A Hybrid Model of Maximum Margin Clustering Method and Support Vector Regression for Noninvasive Electrocardiographic Imaging

Abstract

Noninvasive electrocardiographic imaging, such as the reconstruction of myocardial transmembrane potentials (TMPs) distribution, can provide more detailed and complicated electrophysiological information than the body surface potentials (BSPs). However, the noninvasive reconstruction of the TMPs from BSPs is a typical inverse problem. In this study, this inverse ECG problem is treated as a regression problem with multi-inputs (BSPs) and multioutputs (TMPs), which will be solved by the Maximum Margin Clustering- (MMC-) Support Vector Regression (SVR) method. First, the MMC approach is adopted to cluster the training samples (a series of time instant BSPs), and the individual SVR model for each cluster is then constructed. For each testing sample, we find its matched cluster and then use the corresponding SVR model to reconstruct the TMPs. Using testing samples, it is found that the reconstructed TMPs results with the MMC-SVR method are more accurate than those of the single SVR method. In addition to the improved accuracy in solving the inverse ECG problem, the MMC-SVR method divides the training samples into clusters of small sample sizes, which can enhance the computation efficiency of training the SVR model.

Study on Parameter Optimization for Support Vector Regression in Solving the Inverse ECG Problem

“…In order to increase the diversity of the perturbed parameter vectors, crossover is introduced by the following formula: $\begin{array}{c}{u}_{ji,G+\mathrm{1}}^{}\\ =\{\begin{array}{cc}{v}_{ji,G+\mathrm{normal1}}^{}\hfill & \text{if}\hspace{0.17em}\hspace{0.17em}(\text{randb}\left(j\right)\le \text{CR})\mathrm{\hspace{0.17em}\hspace{0.17em}}\text{or}\mathrm{\hspace{0.17em}\hspace{0.17em}}j=\text{rnbr}\left(i\right)\hfill \\ x_{ji,G+\mathrm{normal1}}\hfill & \text{if}\hspace{0.17em}\hspace{0.17em}\left(\hspace{0.17em}\text{randb}\hspace{0.17em}\left(j\right)>\text{CR}\right)\text{and}\mathrm{\hspace{0.17em}\hspace{0.17em}}j\ne \text{rnbr}\left(i\right),\hfill \end{array}\end{array}$ where u i , G +1 = ( u 1 i , G +1 , u 2 i , G +1 , u 3 i , G +1 ), randb( j )∈[0,1] is the j th evaluation of a uniform random number generator, and rnbr( i ) is a randomly chosen integer in the range in [1, 3] to ensure that u i , G +1 gets at least one element from v i , G +1 .…”

“…The inverse ECG problem is to obtain myocardial transmembrane potential (TMPs) distribution from body surface potentials (BSPs), thus noninvasively imaging the electrophysiological information on the cardiac surface [1, 2]. Generally, approaches to solving this inverse ECG problem can be relied on potential-based model, including epicardial, endocardial, or transmembrane potentials, which is used to evaluate the potential values on the cardiac surface [3] at certain time instants.…”

“…Therefore, an alternative method, support vector regression (SVR) method [7], was proposed to solve the inverse ECG problem. Compared with conventional regularization methods, SVR method can produce more accurate results in terms of reconstruction of the transmembrane potential distributions on epi- and endocardial surfaces [1, 8]. SVR is an extension version of support vector machine (SVM) to solve nonlinear regression estimation problems, which aims at minimizing an upper bound of the generalization error instead of the training error [9] by adhering to the principle of structural risk minimization (SRM).…”

Noninvasive reconstruction of cardiac transmembrane potentials using a kernelized extreme learning method

“…Although these regularization methods are quite useful for solving the inverse ECG problem, they are vulnerable to system noises, especially the geometry noise; therefore, the reconstruction quality of TMPs is not robust. The machine learning method is another powerful technique for solving the nonlinear regression problem such as support vector regression (SVR) Wang 2007, Wu et al 2009), which has been applied in solving the inverse ECG problem (Jiang et al 2012(Jiang et al , 2013a. In order to develop an effective SVR model, all available indicators can be used as inputs for the SVR, but irrelevant features or correlated features could deteriorate the regression ability of the SVR model.…”

“…Through the combination of the self-organizing map(SOM) with SVR or LS-SVM, the hybrid method has the potential to find more accurate inverse solutions than using a single SVR model (Hsu et al 2009, Ismail et al 2011, Jiang et al 2013a. In addition, the hybrid MCC-SVR method can reconstruct TMPs more accurately than those of single SVR methods (Jiang et al 2012), which integrate the Maximum Margin Clustering (MMC) (Zhang et al 2009) method with SVR. However, the SVR method is sensitive to users' defined free parameters (that is, the hyper-parameters).…”