum number of iterations is also 10. From comparing the algorithms, it is shown that CLA leads to lower scores in J, IAI, SMI and SMI2. The most superior operation in CDI and CH is observed from FDL. In the case of the CDI, the difference between FDL and CLA is not large. In the cases of MIA and WCBCR, IRC is more efficient than the rest. Finally, CSC outmatches the rest in DBI and MDI and SVC in IEI and SL.