SIGNATURE VERIFICATION USING ART-2 NEURAL NETWORK ...

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SIGNATURE VERIFICATION USING ART-2 NEURAL NETWORK Pavel Mautner1 , Ondrej Rohlik1 , Vaclav Matousek1 , Juergen Kempf2 University of West Bohemia, Faculty of Applied Sciences, Univerzitni 8, CZ – 306 14 Plzen (Pilsen), Czech Republic e-mail: mautner | rohlik | [email protected] 2 University of Technology (Fachhochschule) Regensburg, Pruefeninger Straße 58 D – 93049 Regensburg, Germany e-mail: [email protected] 1

ABSTRACT The ART neural network models have been developed for the clustering of input vectors and have been commonly used as unsupervised learned classifiers. In this paper we describe the use of the ART-2 neural network model for signature verification. The biometric data of all signatures were acquired by a special digital data acquisition pen and fast wavelet transformation was used for feature extraction. The part of authentic signature data was used for training the ART verifier. The architecture of the verifier and achieved results are discussed here and ideas for future research are also suggested.

Figure 1: Digital Data Acquisition Pen

1. INTRODUCTION There are many commercial systems designed for person identification worldwide. Among the most popular ones are those based on fingerprints, ID cards and signature recognition using optical character recognition (OCR) methods. The current identification systems are based on input devices that consist of at least two parts (pen and tablet, pen with an infrared transmitter and one or two receivers, etc.) The obvious problem of such an approach is the limited mobility of a system composed of several parts. For the purpose of verification a special digital data acquisition pen was developed at the University of Technology Regensburg. The pen produces three signals in which information about the pressure applied to ballpoint and about the side pressure in x and in y directions is involved. Detailed information about an acquisition device is given in Section 2. Section 3 deal with the pen output signal feature extraction method and Section 4 describes the neural network verifier based on the unsupervised learned neural network model of ART2. Results of verification experiments, and possible future works are discussed in Section 5 and Section 6, respectively.

Figure 2: Transformed output signal waveforms 2. DATA ACQUISITION DEVICE As was mentioned above signature verification is performed by the special digital data acquisition pen. The first experimental pen was built at University of Technology Regensburg during the spring of 2000. Our experiences with this pen were discussed in [1]. The pen consists of two sensors integrated in the pen. These are a 2-axis acceleration sensor (based on the principle of moving mass between two capacitors) and a pressure sensor (based on the piezoelectric effect). As the acceleration sensor was not very sensitive and the output signal was noisy, it was later replaced by sensors working on a principle similar to that of the piezoelectric

pressure sensor. These new sensors scan the side pressure applied to the ball-pen in x and y directions. The third sensor scanning the pressure to the ball-pen nib is integrated into the pen and is the same as in the previous version of the pen. The prototype of the pen is illustrated at Figure 1. To obtain the right signal waveform, the pen should be held so that the x side sensors are parallel to the writing axis and the y sensors are perpendicular to it. Failing that, the signals corresponding to the x and y side pressure are distorted. In order to reduce this effect, these signals are transformed to polar coordinates mag and phi. The transformed output signal waveforms are illustrated in Figure 2.

4. NEURAL NETWORK SIGNATURE VERIFIER The neural network models are commonly used for processing classification problems. But signature verification differs from the general classification problem. The goal of the general classification problem is to choose one class from several classes, whereas the training data contain data from all classes. For our application all the training data are authentic signatures and we have no data for the second class fake signatures. This is the reason why the frequently used supervised learned neural network model such as multi-layer perceptron cannot be applied to the signature verification task.

3. FEATURE EXTRACTION Before the feature vector is evaluated from the output signals, only the active part of the signature has to be determined. This is done from the first difference of output signal z . To determine of the beginning (or the end) of the signature, the z signal is scanned from left to right (or conversely) and the first difference is evaluated. The beginning (or the end) of the signature is determined if the value of the first difference of signal z exceeds the threshold value Θ at the first occurrence and value of the signal is greater than the reference value σ The threshold values Θ and σ are determined according to the type of the piezoelectric sensor used. For the extraction of features from signals, the fast wavelet transform (FWT) was used. At first, each signal of the signature was filtered by an average filter, afterwards it was S decomposed by FWT and coefficients of AS5 and Dm , for m = 1, 2, 5, were determined [2]. For decomposition the Daubechies and Coiflet wavelet families were tested, the 5th order Daubechies wavelet gave the best result. Using of this wavelet, the following features were used to describe the signature: • rl = sl n , where sl is the number of samples of the signature and n is the total number of samples in one scan (n = 500 for all tested signatures). S • Dm =

Nm X

d2mj ,

m = 1, 2, ..., 5;

s = x, y, z,

j=1

where Nm is the number of coefficients in scale m. •

AS5

=

N5 X

a25j ,

m = 1, 2, ..., 5;

s = x, y, z,

j=1

where N5 is the number of coefficients in scale 5. s Features AS5 and Dm represent the energy of the m-th signal decomposition level, rl represents the relative length of the active signature signal. These features are components of the feature vector F vi of the i-th signature. The feature vector is presented to the input of the signature verifier.

A

F F

2

G

ρ

ri F1

R

Fv Figure 3: ART-2 signature verifier

4.1. Architecture of the neural network verifier The adaptive resonance theory (ART), developed by Carpenter and Grossberg, was designed for clustering binary input vectors (ART-1) or continuous-valued input vectors (ART-2). With regards to the features what we used for description of signals, the ART-2 model is suitable for signature verification. The general architecture and description of the ART-2 network is not discussed here, for details see [3],[4]. The basic structure of the network verifier is illustrated in Figure 3. The network consists of two layers of processing elements labelled F1 (input and interface units) and F2 (cluster units), each fully interconnected with the others, and supplemental unit G and R (called gain control unit and reset unit), which are used to control the processing of the input data vector and creating of the clusters.

a)

a)

b)

b)

Figure 4: a) Authentic signatures with quality mark b) corresponding fake signatures

Figure 5: Example of the output signal waveforms for authentic and fake signatures in Figure 4

The input and interface layer F1 consists of six sublayers (these are not illustrated in Figure 3); each sub-layer has the same number of processing units as is the size of the feature vector. The purpose of these sub-layers is to allow the ART-2 network to process continuously varying inputs. Moreover, they normalize the components of the feature vector and suppress the noise. The size of the F1 layer (and hidden sub-layers) was 19 in our application. The clustering layer F2 consists of two processing units only, the former (labelled A) is active only if the feature vector corresponding to the authentic signature appears at the input of the network, the latter (labelled F) is active in other cases. More clusters are not enabled in our application.

whole training procedure (the network places the template signatures only in one cluster and adapts the corresponding weights between F1 and F2 layers). When the training is completed, the network is prepared for verification. The parameters of F1 sub-layers are not changed during the verification, only the vigilance parameter ρ have to be set properly to the authentic and the fake signatures were set to right clusters. The three methods of setting the vigilance parameter were tested in our work: • manual setting M : vigilance parameter ρ is set to the fixed value (ρ = 0.98) manually, for all verifications, • automatic setting A1 : ρA1 = min {ri } i = 1 · · · Nt , i

4.2. Training and verification As was mentioned above, only the data for the authentic signature are known. Moreover, the number of template signatures cannot be too high because the acquisition of a large training set, e.g. at a bank counter could be boring and unpleasant for the customer. Hence only 5 signatures were used for the training of the ART neural network in our application. For these signatures corresponding feature vectors were evaluated and repeatedly presented to the input layer of the network (the slow learning mode was used for ART-2 network training). The parameters of the hidden sub-layers of F1 and vigilance parameter ρ were set so that only the unit labelled A of layer F2 was active during the

• automatic setting A2 : ρA2 =

Nt 1 X ri Nt i

i = 1 · · · Nt .

In the equations above, Nt is a number of training vectors and ri is activation level of unit R (see Figure 3 and [3],[4] for detailed description and evaluation of ri ). The results achieved by corresponding setting of parameter ρ are presented in Table 1. 5. EXPERIMENTAL RESULTS To test the verifier, signatures by 10 authors were taken. For each author, 20 authentic signatures and 15 fakes were

recorded. The fake signatures were written by three different authors (5 fakes for each person). Sometimes the author is not satisfied with his/her own signature. The quality of signature depends on his/her physical and mental condition. In such a case the signatures can be classified as fakes. For the evaluation of such cases, the authors marked their authentic signatures by a mark from the scale 1 - 4 (1 means a best form of the signature). For the verifier training, only the five signatures labelled by mark 1 or 2 were chosen. Examples of the authentic signatures of one author and their fakes are presented in Figure 4, corresponding output signal waveforms are presented in Figure 5. The summary of test results for 10 authors is presented in Table 1. The overall accuracy ratio presented in Table 1a) was evaluated without the respect of signature quality mark mentioned above. But in most cases the authentic signatures classified as fakes are the ones labelled by their authors as poor signatures (with a quality mark worse than 2). It means that the overall accuracy ratio will be a slightly higher if these signatures will be recognized as a fakes. The Table 1b) show this situation. Accuracy ratio presented here was evaluated with the respect of signature quality mark assigned to each signature by its author. We can see the accuracy ratio is getting higher for all kind of vigilance parameter setting. The best result was achieved if the vigilance threshold ρ was set automatically during training process as the minimum value of activation level of unit R (automatic setting A1 ). 6. CONCLUSION AND FUTURE WORK The using of unsupervised learned ART-2 network for signature verification was discussed here. The tests showed that this network can be used as signature verifier and gives a good result with respect to the training set size. Before the network training and the verification, only a small number of the network parameters had to be set manually. These parameters have remained at most the same in verification process too. In our future work, we plan to focus it on the setting of these parameters automatically during the training phase. To improve the overall accuracy ratio, we plan to include the new valuable features to the feature vector describing the signature. Finally, we also plan to check the possibility of the application of other unsupervised learned neural network models (e.g. Kohonen self organizing feature map) for further improving of the signature verification task. 7. REFERENCES [1] O.Rohlik et al., A New Approach to Signature Verification: Digital Data Acquisition Pen , Neural Network World, Vol. 11, No. 5, pp. 493-501,2001

No.

1 2 3 4 5 6 7 8 9 10

Authentic signatures classified as authentic fakes M A 1 A2 M A 1 17 19 16 3 1 14 15 9 6 5 19 17 12 1 3 19 18 12 1 2 20 20 11 0 0 16 18 8 4 2 16 18 8 4 2 19 18 9 1 1 19 19 14 1 1 14 13 12 6 7

A2 4 11 8 8 9 12 12 11 6 8

Overall Accuracy Ratio [%] M A1 A2 85.7 91.4 85.7 80.0 80.0 68.6 88.6 91.4 77.1 94.3 91.4 77.1 100 100 74.3 88.6 94.3 65.7 85.7 91.4 62.9 88.6 91.4 68.6 91.4 94.3 82.8 77.1 77.1 74.3

Fake signatures classified as fakes authentic A 1 A2 M A 1 A2 13 14 2 2 1 13 15 1 2 0 15 15 3 0 0 14 15 1 1 0 15 15 0 0 0 15 15 0 0 0 14 14 1 1 1 14 15 3 1 0 14 15 2 1 0 14 14 2 1 1

Overall Accuracy Ratio [%] M A1 A2 91.4 94.3 94.3 91.4 91.4 88.6 88.6 91.4 82.9 97.1 94.2 82.9 100 100 85.7 88.6 94.3 71.4 91.4 94.3 74.3 91.4 94.3 82.9 94.3 97.1 88.6 85.7 85.7 82.9

a) No.

1 2 3 4 5 6 7 8 9 10

M 13 14 12 14 15 15 14 12 13 13

b)

Table 1: Results of verification tests for different setting of vigilance parameter ρ

[2] S. Pitnerr and S.V. Kamarthi, Feature Extraction from Wavelet coefficients for Pattern Recognition Tasks, IEEE Transactions on PAMI, Vol. 21, No. 1, 1999 [3] L. Fausett, Fundamentals of Neural Networks, Prentice-Hall, New Jersey, 1994. [4] G.A. Carpenter and S. Grossberg, ART-2: Selforganization of Stable Category Recognition Codes for Analog Input Patterns, Applied Optics, No. 26, pp. 4919-4930, 1987