**3.2 Training and evaluation of the models**

For the performance analysis of the networks (SOM, TKM and RSOM) 3 maps were constructed, for each network type, in the grids: 5 x 5 units, 7 x 7 units and 9 x 9 units, therefore 9 maps in total.

Each network was trained with 600 examples extracted of the data set, with 200 examples of each cluster, randomly chosen. After training, the units of the maps were labeled according to their winning histories during training. This allowed that the networks were used as classifiers to evaluate their discrimination power.

The parameters used in the training of the SOM, TKM and RSOM networks were:

Random weight initialization;

160 Recurrent Neural Networks and Soft Computing

For the evaluation of the applicability of SOM and two of its temporal extensions: Temporal Kohonen Map (TKM) and Recurrent Self-Organizing Map (RSOM) for the weather patterns recognition related to atmospheric instability factors, clusters were built using the K-means technique, which generated three clusters, containing 697, 484 and 593 examples, for the cluster 1, 2 and 3, respectively. Figure 6 shows the characteristics of the three clusters

In describing some of the differential characteristics between the clusters, it is noticed that in cluster 1 CAPE and PWAT have their concentrations at low values, while in cluster 2 the concentration of the CAPE is in low values, however for PWAT the values are high. In cluster 3 both CAPE and PWAT have their concentrations at high values. Another distinctive feature among clusters is the gradual rise of the LFCT median value for the clusters 1, 2 and 3, respectively. It is also noticed that the cluster 1 has a SWET median value

For the performance analysis of the networks (SOM, TKM and RSOM) 3 maps were constructed, for each network type, in the grids: 5 x 5 units, 7 x 7 units and 9 x 9 units,

Each network was trained with 600 examples extracted of the data set, with 200 examples of each cluster, randomly chosen. After training, the units of the maps were labeled according to their winning histories during training. This allowed that the networks were used as

Where:

 min A is the minimum value of the variable A; max A is the maximum value of the variable A.

according to the four variables analyzed.

lower when compared with clusters 2 and 3.

Fig. 6. Characteristics of the clusters

therefore 9 maps in total.

**3.2 Training and evaluation of the models** 

classifiers to evaluate their discrimination power.

**3.1.5 Clusters formation for evaluation of the models** 


Specifically for the TKM network was used the time constant *d* equal to 0.65 and for the RSOM network was used the leaking coefficient equal to 0.35.

Subsequently it was evaluated the performance of the TKM and RSOM classifiers for different values of the constants and *d*.

The results were presented in confusion matrices. In the confusion matrix each column represents the expected results, while each row corresponds to the actual results. During the simulation 1174 remaining examples of the data set were used.

After, a ROC analysis was done. The ROC graph is a technique for visualizing and evaluating classifiers based on their performance (Fawcett, 2006). A ROC graph allows identifying relative tradeoffs of a discrete classifier (one that your output is only a class label). In ROC graph the true positive rate (tp rate) of a classifier is plotted on the Y axis, while the false positive rate (fp rate) is plotted on the X axis. Fig. 7 shows a ROC graph with three classifiers labeled A through C.

Fig. 7. ROC graph showing three discrete classifiers

Some points in ROC graph are very important. The lower left point (0, 0) represents a classifier that commits no false positive errors but also gains no true positives. The opposite situation is represented by the upper right point (1, 1). The upper left point (0, 1) represents a perfect classification (tp rate = 1 and fp rate = 0). In Fig 7, the point A is the ideal classifier; the point B represents a conservative classifier; and the point C represents a liberal classifier. Conservative classifiers make positive classifications only with strong evidence, i.e., their

Recurrent Self-Organizing Map for Severe Weather Patterns Recognition 163

Fig. 9 displays the ROC graph of the analyzed models for the 7x7 grid. It is evident that the RSOM network has a larger tp rate and a smaller fp rate for labels 1 and 2. For the label 3 the SOM and TKM networks presented similar liberal characteristics, while the RSOM network showed a more conservative behavior. For these dimensions the results also indicated a better performance of the RSOM classifier when compared to the SOM and TKM network options.

Fig. 8. ROC graph for the SOM, TKM and RSOM in 5x5 grid

Fig. 9. ROC graph for the SOM, TKM and RSOM in 7x7 grid

false positive rates are low but they also have low true positive rates. Liberal classifiers have high true positive rates but they also have high false positive rates.
