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

Abstract

Non-invasively reconstructing the cardiac transmembrane potentials (TMPs) from body surface potentials can act as a regression problem. The support vector regression (SVR) method is often used to solve the regression problem, however the computational complexity of the SVR training algorithm is usually intensive. In this paper, another learning algorithm, termed as extreme learning machine (ELM), is proposed to reconstruct the cardiac transmembrane potentials. Moreover, ELM can be extended to single-hidden layer feed forward neural networks with kernel matrix (kernelized ELM), which can achieve a good generalization performance at a fast learning speed. Based on the realistic heart-torso models, a normal and two abnormal ventricular activation cases are applied for training and testing the regression model. The experimental results show that the ELM method can perform a better regression ability than the single SVR method in terms of the TMPs reconstruction accuracy and reconstruction speed. Moreover, compared with the ELM method, the kernelized ELM method features a good approximation and generalization ability when reconstructing the TMPs.

Contribuciones de las técnicas machine learning a la cardiología. Predicción de reestenosis tras implante de stent coronario

“…]: print('PRESTO 1: ', mean_confidence_interval_corrected(rocs_presto1)) print('PRESTO 2: ', mean_confidence_interval_corrected(rocs_presto2)) print('TLR: ', mean_confidence_interval_corrected(rocs_TLR)) print('PRESTO 1 acc: ', mean_confidence_interval_corrected(rocs_presto 1_acc)) print('PRESTO 2 acc: ', mean_confidence_interval_corrected(rocs_presto 2_acc)) print('TLR acc: ', mean_confidence_interval_corrected(rocs_TLR_acc)) presto1_conf = mean_confidence_interval_corrected(rocs_presto1) presto2_conf = mean_confidence_interval_corrected(rocs_presto2) TLR_conf = mean_confidence_interval_corrected(rocs_TLR) presto1_acc_conf = mean_confidence_interval_corrected(rocs_presto1_acc ) presto2_acc_conf = mean_confidence_interval_corrected(rocs_presto2_acc ) TLR_acc_conf = mean_confidence_interval_corrected(rocs_TLR_acc) PRESTO 1: (0.5672395833333334, 0.42978712900171223, 0.704692037664954 5) PRESTO 2: (0.5802083333333333, 0.4371469845278454, 0.7232696821388213 ) TLR: (0.6174131944444444, 0.49840496303296705, 0.7364214258559217) PRESTO 1 acc: (0.5696354166666667, 0.42548465436756233, 0.71378617896 57711) PRESTO 2 acc: (0.5610069444444444, 0.4138755754414542, 0.708138313447 4346) TLR acc: (0.6144444444444445, 0.49644129927028835, 0.7324475896186006 )In[126]: print('LR: ', mean_confidence_interval(rocs_lr)) print('RF: ', mean_confidence_interval(rocs_rf)) print('ert: ', mean_confidence_interval(rocs_ert)) print('SVC: ', mean_confidence_interval(rocs_svc)) print('GB: ', mean_confidence_interval(rocs_gb)) print('LR_noreg: ', mean_confidence_interval(rocs_lr_noreg)) lr_conf = mean_confidence_interval(rocs_lr) rf_conf = mean_confidence_interval(rocs_rf) ert_conf = mean_confidence_interval(rocs_ert) svc_conf = mean_confidence_interval(rocs_svc) gb_conf = mean_confidence_interval(rocs_gb) lr_noreg_conf = mean_confidence_interval(rocs_lr_noreg) LR: (0.7417534722222223, 0.7176171797358428, 0.7658897647086018) RF: (0.7518402777777777, 0.7259682375983111, 0.7777123179572444) ert: (0.7723090277777778, 0.7480912723541336, 0.7965267832014219) SVC: (0.5312152777777777, 0.49851098206738326, 0.5639195734881721) GB: (0.6783680555555555, 0.6473385050355935, 0.7093976060755174) LR_noreg: (0.6988194444444444, 0.6734754140167117, 0.7241634748721771 )In[127]: print('LR: ', mean_confidence_interval_corrected(rocs_lr)) print('RF: ', mean_confidence_interval_corrected(rocs_rf)) print('ert: ', mean_confidence_interval_corrected(rocs_ert)) print('SVC: ', mean_confidence_interval_corrected(rocs_svc)) print('GB: ', mean_confidence_interval_corrected(rocs_gb)) print('LR_noreg: ', mean_confidence_interval_corrected(rocs_lr_noreg))lr_conf = mean_confidence_interval_corrected(rocs_lr) rf_conf = mean_confidence_interval_corrected(rocs_rf) ert_conf = mean_confidence_interval_corrected(rocs_ert) svc_conf = mean_confidence_interval_corrected(rocs_svc) gb_conf = mean_confidence_interval_corrected(rocs_gb) lr_noreg_conf = mean_confidence_interval_corrected(rocs_lr_noreg) LR: (0.7417534722222223, 0.6254420279909381, 0.8580649164535066) RF: (0.7518402777777777, 0.6271643624448107, 0.8765161931107448) ert: (0.7723090277777778, 0.6556050182057345, 0.8890130373498211) SVC: (0.5312152777777777, 0.37361510497619416, 0.6888154505793611) GB: (0.6783680555555555, 0.5288383862055075, 0.8278977249056034) LR_noreg: (0.6988194444444444, 0.5766879785884229, 0.820950910300466) In [128]: # t-test corregido, devuelve media de la diferencia entre las dos mues tras y p-valor t_test_corregido(rocs_ert, rocs_svc) Out[128]: (0.24109375, 0.0028584540146056993) In [129]: t_test_corregido(rocs_ert, rocs_TLR) Out[129]: (0.15489583333333334, 0.022011844785024097) In [130]: ## CURVAS #Curvas roc. Comparación de modelosplt.figure(figsize=(15,10)) plt.xlim([0.0, 1.0]) plt.ylim([0.0, 1.0]) model_names = ['ert', 'rf', 'lr', 'lr_noreg', 'gb', 'svc'] colors = ['cornflowerblue', 'limegreen', 'indianred', 'pink', 'black', 'orange'] model_zoo =...…”