

![0_image_0.png](0_image_0.png)

## 3.2 Training Of Neural Network

In this paper a supervised training is used. For this purpose 'Variable Learning Rate (traingdx) is used as a training function. Gradient descent with momentum weight and bias learning function (learngdm) is used by default. Mean square error (mse) is network performance function. It measures the network's performance according to the mean of squared errors. All other parameters of the neural network are set as by default including the initial weights. It is cleared by the graph in Fig. 5 that as the number of epochs are increasing during training then accordingly the mean square error is reducing. The black horizontal line is showing the reference (set at the time of preparing of NN) and the blue is denoting the reducing mse i.e. 

actual mse. The goal of training is to reduce mse till the extent that it will meet the reference. The training will stop when either the set goal has achieved or the maximum number of epochs reached. 

4 **Results** 
For comparison and performance evaluation of the proposed methodology we have used equal number of genuine and forgery samples for training and 100 numbers (50 Genuine + 50 Forgeries) are used for classification. Author increased the training signature samples from 10 (5 Genuine + 5 Forgeries) to 100 
(50 Genuine + 50 Forgeries) and observe the effect of increasing training samples for all of the methods. 

For performance evaluation author used some common parameters like time required for training, accuracy, FAR (False Acceptance Ratio) i.e. the percentage of forgeries accepted as genuine & FRR 
(False Rejection Ratio) i.e. the percentage of rejecting the genuine signatures. A comparison for all the three methods has done on the basis of above mentioned parameters. Table I, II, III & IV along with graphs respectively of Fig. 6 elaborate the comparison of all the methods. 

| Result                                                | Elapsed Time  (in Sec.)  (Directional  feature with  Energy Method)   |       |        |        |
|-------------------------------------------------------|-----------------------------------------------------------------------|-------|--------|--------|
| 1                                                     | 10                                                                    | 6.156 | 7.375  | 7.672  |
| 2                                                     | 20                                                                    | 6.453 | 7.89   | 8.718  |
| 3                                                     | 30                                                                    | 6.593 | 8.39   | 9.141  |
| 4                                                     | 40                                                                    | 7.312 | 9.282  | 9.594  |
| 5                                                     | 50                                                                    | 6.625 | 10.718 | 11.64  |
| 6                                                     | 60                                                                    | 7.671 | 8.172  | 8.5    |
| 7                                                     | 70                                                                    | 7.797 | 8.281  | 8.5    |
| 8                                                     | 80                                                                    | 6.313 | 8.594  | 11.688 |
| 9                                                     | 90                                                                    | 6.704 | 9.188  | 9.531  |
| 10                                                    | 100                                                                   | 6.969 | 9.125  | 9.532  |
| No. of Taining  Samples (50%  Genuine + 50%  Forgery) | Elapsed Time  (in Sec.)  (Directional  feature only)                  |       |        |        |
| S.  No.                                               | Elapsed Time  (in Sec.) (Energy  Density Method)                      |       |        |        |
