## 4 Experiments  
### Experimental Settings  
As no public test set of dynamic signatures has been conducted on smartphones, we constructed a test set by ourselves. We gathered 20 signatures per person from 20 subjects, that we denoted as the original signature. After a month, we acquired 20 signatures per person from 10 subjects, that we denoted as the time-deferred signatures. Each subject's signature was shown to four forgers for imitating five signatures. Thus, 20 forged signatures were created for each subject. Figure 7 shows  
Figure 6: Structure of autoencoder.  
the samples of original signatures and forged signatures. Experiment participants were composed of 16 people in their twenties, 3 in their thirties, and 1 in their forties. The gender ratio is 15 males and 5 females. They signed their real signatures with a finger, holding a smartphone with other hand. The smartphone device was Galaxy S3 and the embedded application for signature registration was used. Average signing time was about 3 min for 20 signatures.  
The experiments have some limitations. For the accurate and practical experiment, we collected the real signatures of the users. The data set therefore is relatively small due to a privacy issue. Signatures are also drawn on same model of smartphone. If the type of smartphone is different, some technical details such as sampling rate may also be different. Therefore, other normalization process may be needed. The accuracy decline caused by time difference is an inherent problem in behavioral biometrics authentications. The proposed method obtains the better accuracy for time-deferred signatures by experimental approach but could not suggest explicit solution.  
Using different configurations of the training data, four different CNN feature extractors were created, as shown in Table 1. CNN_A is a two-class classifier trained with all the subjects' original signatures as one class and all the subjects' forged signatures as the other class. CNN_B is a 20-class classifier trained with 20 subjects' original signatures. CNN_C is made for each subject with the subject's and others' original signatures. CNN_D is made for each subject with the subject's original and forged signatures. CNN_D is possible only in an experimental setup as it is impossible to acquire forged signatures for a newly enrolled subject. However, we included CNN_D for evaluating the  
Figure 7: Samples of: (**a**) original signatures; and (**b**) forged signatures.  
effect of a CNN trained for a special purpose. To find the best result, the experiment was repeated with different CNN parameters. The adjusted values of major parameters are as follows. Each CNN consisted of 2 convolution layers and 2 max-pooling layers. The window sizes of the convolution layer and the pooling layer were 3 and 2, respectively. The training epoch was 100.  
Each subject model was built with the subject's 10 original signatures. The AE consisted of an input layer of 128 nodes, hidden layers, and an output layer of 128 nodes. The node activation function was ReLU [26] and training optimizer was RMSprop [27]. In the test phase, we conducted three types of signature verification tests and the test data configuration is shown in Table 2. For the base result, the adjusted values of major AE parameters are as follows. The number of hidden layers was 3 and the number of nodes were 30, 20, and 30 for each layer. The training epoch was 500.  
The equal error rate (EER) is used as an evaluation metric for signature verification. All machine-learning models were implemented using the Theano [28] library, which is a well-known open source machine-learning library.