The paper is about some aspects concerning person biometric identi cation based on using of electrocardiograms. Signal preprocessing routing is considered in the paper. Classi cation was carried out with support vector machines algorithm. Tuning of hyper parameters of classi cation is considering. The problem of person biometric identi cation concerns classi cation problems. To solve it, we have to consider algorithms from some nite set and choose an algorithm that gives the least error of the forecast [3]. Let's introduce some notation. Let us suppose X is a space of objects.
Various biometric methods of person identi cation are getting more popular.
Fingerprinting, face, voice and retina recognition are widely used in various
security systems. The vulnerabilities of traditional methods of biometric identi
cation were revealed over time. Researchers are increasingly turning their attention
to such person biometric features as electrocardiograms, electroencephalograms
and DNA [
Copyright c by the paper's authors. Copying permitted for private and academic purposes. In: S. Belim et al. (eds.): OPTA-SCL 2018, Omsk, Russia, published at http://ceur-ws.org Xl = (xi; yi)li=1
yi = y (xi); At = fa : X ! Y g t : (X
Y )l ! At are a models of algorithms, t 2 T , T is a number of algorithms under consideration. are learning methods. It is required to nd a method t with the best generalizing power.
When nding a method t, we often have to solve the following subtasks: { Choice of the best model At (model selection). { Choice of learning method t for a given model At (in particular, optimization of hyperparameters). { Features selection:
F = ffj : X ! Dj : j = 1; :::; ng is a set of features. The method of learning j uses only features J To assessment the quality of learning by precedents it's used: L(a; x) is a cost function of algorithm a on the object x.
F .
Y is a set of answers.
is a training set, l is a sample size.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
is a functional of accuracy a on X. In this case we consider an internal quality
criterion that is measured on the training set Xl:
and an external criterion evaluating the quality of learning on hold-out set Xk[
i=1
Q (Xl) = Q( (Xl); Xl)
Q (Xl; Xk) = Q( (Xl); Xk): In the paper presented we will consider such aspects of person biometric identi cation as feature selection, model selection, choice of methods (tuning of hyperparameters), assessment of the quality of learning. 3
We used the MGH/MF Waveform Database hosted at physionet.org
resource [
The typical recording includes three ECG leads, arterial pressure, pulmonary
arterial pressure, central venous pressure, respiratory impedance, and airway
CO2 waveforms. The raw sampling rate of 1440 samples per second per signal
was reduced by a factor of two to yield an e ective rate of 360 samples per
second per signal relative to real time [
When preprocessing stage we used a biopsy python library by John Reid. The
package enables the development of Pattern Recognition and Machine Learning
work ows for the analysis of biosignals including ECG [
We used a Support Vector Machines (SVM) algorithm for classi cation.
Support Vector Machines are based on the concept of decision planes that de ne
decision boundaries. A decision plane is one that separates between a set of
objects having di erent class memberships. SVM is primarily a classier method that
performs classi cation tasks by constructing hyperplanes in a multidimensional
space that separates cases of di erent class labels. SVM supports both
regression and classi cation tasks and can handle multiple continuous and categorical
variables [
To construct an optimal hyperplane, SVM employs an iterative training algorithm, which is used to minimize an error function. According to the form of the error function, SVM models can be classi ed into four distinct groups: { Classi cation SVM Type 1 (also known as C-SVM classi cation) { Classi cation SVM Type 2 (also known as nu-SVM classi cation) { Regression SVM Type 1 (also known as epsilon-SVM regression) { Regression SVM Type 2 (also known as nu-SVM regression)
We used a Classi cation SVM Type 1 (also known as C-SVM classi cation) model.
For this type of SVM, training involves the minimization of the error function:
N 1 wT w + C X 2 i=1 i subject to the constraints: yi(wT (xi) + b) 1 i 0; i = 1; :::; N; where C is the capacity constant, w is the vector of coe cients, b is a constant, and i represents parameters for handling nonseparable data (inputs). The index i labels the N training cases. Note that y 2 1 represents the class labels and xi represents the independent variables. The kernel is used to transform data from the input (independent) to the feature space. It should be noted that the larger the C, the more the error is penalized. Thus, C should be chosen with care to avoid over tting. (9) (10) (11) 6
K(Xi; Xj ) = 8 > > <
Xi Xj ( Xi Xj + C)d > exp( jXi Xj j2) >: tanh( Xi Xj + C)
Linear >9 P olynomial =>
SiRgBmFoid ;>> ; where K(Xi; Xj ) = (Xi) (Xj ) that is, the kernel function, represents a dot product of input data points mapped into the higher dimensional feature space by transformation . 7
The RBF is by far the most popular choice of kernel types used in Support
Vector Machines. This is mainly because of their localized and nite responses
across the entire range of the real x-axis [
Support vector machine classi er supported by sklearn python library uses as
default following hyper parameters: C=1.0, kernel='rbf', gamma='auto'. When
using of default parameters while performing of classi cation of
electrocardiograms we had accuracy score equal to 0.93. We tuned hyper parameters of
classi cation with Grid Search procedure varying C parameter in range of [
During the preprocessing of electrocardiograms we extracted rst leads of signal and performed low-pass lter for reducing redundancy. Then we extracted cardiac cycles from the leads and extracted Q, R and S peaks from cardiac cycles. Using amplitude and temporal features of peaks we composed a feature table containing 6 features (Qx, Qy, Rx, Ry, Sx, Sy) and class labels vector y. Further we randomly splitted a feature table and class labels vector into training set and testing set on ration of 75:25 for further cross-validation. Training set was used for learning a classi er and testing set was used for assessment of quality of learning. SVM classi er supported by sklearn python library using default options show accuracy score equal to 0.93. We found the best hyper parameters are following: 'kernel': 'rbf', 'C': 10, 'gamma': 0.001. Using these parameters we could improved accuracy score up to 0.99.