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.
Nowadays password-based authentication is the main identification tool, but it is insecure for a
number of reasons [
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).
For the experiment, the international PhysioBank ATM database of measurements of normal heart rate MIT-BIH nsrdb was used2. 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.
The original data requires preliminary processing, as it contains noise and various distortions. The
signal was filtered using a Butterworth bandpass filter (BFB) of 0.5–45 Hz [
After filtering, it is necessary to highlight the signs of the ECG signal, mainly the QRS complex, P
and T waves [
Divide into ECG cycles between adjacent R waves. 1. 2. 4. 5.
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 [
Normalize ECG cycles using the algorithm [
Next, you need to select a single template, for this the average value at each point is calculated, i.e.
for each ∈ [0 ∶ 0,01 ∶ 1] calculate the mean value ( ) = ( ) , where ∈ [0 ∶ 0,01 ∶ 1] and ∈ [0 ∶ 1 ∶ 10]; display the ECG cycle = ( ), where ∈ [0 ∶ 0,01 ∶ 1]. 2.2.
In deep learning, a convolutional neural network (CNN or ConvNet) is a class of deep neural
networks most commonly used to analyze visual images [
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.
( ) = max {0, }. (1) 2 Open access databases on PhysioNet, 2021. URL: https://physionet.org/about/database/.
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 [
( ) =
2 −1 =−2 +1 (−1 ≤ ≤ 1).
Let's consider the capabilities of AF for the presentation of activation functions. We will choose the simplest AF ( ) as the basic one.
( ) =
( ) −1 = 1 , 1 2 1 2 − , при ≤ 1
.
при ≤ 1
Then, by virtue of the main functional differential equation for the AF ( ), we obtain a simple expression for the derivative: ( ) = ( ) = (2 + 1) − (2 − 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.
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. 3.1.
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 crossvalidation 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 [
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.
Metrics
F-мера
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 Wearables3 and ECG/EKG algorithms4), 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.bsecur.com/heartkey/.