**4.4.1** *d* **variation**

166 Recurrent Neural Networks and Soft Computing

Legend: Blue for the cluster 1. Green for the cluster 2. Red for the cluster 3

**4.4 Time constants variation of the TKM and RSOM classifiers** 

the range 0 to 1.

Table 3. Labeling of the SOM, TKM and RSOM networks neurons in different grids

One difference between the SOM network and its temporal extensions TKM and RSOM is the change in the performance when occur variation in the time constants. In the section 4.4.1 and 4.4.2 are shown the results when the time coefficients (*d* and ) vary in For different *d* values the TKM network presented different global accuracies, reducing their values in the range limits of 0 to 1. The table 4 shows the confusion matrices and Figure 11 shows the superposition of the global accuracies due to the *d* variation. For each TKM dimension studied the points were spaced at 0.25 intervals.



Table 4. *d* variation and global accuracy of the TKM network in different grids

Fig. 11. Superposition of the TKM networks global accuracies due to the *d* variation

Recurrent Self-Organizing Map for Severe Weather Patterns Recognition 169

The results relative to the TKM model with 9x9 grid and *d* variation are graphically displayed in Figure 14. For this case, one may notice an approximation among the performances of the model for *d*=0.60 and the results obtained for lower values of d, such as the cases for *d*=0.10 and *d*=0.35. This togetherness was also observed for the *d*=0.85 case, even though it remains as the worst performance case for the TKM model. Therefore, the conclusion was that the smaller values of d provided the best performances for the clusters

classification by this network type.

Fig. 14. ROC graph for the TKM model in 9x9 grid with *d* variation

Fig. 15. Superposition of the RSOM networks global accuracies due to the variation

Figure 12 shows the ROC graph of the TKM model with 5x5 map units and *d* variations. It indicates that for lower values of *d* (*d*=0.10 and *d*=0.35) this classifier presented more conservative characteristics for labels 1 and 3, and the most liberal behaviour for the label 2. On the other hand, for higher values of *d* (*d*=0.60 and *d*=0.85), in general one notices a decrease of the tp rate values and an increment of the fp rate for all labels. One may conclude therefore, that the TKM better performances were observed for the lower values of *d*.

Fig. 12. ROC graph for the TKM model in 5x5 grid with *d* variation

Figure 13 displays a ROC graph for the TKM model with 7x7 grid and *d* variation. In this particular case, it is even more evident the superior performance of this classifier when one uses the lower values of d. Indeed, its best performance was found for *d*=0.35 and the worst corresponded to *d*=0.85.

Fig. 13. ROC graph for the TKM model in 7x7 grid with *d* variation

Figure 12 shows the ROC graph of the TKM model with 5x5 map units and *d* variations. It indicates that for lower values of *d* (*d*=0.10 and *d*=0.35) this classifier presented more conservative characteristics for labels 1 and 3, and the most liberal behaviour for the label 2. On the other hand, for higher values of *d* (*d*=0.60 and *d*=0.85), in general one notices a decrease of the tp rate values and an increment of the fp rate for all labels. One may conclude therefore,

that the TKM better performances were observed for the lower values of *d*.

Fig. 12. ROC graph for the TKM model in 5x5 grid with *d* variation

Fig. 13. ROC graph for the TKM model in 7x7 grid with *d* variation

corresponded to *d*=0.85.

Figure 13 displays a ROC graph for the TKM model with 7x7 grid and *d* variation. In this particular case, it is even more evident the superior performance of this classifier when one uses the lower values of d. Indeed, its best performance was found for *d*=0.35 and the worst The results relative to the TKM model with 9x9 grid and *d* variation are graphically displayed in Figure 14. For this case, one may notice an approximation among the performances of the model for *d*=0.60 and the results obtained for lower values of d, such as the cases for *d*=0.10 and *d*=0.35. This togetherness was also observed for the *d*=0.85 case, even though it remains as the worst performance case for the TKM model. Therefore, the conclusion was that the smaller values of d provided the best performances for the clusters classification by this network type.

Fig. 14. ROC graph for the TKM model in 9x9 grid with *d* variation

Fig. 15. Superposition of the RSOM networks global accuracies due to the variation

Recurrent Self-Organizing Map for Severe Weather Patterns Recognition 171

Fig. 16. ROC graph for the RSOM model in 5x5 grid with variation

Fig. 17. ROC graph for the RSOM model in 7x7 grid with variation

parameters.

Figure 18 shows a ROC graph for the RSOM model with 9x9 grid and variation. This figure indicates a superior performance of this classifier, when one uses intermediate values of (=0.35 and =0.60). In such cases the classifier becomes nearly ideal, with tp rate approaching 100% and fp rate near 0%. On the other hand, this classifier performance becomes very poor for the lowest extreme (=0.10) when compared to the other
