Application of kernel principal component analysis and support vector regression for reconstruction of cardiac transmembrane potentials

Non-invasively reconstructing the transmembrane potentials (TMPs) from body surface potentials (BSPs) constitutes one form of the inverse ECG problem that can be treated as a regression problem with multi-inputs and multi-outputs, and which can be solved using the support vector regression (SVR) method. In developing an effective SVR model, feature extraction is an important task for pre-processing the original input data. This paper proposes the application of principal component analysis (PCA) and kernel principal component analysis (KPCA) to the SVR method for feature extraction. Also, the genetic algorithm and simplex optimization method is invoked to determine the hyper-parameters of the SVR. Based on the realistic heart-torso model, the equivalent double-layer source method is applied to generate the data set for training and testing the SVR model. The experimental results show that the SVR method with feature extraction (PCA-SVR and KPCA-SVR) can perform better than that without the extract feature extraction (single SVR) in terms of the reconstruction of the TMPs on epi- and endocardial surfaces. Moreover, compared with the PCA-SVR, the KPCA-SVR features good approximation and generalization ability when reconstructing the TMPs.