=Paper=
{{Paper
|id=Vol-3035/paper06
|storemode=property
|title=The Use of Neural Network Methods and Atomic Functions in the Problem of Biometric Authentication by ECG
|pdfUrl=https://ceur-ws.org/Vol-3035/paper06.pdf
|volume=Vol-3035
|authors=Natalia Konnova,Albina Safina
}}
==The Use of Neural Network Methods and Atomic Functions in the Problem of Biometric Authentication by ECG==
https://ceur-ws.org/Vol-3035/paper06.pdf
The Use of Neural Network Methods and Atomic Functions in the
Problem of Biometric Authentication by ECG
Natalia Konnova 1 and Albina Safina 1
1
Bauman Moscow State Technical University, 5/1 2nd Baymanskay st., Moscow, 105005, Russia
Abstract
The most widespread methods of biometric authentication are not resistant to falsification
today. So other more secure individualized features are sought for the biometric authentication
problem. One alternative is the heartbeat signal and the electrocardiogram (ECG) signal, in
particular. It is individual-specific in the sense of amplitude, peak and other characteristics,
and thus difficult to be faked. This article discusses an algorithm for biometric ECG
authentication system based on convolutional neural networks. The use of the atomic activation
function will also be considered in comparison with the ReLU, which is often used in this type
of neural networks. To evaluate the results obtained, metrics are introduced, a numerical
experiment is set up using the developed software, within the framework in which the
convolutional neural networks have been implemented. To compare the efficiency of
classifiers, the estimates of Accuracy, Recall, Specificity, Precision, F1-measure are given.
Loss functions and ROC curves have been plotted for each algorithm and dataset.
Keywords 1
Neural network, Convolutional neural network, Activation function, atomic function
1. Introduction
Nowadays password-based authentication is the main identification tool, but it is insecure for a
number of reasons [1, 2]. The main reason is insufficiently complex passwords, despite the emergence
of password storage services. Therefore, biometric authentication is now increasingly used, which
utilizes distinctive characteristics that can be used to recognize and verify the legitimacy of users. The
ECG signal has great potential to become a powerful authentication tool due to its properties. Moreover,
recently, heart rate variability has been deeply studied and it has been proven that due to the
characteristics of human anatomy, the ECG cannot be faked [3]. It is also worth noting that this
characteristic cannot be removed without special sensors, which prevents information leakage. Its
further use as biometrics, in addition to diagnostics in medicine, is due to the factors described in [4].
In general, two types of errors are considered in biometric systems: false positive (type I error),
which leads to denial of access to a legitimate user, and omission of events (type II error), which leads
to access to the system by an illegitimate user. These errors are inversely related and are regulated by
the decision threshold by the classifier in favor of convenience (reduction of type I errors), or in favor
of safety (minimization of type II errors).
BIT-2021: XI International Scientific and Technical Conference on Secure Information Technologies, April 6-7, 2021, Moscow, Russia
EMAIL: nkonnova@bmstu.ru (A. 1)
ORCID: 0000-0002-7883-6145 (A. 1)
Β© 2021 Copyright for this paper by its authors.
Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR Workshop Proceedings (CEUR-WS.org)
51
2. Materials and Methods
For the experiment, the international PhysioBank ATM database of measurements of normal heart
rate MIT-BIH nsrdb was used 2. This database includes 18 long term ECG records of subjects. The
subjects included in this database did not have significant deviations from the norm; these include 5
men between the ages of 26 and 45 and 13 women between the ages of 20 and 50. For a randomly
selected legitimate user, 18 signals of 10 seconds each were collected from the total recording, for the
rest, 2-3 segments were selected, also 10 seconds each.
2.1. Preprocessing of ECG signals
The original data requires preliminary processing, as it contains noise and various distortions. The
signal was filtered using a Butterworth bandpass filter (BFB) of 0.5β45 Hz [5, 18], which allows one
to reduce the frequency and remove signal distortions while retaining significant components.
After filtering, it is necessary to highlight the signs of the ECG signal, mainly the QRS complex, P
and T waves [6]. The features were extracted according to the following algorithm:
1. Detect R waves in the general ECG signal.
2. Divide into ECG cycles between adjacent R waves.
3. Interpolate ECG cycles (since templates can have different lengths and frequencies, it is
necessary to interpolate each cycle before normalization; in this work, interpolation was carried
out using the cubic spline algorithm [7]).
4. Normalize ECG cycles using the algorithm [7].
5. Next, you need to select a single template, for this the average value at each point is calculated,
i.e. for each ππππ β [0 βΆ 0,01 βΆ 1] calculate the mean value ππ(ππππ ) =
ππππππππππππ οΏ½πΆπΆππ (ππππ )οΏ½ , where ππππ β [0 βΆ 0,01 βΆ 1] and ππ β [0 βΆ 1 βΆ 10]; display the ECG cycle
ππ = ππ(ππππ ), where ππππ β [0 βΆ 0,01 βΆ 1].
2.2. Overview of Neuron Network Architecture
In deep learning, a convolutional neural network (CNN or ConvNet) is a class of deep neural
networks most commonly used to analyze visual images [8]. The essence of convolution is to create
another set of values, which is called a kernel or filter. Today, there are other layers in the traditional
convolutional neural network that are interspersed with convolutional layers. Activation layer is a layer
that is a kind of non-linear function (usually ReLU and its modifications), often logically combined
with a convolution layer. The pooling layer is a layer that is a non-linear compaction of the feature map.
The maximum function (or Softmax) is usually used. The last layer of the network is the fully connected
layer. Each neuron in this layer is a perceptron with a nonlinear activation function.
A schematic diagram of the convolutional neural network used in this study is shown in Fig. 1.
The unique approximation properties of artificial neural networks are largely achieved due
to activation functions that determine the dependence of the output signal on the weighted sum
of signals at the input of the neuron. Thus, the artificial neuron is characterized by its activation
function. Non-linear activation functions allow neural networks to solve non-trivial problems
with a small number of nodes. Let's consider the used activation functions.
ReLU is a rectified activation function, its idea is that the excitation of biological neurons
cannot be expressed with a negative value (1). Neurons introduce nonlinearity at zero that can
be used to make decisions.
ππ(π₯π₯) = max {0, π₯π₯}. (1)
2
Open access databases on PhysioNet, 2021. URL: https://physionet.org/about/database/.
52
Figure 1: Convolutional neural network scheme
Sigmoidal functions based on finite infinitely smooth solutions of functional differential equations
with deviating argument are often called atomic functions (AF); they were first introduced in the works
of V.L. Rvachev and V.A. Rvachev [9, 10]. Atomic functions are a convenient tool for numerical
analysis, approximation theory, digital signal processing [11-13]. Despite the fact that AF π’π’π’π’(π₯π₯) is not
an entire function and has an infinite spectrum, expansion (2) provides a satisfactory quality of
approximation in the interval [-1,1]. The appearance of the function, as well as its derivative, is shown
in Fig. 2.
2ππ β1
ππ
π’π’π’π’(π₯π₯) = οΏ½ π’π’π’π’ οΏ½ ππ οΏ½ π π π π π π π π [ππ(2ππ π₯π₯ β ππ)], (β1 β€ π₯π₯ β€ 1). (2)
2
ππ=β2ππ +1
Let's consider the capabilities of AF for the presentation of activation functions. We will choose the
simplest AF π’π’π’π’(π₯π₯) as the basic one.
π₯π₯ 1 1
π’π’π’π’ οΏ½ π₯π₯ β οΏ½ , ΠΏΡΠΈ π₯π₯ β€ 1
ππ(π₯π₯) = οΏ½ π’π’π’π’(π‘π‘)ππππ = οΏ½ 2 2 . (3)
β1 1 , ΠΏΡΠΈ π₯π₯ β€ 1
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Figure 2: Atomic function up(x) and its first derivative
Then, by virtue of the main functional differential equation for the AF π’π’π’π’(π₯π₯), we obtain a simple
expression for the derivative:
ππ(π₯π₯) = π’π’π’π’(π₯π₯) = ππ(2π₯π₯ + 1) β ππ(2π₯π₯ β 1). (4)
Based on the properties described above, it can be assumed that using these functions, the result of
neural network classification can be expected at least no worse than using the rectified activation
function ReLU [17]. To test this hypothesis, a numerical experiment was carried out, described below.
3. Numerical experiment
After preliminary preprocessing of the ECG signal and the stage of feature extraction, a vector of
122 coefficients representing the signal template was obtained for each signal. Figure 3 shows a view
of several templates from the general sample, superimposed for clarity of data variability.
Figure 3: Superimposed ECG signal templates
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3.1. Performance evaluation strategies
The neural network parameters were selected empirically. CNN consists of two convolutional layers,
between which are pooling layers and two fully connected layers of 125 neurons each, with FA ReLU,
or atomic FA; there are two neurons with Softmax FA on the output layer. During training, the cross-
validation coefficient was zero, since in biometrics tasks it is necessary to achieve overfitting of the
neural network for better recognition of a legitimate user.
In the NN model, a binary classification is used to recognize ECG signals: class "1" defines a
legitimate user, and class "0" is an illegitimate user. To assess the effectiveness of the binary classifier,
the following assessment metrics are calculated: the proportion of correct answers (accuracy);
precision; recall; sensitivity; specificity, F-measure [14, 15] and ROC-curve [16].
4. Results
Table 1 shows the metrics of the effectiveness of the compared activation functions in training
process of the constructed neural network.
Table 1
Comparison of the AF effectiveness
AF ReLU Atomic
Metrics Train Test Train Test
Accuracy 0.9753 1.0000 0.9877 1.0000
Recall 0.9753 1.0000 0.9877 1.0000
Precision 0.9753 1.0000 0.9877 1.0000
ROC-AUC 0.9476 1.0000 0.9877 1.0000
FN 0.0322 0.0000 0.0163 0.0000
FP 0.0322 0.0000 0.0163 0.0000
Loss 0.2948 0.2353 0.0957 0.0190
Specificity 0.9545 1.0000 0.9772 1.0000
F-ΠΌΠ΅ΡΠ° 0.9505 1.0000 0.9681 1.0000
Further in Fig. 4 there are shown the ROC curves for assessing the quality of binary classification,
graphs of recognition accuracy, graphs of loss functions, and a graph of changes in the number of type
II errors (FP) during training.
For testing, samples were selected that did not participate in training the neural network model. In
total, 20 samples were used for testing, 10 of which belong to a legitimate user.
When using a ReLU activation function, the probability of a legitimate user's samples belonging to
class "1" is on average 0.9979, and of samples of other users to class "0" - ~ 1.0000. This indicates both
that the model is well trained and type II errors are minimized, and that the probability of false positives
is small.
When using Atomic AF, the probability of a legitimate user's samples belonging to class "1" is on
average 0.9667, and of samples of other users to class "0" - 0.9758. Slightly worse than using ReLU.
55
Figure 4: Superimposed ECG signal templates
5. Conclusions
This paper describes the results of using a convolutional neural network in combination with the use
of an atomic activation function in the task of biometric authentication.
When comparing the two activation functions, we notice that for the submitted model of the neural
network, ReLU and atomic AF, which is often used in similar architectures, the atomic AF showed
itself better during training (1% of skipping events during training, F-measure equal to 0.9681). But in
testing, ReLU performed better, which shows its suitability for the authentication task. However, taking
into account the specifics of the operation of neural networks in authentication systems, the indicator
of efficiency during training is of decisive importance, since when a new user is added to the system,
the template of this user of the neural network will be presented. And in the future, during the operation
of the network, it deals with those objects of marked data that have already been presented to it. Since
within the framework of the authentication procedure, only the verification of the data presented by the
user is carried out for the possibility of issuing rights to access limited resources.
As we can see, convolutional neural networks show high results in training and testing in biometric
authentication tasks, which indicates that they can be effectively used to implement these information
security systems, including to check the user's access rights by heart rate. Research shows that such
authentication methods are quite promising [19]. A number of products are already on the market and
are becoming widespread (e.g. Nymi Workplace Wearables 3 and ECG/EKG algorithms 4), and many
more will appear in the near future. Questions of practical implementation and directions for improving
the software and mathematical part of such systems will be relevant for quite a long time.
3
Nymi Workplace Wearables, 2021. URL: https://www.nymi.com/nymi-band.
4 A suite of powerful ECG/EKG algorithms and analytics for user identification, 2021. URL: https://www.b-
secur.com/heartkey/.
56
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