Comparison of ART-2 and SOFM Based Neural
Network Verifiers
?
P. Mautner, V. Matousek, T. Marsalek, and O. Rohlik
University of West Bohemia,
Faculty of Applied Sciences,
Univerzitni 8,
CZ – 306 14 Plzen (Pilsen),
Czech Republic
Abstract. The Carpenter-Grosberg ART-2 and Kohonen Self-organizing Feature
Map (SOFM) have been developed for the clustering of input vectors and have
been commonly used as unsupervised learned classifiers. In this paper we de-
scribe the use of these neural network models for signature verification. The bio-
metric 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
genuine signature data was used for training both signature verifiers. The archi-
tecture of the verifiers and achieved results are discussed here and ideas for future
research are also suggested.
1 Introduction
Commercial systems designed for handwritten text acquisition use as an input device
a scanner, a pen with a tablet or a GPS-based pen with a (infrared or ultrasound) trans-
mitter and several receivers (see [11], [13], [14]). Obvious disadvantage of these devices
is the limited mobility of a system composed of two or more pen parts. System based
on optical (OTM) technology require additional light sources (usually built-in inside
the pen) in order to work properly which is intrusive an uncomfortable.
Under the BISP (Biometrical Smart Pen for Personal Identification) project several
pen prototypes were constructed. These prototypes integrate all the electronic devices
needed for the data acquisition inside the pen and are ergonomic and non-invasive as
they do not emit light, sound, or electromagnetic radiation and provide a comfortable
feeling while writing.
In our paper, we focused on two famous neural network architectures: the Carpenter-
Grosberg ART-2 and Kohonen Self-organizing Feature Map (SOFM). These networks
can be used as the signature verifiers for the data acquisition pen developed under BiSP
project. The first experiments with these neural network verifiers were published in [1],
the new feature set and results of new tests are presented here. The block scheme of the
developed system using neural network verifier is shown in Figure 1. Short description
?
This work was supported by the Ministry of Education of the Czech Republic - Project No.
MSM235200005 and the Bilateral Czech-German Research Project No. TSR 007/99
Mautner P., Matousek V., Marsalek T. and Rohlik O. (2004).
Comparison of ART-2 and SOFM Based Neural Network Verifiers.
In Proceedings of the First International Workshop on Artificial Neural Networks: Data Preparation Techniques and Application Development, pages
41-48
DOI: 10.5220/0001149300410048
Copyright
c
SciTePress
of this pen can be found in Section 2, Section 3 deals with the pen output signal fea-
ture extraction method and Section 4 describes both neural network signature verifiers.
Results of verification experiments, and possible future work are discussed in Section 5
and Section 6, respectively.
Fig. 1. Block Scheme of Signature Verification System
2 Data Acquisition Device
As mentioned above, data acquisition is performed by a special electronic pen which
was built at the University of Applied Sciences in Regensburg during the spring 2002
(Figure 2). The pen consists of two pairs of mechanical sensors that measure the hori-
zontal and vertical movements of the ballpoint nib and a pressure sensor that is placed
in the top part of the pen. The pen produces a total of three signals (Figure 3). The upper
signal corresponds to the pressure sensor and the other two correspond to the horizontal
and vertical movements of the pen. The data were acquired while writing the signature
”Dobner” (Figure 3).
Four strain gauge sensors that measure the horizontal and vertical movements of the
pen are located near the pen nib and are placed orthogonally to each other. The signal
produced by the horizontal pair of sensors is called x and the one produced by the
Fig. 2. Digital Data Acquisition Pen
42
Fig. 3. Signature ”Dobner” and signals produced by the pen (reprinted from [1])
vertical sensors y. Each pair of sensors is connected to a Wheatstone bridge. Therefore
there is only one output signal corresponding to the horizontal movement of the pen (x)
and one corresponding to the vertical movement (y). We cannot provide more detailed
description of the pen because of the patent pending status.
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 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 the signals, the fast wavelet transform (FWT)
was used. At first, each signal of the signature was filtered by an average filter, after-
wards it was decomposed by FWT and coefficients of a
5
and d
m
, for m = 1, 2, ..., 5
were determined [6]. The Daubechies and the Coiflet wavelet families were tested for
decomposition, the 5-th order Daubechies wavelet gave the best result. Using of this
wavelet, the following features were evaluated:
W
energy
- energy values kd
m
k
2
and ka
5
k
2
W
statistic
- mean values and standard deviation of coefficients d
m
and a
5
where d
m
and a
5
are the detailed and the approximation coefficients of FWT in scale
m and 5, respectively.
43
4 Neural Network Signature Verifiers
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 genuine signatures and we have no data for the class of forgery signatures. This is
the reason why the frequently used supervised learned neural network model such as
multi-layer perceptron are not suitable for the signature verification task.
ρ
2
1
F
R
i
r
v
G
F
F
FA
Fig. 4. ART-2 signature verifier (reprinted from [1])
4.1 Architecture of the ART-2 Neural Network Verifier
The adaptive resonance theory (ART), developed by Carpenter and Grossberg, was de-
signed 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 [7], [8].
The basic structure of the network verifier is illustrated in Figure 4. The network
consists of two layers of processing elements labelled F
1
(input and interface units)
and F
2
(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 pro-
cessing of the input data vector and creating of the clusters.
The input and interface layer F
1
consists of six sub- layers (these are not illustrated
in Figure 4); 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
44
feature vector and suppress the noise. The size of the F
1
layer (and hidden sub-layers)
was 18 in case of W
energy
features and 36 for W
statistic
features.
The clustering layer F
2
consists of two processing units only, the former (labelled
A) is active only if the feature vector corresponding to the genuine 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.
4.2 Training and Verification
As was mentioned above, only the data for the genuine 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 re-
peatedly 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 F
1
and vigi-
lance parameter ρ were set so that only the unit labelled A of layer F
2
was active during
the whole training procedure (the network places the template signatures only in one
cluster and adapts the corresponding weights between F
1
and F
2
layers). When the
training is completed, the network is prepared for verification. The parameters of F
1
sub-layers are not changed during the verification, only the vigilance parameter ρ have
to be set properly to the genuine and the forgery 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) man-
ually, for all verifications,
automatic setting A
1
: ρ
A1
= min
i
{r
i
} i = 1 · · · N
t
,
automatic setting A
2
: ρ
A2
=
1
N
t
N
t
X
i
r
i
i = 1 · · · N
t
.
In the equations above, N
t
is a number of training vectors and r
i
is activation level of
unit R (see Figure 4 and [7], [8] for detailed description and evaluation of r
i
). The best
results were achieved by automatic setting A
1
.
4.3 Architecture of the SOFM Neural Network Verifier
The self-organizing feature map (SOFM) has been developed by Theuvo Kohonen and
it has been described in several research papers and books [3], [4]. The purpose of the
self-organizing feature map is basically to map a continuous high-dimensional space
into discrete space of lower dimension (usually 1 or 2). The principal architecture of
the SOFM is illustrated in Figure 5. The map contains one layer of neurons, arranged
in a two-dimensional grid, and two layers of connections. In the first layer of connec-
tions, each element is fully connected (through weights) to all feature vector compo-
nents. Computations are feed-forward in the first layer of connection: the network com-
putes the scalar product between the input vector F
v
i
and each of the neuron weight
45
vectors w
i,j
. The second layer of connections acts as a recurrent excitatory/inhibitory
network, the aim of which is to implement the winer-take-all strategy, e.g. only the neu-
ron with the highest activation level is selected and labelled as the best matching unit
(BMU). The weight vector of this neuron then corresponds to the vector which is the
most similar to the input feature vector F
v
i
.
Fig. 5. Principal architecture of SOFM signature verifier
4.4 Training of the Signature Verifier
As in the case of ART-2 network, only 5 signatures were used for training of the SOFM.
For these signatures the corresponding feature vectors were evaluated and repeatedly
presented to the input layer of the network. To train the SOFM, the sequential training
algorithm was used (see [3]). During the training, the output layer of SOFM is being
arranged according to the training data and clusters corresponding to the genuine signa-
tures are created. In the most cases, the genuine signatures are projected to one part of
the two-dimensional grid, the forgeries are then projected to the other parts. After the
training procedure the position of the BMU’s for the genuine signature feature vectors
are recorded and the location threshold l
t
is evaluated. This threshold is used to de-
cide whether the input feature vector corresponds to the genuine signature or forgery.
In some cases the feature vectors corresponding to the forgery signatures are mapped
to the location of genuine ones, i.e. distance between units signed as BMU’s during the
training process is smaller than location threshold. In this case, the genuine signatures
and forgeries are separated according to the quantization error, i.e. euclidian distance
between BMU’s weight vector and input feature vector F
v
. Quantization error threshold
is also evaluated during the training procedure.
4.5 Verification Process
After the training of the SOFM and setting up corresponding parameters, i.e. location
thresholds l
t
, quantization error threshold Q
t
, the neural network is ready for verifica-
tion. The overall verification process consist of the following three steps:
1. the verified signature is scanned by the acquisition pen and corresponding feature
vector is evaluated,
2. the feature vector is passed through the SOFM and the location and quantization
error of BMU is evaluated,
46
3. the signature is classified as genuine if the both following rules are true:
min
L
T
s
d(L
t
i
, L
F
v
) l
t
(1)
Q
err
Q
t
(2)
where T
s
= { t
i
| i = 1, 2, 3} is the set of feature vectors t
i
of the signatures used
for training, L
t
i
and L
F
v
are the locations of BMU of the i-th training signature and the
unknown signature respectively.
5 Experimental Results
To test the verifier, signatures by 10 authors were taken. For each author, 20 genuine
signatures and 36 skilled forgeries were recorded. The skilled forgeries were written by
three different authors (12 forgeries for each person). Moreover, the signatures of other
authors were used as the random forgeries. Both verifiers were also tested by these set
of random forgeries (totally 5040 signatures).
Sometimes the author was not satisfied with his/her own signature. The quality of
the signature depended on his/her physical and mental condition. In such a case the sig-
natures were classified as forgery. For the evaluation of such cases, the authors marked
their genuine signatures by a mark from a 1 - 4 scale (1 is the best form of signature).
For the verifiers training, only the five signatures labelled by mark 1 or 2 were chosen.
In case of ART-2 verifier, the some parameters of input sub-layers have to be set up
(see [7]) before the training process. The FAR (False Accept Ratio) and FRR (False
Reject Ratio) strongly depends on the setting of these parameters. In our application
we set up the parameters experimentally, but next tests have to be performed to find
optimal setting.
For the SOFM, different sizes of the output layer, different topologies and differ-
ent number of training steps were also tested. Finally the network size 30 × 30 units
with rectangular topology was chosen as a good compromise between the length of the
network training (100 training epochs) and the achieved results. The neural network
weight vectors w
ij
were initially set up linearly (see [3]).
The results of verification process for ART-2 and SOFM verifiers are presented in
Table 1.
Table 1. Results of verification process
W
energy
W
statistic
FAR [%] FAR [%]
verifier forgeries FRR [%] forgeries FRR [%]
skilled random skilled random
ART-2 8 5 14 4 2 12
SOFM 9.5 4.5 11.5 6 4 10
47
6 Conclusion and Future Work
We have shown the application of two types of artificial neural networks for signature
verification. It can be seen (Tab. 1) that classification of genuine and forgery signatures
is reliable if the parameters of networks are trained by a sufficient number of dutifully
prepared training patterns. The achieved FRR and FAR are fully comparable with the
results obtained by standard statistical or structural methods, the wide range testing of
both types of ANNs will be carried out in the future.
In our future work, we plan to focus on the following tasks which could improve
the results of verification process:
including the new valuable features to the feature vector describing signature,
optimal setting of the parameters of the input and interface layer of ART-2,
optimal setting of the thresholds l
t
and Q
t
of SOFM verifier,
checking the possibility of the application of other neural networks (supervised or
unsupervised learned).
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48