# Investigating Feature Selection and Random Forests for Inter-Patient Heartbeat Classification
## 4 Discussion
Table 5 shows a comparison between the results obtained with the test set DS2 in this work and some of the approaches with the best heartbeat classification performances following the AAMI guidelines and the inter-patient paradigm reported in the literature. It can be observed that the overall accuracy reported in the present study is one of the highest ever obtained with the same evaluation methodology (\(Acc=96.14\%\)), almost the same performance reported by [PERSON] et al. (2015) (\(Acc=96.15\%\)), which is the highest in the literature to the best of our knowledge. Interestingly, though [PERSON] et al. propose the use of a different set of features, basically by introducing the use of a Gaussian mixture model (GMM) based on the Expectation Maximization (EM) algorithm, they propose a classification method very similar to RF called Bagging Trees (BT), which is also based on an ensemble of decision trees. RF and BT basically differ in the way the problem of high variance and instability of single decision trees is approached. While BT improves variance by averaging/majority selection of outcome from multiple fully grown trees on variants of training set, RF does the same by random selection of feature-subset for split at each node. Since the RF approach produces a lower correlation between trees, it can potentially produce better results as observed by some studies ([PERSON] et al., 2016). The results reported by [PERSON] et al. were obtained with an ensemble of 100 trees, whereas the results presented here were obtained with an ensemble of only 40 trees. \begin{table}
\begin{tabular}{l l l l l l l l l} \hline \hline
**Work** & **Classifier** & **Type of Features** & **Number of Features** & **Number of Features** & **\(F_{1}\) of Class** & **\(F_{1}\) of Class** & **\(F_{1}\) of Class** & _Acc_ \\  & & & **Used** & **NB** & **SVEB** & **VEB** & \\ \hline \multirow{2}{*}{[PERSON] and [PERSON] (2014)} & LD & R–R-intervals, WT, and time domain morphology & 8 & 96.48\% & 17.16\% & 83.89\% & 93\% \\  & & & R–R-intervals, WT, and time domain morphology & & & & & \\ \hline \multirow{2}{*}{[PERSON] et al. (2016)} & Ensemble of SVM + Threshold & R–R-intervals, Random projections & 101 & 97.59\% & 57.68\% & 92.37\% & 93.8\% \\  & & & R-R-intervals, HOS, GMM & & & & & \\ \hline \multirow{2}{*}{[PERSON] et al. (2017)} & SVM & R–R-intervals, DCT Random projections & 33 & 96.88\% & 33.37\% & 77.29\% & 93.1\% \\ \hline \multirow{2}{*}{[PERSON] et al. (2016)} & \multirow{2}{*}{[PERSON]} & HOS & 4 & (65.6\%) & (0.4\%) & (84.7\%) & 94.0\% \\  & & & & * & * & * & \\ \hline \multirow{2}{*}{[PERSON] et al. (2017)} & Ensemble of SVM & R–R-intervals, HOS, WT, and time domain morphology & 45 & 97.04\% & 60.74\% & 94.29\% & 94.5\% \\ \cline{1-1}  & & & HOS, WT, and time domain morphology & & & & \\ \hline \multirow{2}{*}{**This work**} & **RF** & **R–R-intervals, HBF and time domain morphology** & **6** & **97.97\%** & **73.06\%** & **90.85\%** & **96.14\%** \\ \hline \hline \end{tabular} WT: wavelet transform, LD: linear discriminant, HOS: high order statistics, HBF: Hermite basis functions, GMM: gaussian mixture model, BDT: bootstrap aggregated decision trees, DCT: discrete cosine transform, SVM: support vector machine. * In ([PERSON] et al., 2016) +\(P\) values nor the confusion matrix are disclosed; therefore, the harmonic mean of the sensitivity and specificity is reported here instead of \(F_{1}\).  
\end{table} 
Table 5: Comparison of the best results obtained in this work with state-of-the-art approaches. Since the highest performance detecting SVEB was reported by [PERSON] et al. (2019), a possible route for improvement can be to include in our feature selection procedure the GMM-based features proposed by [PERSON] et al. However, given the limitations of the MIT-BIH Arrhythmia Database and the inter-patient protocol proposed by [PERSON] et al. (2018), the performance in the detection of SVEB of the proposed approach as well as many others should not be taken as definitive.