SUPPORT VECTOR MACHINE for the RECOGNITION OF ATRIAL AND VENTRICULAR DEPOLARIZATION IN HOLTER ECG RECORDing

S. Jankowski¹, J. Tijink², G. Vumbaca², M. Balsi², G. Karpinski^3
1Institute of Electronic Systems, Warsaw University of Technology,
Nowowiejska 15/19, 00-665 Warsaw, POLAND
²Department of Electronic Engineering, University of Rome "La Sapienza"
via Eudossiana  18, 18-00184 Rome, ITALY
³Chair and Department of Internal Medicine and Cardiology, Central Teaching Hospital
ul. Banacha 1a, 02-097 Warsaw, POLAND

Abstract: A new approach to the ECG Holter analysis is presented. It enables the signal shape recognition including P, QRS and T waves. The Holter recordings are filtered and segmented into single heartbeats. Each heartbeat is approximated by Gaussian functions whose parameters are set up as vectors for classification. We apply support vector machines for approximation and classification.  The method has been tested on database of the Department of Internal Medicine and Cardiology at the Central Teaching Hospital in Warsaw. We analyzed selected cases of arrhythmia: ventricular and supraventricular ectopic beats and atrial fibrillation by classifying shapes of either atrial (P wave or f wave) or ventricular depolarizations (QRS complexes). We obtained excellent performance of automatic recognition of normal vs. pathological heartbeats in all considered cases.

INTRODUCTION

Automatic recognition of cardiac pathologies from the investigation of Holter ECG recordings is usually based on the analysis of heart rate variability and mainly on the shape of QRS complexes and ST segment. In this paper we present a new promising method that enables to consider the shape of entire heart beat record including P, QRS and T waves. These details are of importance in automatic discrimination of both the atrial and ventricular depolarization. We present the complete toolbox for computer-aided diagnosis of Holter recordings. Its mathematical basis is the theory of support vector machines (SVM) [1,2,3]. SVM are also applied for arrhythmia discrimination [5]. We show the potentials of our method for selected cases:

-          ectopic beat recognition (supra- vs. ventricular);
-          atrial fibrillation.

The excellent performances of our approach, high rate of successful pattern recognition and computational efficiency, make use of our tools possible in clinical practice.

METHOD

Support vector machine performs new ideas of supervised learning from examples. Let X ⊆ Rⁿ - the input space, Y - the output domain, e.g. for binary classification Y= [-1, 1}, for function approximation Y ⊆ R. A training set consists of a collection of training examples:

S = ((x₁, y₁), (x₂, y₂),...,(x_l, y_l)) ⊆ (X Y)^l

l - number of examples, x - examples, y - their labels.

Given a linearly separable set S the optimal separating hyperplane (w,b) solves the following optimization problem:

(1)

subject to

(2)

It realizes the maximal margin hyperplane with the geometric margin γ =1/||w||₂. This problem can be solved by introducing Lagrange multipliers α_i ≥ 0 and a primal Lagrangian L:

(3)

The Lagrangian L has to be minimized with respect to the primal variables w and b and maximized with respect to the dual variables α_i. The dual form is the following:

(4)

The relation shows that the hyperplane can be described as a linear combination of the training points:

(5)

This expansion consists of only a small subset of data from the training set that correspond to non-zero Lagrange multipliers - these points are called the support vectors.

We use the algorithm that quickly solves the support vector machine problem - sequential minimal optimization (SMO) - extreme decomposition of the problem that involves two Lagrange multipliers in one step [4].

NUMERICAL PROCEDURES

The database used in this paper consists of ECG Holter recordings from the Department of Internal Medicine and Cardiology at the Central Teaching Hospital in Warsaw. The signals are digitized with 128 Hz sampling rate and filtered with a 514 coefficients digital FIR filter.

The tools developed in this work can do the following tasks: segmentation, SVM approximation, parameterization, and SVM classification. Given a complete filtered ECG Holter recording as input, the segmentation tool can divide it into a series of single heartbeats. The support vector machine provides an adequate approximation of the waveform as a sum of Gaussian functions. The Lagrange multipliers in this approximation can substitute the discrete samples representing the signal. This new kind of processing stresses the characteristics of a single beat.

In the approximation the parameters are homogeneous in the sense that they all state the height or weight of a Gaussian function at a certain position. This position is inherent to the data as it depends on the position of the parameter within the series.   Parameterization means a careful selection of these multipliers, according to their position within the beat. This selection provides a meaningful representation of a heartbeat for the SVM classifier. The entire heartbeat can be represented by 30 parameters: 7 for P wave, 7 for QRS complex, 16 for ST interval and T wave. We decide to use 7 or more parameters with respect to considered pathology. E.g. for atrial fibrillation we focus our attention on P wave only using 20 parameters. The reduced representation improves the performance of the SVM classification.

After performing parameterization, classification consists of two steps: learning and testing. Our classifier is a learning machine of the supervised type. In the learning phase it receives some patterns as input. These patterns are heartbeats represented by m parameters that can be seen as points in m-dimensional space. Each point has a label assigned by cardiologists that indicates its class corresponding to a type of pathology or at least to some precise feature within the beat shape. Then the machine becomes able to find the labels of new points by comparing them with those used in the learning phase.

RESULTS

Ectopic beats

Patient N3: the presence of ectopic ventricular beats is shown in Fig. 1. SVM classifier was trained with 8 normal sinus beats and 10 ectopic ones with only 7 parameters representing QRS complex. Number of support vectors is 4 (pathological) + 3 (normal). Results of classification of all beats recorded in 24 hours with QRS complex parameters are: SVM recognises correctly every beat with 0.2% error.

Atrial fibrillation

Patients K4 and N87 are affected by paroxysmal atrial fibrillation. Normal sinus beats of these two patients have regular P waves but as atrial fibrillation begins the P wave disappears and there are f waves instead. Figure 2 shows normal (P wave) and pathological (f waves) depolarizations of atria of patient K4. SVM classifier was trained with 10 beats of  f wave and 8 beats of P wave (20 parameters). The beats of both types are taken from patient K4. Number of support vectors is 6 (pathological) + 5 (normal).

Results of classification of 134 beats with P wave parameters are: SVM recognises correctly every beat with 0.3% error.

Then SVM classified 1209 beats of patient N87 affected by atrial fibrillation too with the same training file (only beats of patient K4). Results of classification with P wave parameters are: SVM recognises correctly every beat with 0.3% error.

Figure 1. Normal sinus beat and ectopic ventricular beat

Figure 2. Normal sinus beat (P wave) and atrial fibrillation(f waves). Smooth line - SVM approximation.

DISCUSSION

A trained support vector machine can classify heartbeats according to their shape with low error rate. Apart from classifying beats according to the shape of QRS complexes, the machine can also recognize differences in the lower frequency content of the beat, e.g. in P and T waves or ST segment. ECG tracings of patients with paroxyzmal atrial fibrillation gave promising results. Pathological beats with short series of  f waves substituting the P wave were identified with very low error.

Acknowledgments:  Work supported by Dean of the Faculty of Electronics and Information Technology, Warsaw Univ. of Technology and partially supported by SOCRATES program. J. Tijink and G. Vumbaca were supported by "La Sapienza" University scholarship. We thank Prof. Dr. Med. G. Opolski for stimulating discussions.

REFERENCES

[1] V. N. Vapnik Statistical Learning Theory, Wiley, New York, 1998.

[2] B. Scholkopf, C. J. C. Burges and A. J. Smola (eds.): Advances in Kernel Methods - Support Vector Learning, MIT Press, 1999

[3] N. Cristianini, J. Shaw-Taylor: Support Vector Machines, Cambridge University Press, 2000

[4] J. Platt: Sequential Minimal Optimization: A fast algorithm for training support vector machines, Tech. Rep. MSR-TR-98-14, Microsoft Research, 1998

[5] J. Millet-Roig, R. Ventura-Galiano, F. J. Chorro-Gasco, A. Cebrian; Support Vector Machine for Arrhythmia Discrimination with Wavelet-Transform-Based Feature Selection, Computers in Cardiology 2000, 27, pp. 407-410