The combination of self-organizing feature maps and support vector regression for solving the inverse ECG problem

Noninvasive electrical imaging of the heart aims to quantitatively reconstruct transmembrane potentials (TMPs) from body surface potentials (BSPs), which is a typical inverse problem. Classically, electrocardiography (ECG) inverse problem is solved by regularization techniques. In this study, it is treated as a regression problem with multi-inputs (BSPs) and multi-outputs (TMPs). Then the resultant regression problem is solved by a hybrid method, which combines the support vector regression (SVR) method with self-organizing feature map (SOFM) techniques. The hybrid SOFM-SVR method conducts a two-step process: SOFM algorithm is used to cluster the training samples and the individual SVR method is employed to construct the regression model. For each testing sample, the cluster operation can effectively improve the efficiency of the regression algorithm, and also helps the setup of the corresponding SVR model for the TMPs reconstruction. The performance of the developed SOFM-SVR model is tested using our previously developed realistic heart-torso model. The experiment results show that, compared with traditional single SVR method in solving the inverse ECG problem, the proposed method can reduce the cost of training time and improve the reconstruction accuracy in solving the inverse ECG problem.

[1]  Ruhaidah Samsudin,et al.  A hybrid model of self-organizing maps (SOM) and least square support vector machine (LSSVM) for time-series forecasting , 2011, Expert Syst. Appl..

[2]  Vladimir Vapnik,et al.  An overview of statistical learning theory , 1999, IEEE Trans. Neural Networks.

[3]  Y. Rudy,et al.  Noninvasive electrocardiographic imaging for cardiac electrophysiology and arrhythmia , 2004, Nature Medicine.

[4]  R. Macleod,et al.  Short titles: Inverse Problems in Electrocardiology , 2022 .

[5]  Ling Xia,et al.  Effect of Cardiac Motion on Solution of the Electrocardiography Inverse Problem , 2009, IEEE Transactions on Biomedical Engineering.

[6]  M. Lysaker,et al.  On the possibility for computing the transmembrane potential in the heart with a one shot method: an inverse problem. , 2007, Mathematical biosciences.

[7]  Ling Xia,et al.  The application of subspace preconditioned LSQR algorithm for solving the electrocardiography inverse problem. , 2009, Medical engineering & physics.

[8]  Chih-Jen Lin,et al.  LIBSVM: A library for support vector machines , 2011, TIST.

[9]  F. Tay,et al.  Application of support vector machines in financial time series forecasting , 2001 .

[10]  Ling Xia,et al.  Truncated Total Least Squares: A New Regularization Method for the Solution of ECG Inverse Problems , 2008, IEEE Transactions on Biomedical Engineering.

[11]  L. Weixue,et al.  Computer simulation of epicardial potentials using a heart-torso model with realistic geometry. , 1996, IEEE transactions on bio-medical engineering.

[12]  Dana H. Brooks,et al.  Wavefront-based models for inverse electrocardiography , 2006, IEEE Transactions on Biomedical Engineering.

[13]  Ling Xia,et al.  Analysis of cardiac ventricular wall motion based on a three-dimensional electromechanical biventricular model , 2005, Physics in medicine and biology.

[14]  Li Cao,et al.  The combination of Self-Organizing Feature Maps and support vector regression for solving the inverse ECG problem , 2012, 2012 8th International Conference on Natural Computation.

[15]  Mohamed M. Mostafa,et al.  Clustering the ecological footprint of nations using Kohonen's self-organizing maps , 2010, Expert Syst. Appl..

[16]  Cheng-Lung Huang,et al.  A hybrid SOFM-SVR with a filter-based feature selection for stock market forecasting , 2009, Expert Syst. Appl..

[17]  Bin He,et al.  Noninvasive reconstruction of three-dimensional ventricular activation sequence from the inverse solution of distributed equivalent current density , 2006, IEEE Transactions on Medical Imaging.

[18]  Sheng-Hsun Hsu,et al.  A two-stage architecture for stock price forecasting by integrating self-organizing map and support vector regression , 2009, Expert Syst. Appl..

[19]  Nello Cristianini,et al.  An introduction to Support Vector Machines , 2000 .

[20]  Andrew J. Pullan,et al.  Comparison of potential- and activation-based formulations for the inverse problem of electrocardiology , 2003, IEEE Transactions on Biomedical Engineering.

[21]  Bernhard Schölkopf,et al.  A tutorial on support vector regression , 2004, Stat. Comput..

[22]  F. Liu,et al.  On epicardial potential reconstruction using regularization schemes with the L1-norm data term , 2011, Physics in medicine and biology.

[23]  Bernhard Schölkopf,et al.  Learning with kernels , 2001 .

[24]  Feng Liu,et al.  A Hybrid Model of Maximum Margin Clustering Method and Support Vector Regression for Noninvasive Electrocardiographic Imaging , 2012, Comput. Math. Methods Medicine.

[25]  Kyoung-jae Kim,et al.  Financial time series forecasting using support vector machines , 2003, Neurocomputing.

[26]  Lijuan Cao,et al.  Support vector machines experts for time series forecasting , 2003, Neurocomputing.

[27]  Robert Modre,et al.  A comparison of noninvasive reconstruction of epicardial versus transmembrane potentials in consideration of the null space , 2004, IEEE Transactions on Biomedical Engineering.

[28]  Ioannis Kompatsiaris,et al.  GPU acceleration for support vector machines , 2011, WIAMIS 2011.

[29]  Ingo Steinwart,et al.  On the Influence of the Kernel on the Consistency of Support Vector Machines , 2002, J. Mach. Learn. Res..

[30]  Pheng Ann Heng,et al.  Application of L1-norm regularization to epicardial potential reconstruction based on gradient projection , 2011, Physics in medicine and biology.

[31]  Y Rudy,et al.  The inverse problem in electrocardiography: solutions in terms of epicardial potentials. , 1988, Critical reviews in biomedical engineering.

[32]  A. van Oosterom,et al.  Non-Invasive Imaging of Cardiac Activation and Recovery , 2009, Annals of Biomedical Engineering.

[33]  WANGLing,et al.  Combining Self-organizing Feature Map with Support Vector Regression Based on Expert System , 2005 .

[34]  Liu Fang,et al.  Face recognition using self-organizing feature maps and support vector machines , 2003, Proceedings Fifth International Conference on Computational Intelligence and Multimedia Applications. ICCIMA 2003.

[35]  Nello Cristianini,et al.  An Introduction to Support Vector Machines and Other Kernel-based Learning Methods , 2000 .

[36]  Robert Modre,et al.  A new spatiotemporal regularization approach for reconstruction of cardiac transmembrane potential patterns , 2004, IEEE Transactions on Biomedical Engineering.

[37]  Lutgarde M. C. Buydens,et al.  Using support vector machines for time series prediction , 2003 .

[38]  F. Liu,et al.  Application of kernel principal component analysis and support vector regression for reconstruction of cardiac transmembrane potentials , 2011, Physics in medicine and biology.

[39]  Qi Li,et al.  GPUSVM: a comprehensive CUDA based support vector machine package , 2011, Central European Journal of Computer Science.