Table 1.
Sample size, including the total number of N, S, V, F beats in ECG databases.
Fig 1.
Concept diagram of the two-stage beat classifier.
Fig 2.
General view of an example CT model.
CT has a total number of 73 nodes, 36 branches, 20 decision nodes, including 31 variables (identification numbers are assigned as x114, x154, x121, etc. counting the input vector of 210 features). The classification process starts at the root of the tree. An incoming beat travels down the branches of the tree depending on the result of the test on a feature. The procedure ends when the beat arrives at a leaf ‘1’ (SVB-class) or ‘0’ (VB-class). The tree is backwards pruned to level 10, and the pruned nodes and branches are shown with dotted lines. The subsequently pruned groups of nodes and branches are highlighted in common areas, starting from pruning level PL = 1, 2, …10.
Fig 3.
Block-diagram of the training and test-validation of the two-stage beat classifier.
It shows the performance evaluation of Stage 1, the training process of Stage 2 and the performance evaluation of the combined classifier (Stage 1+Stage 2).
Table 2.
Classification performance of Stage 1.
Fig 4.
Training process of the stepwise cluster analysis: influence of the number of features entered in the model.
The trend of Se, PPV, Mean(Se,PPV) is reported for 3, 6, 9 clusters. The optimal iteration step is defined for 7 features (3 clusters, ‘*’ mark), 6 features (6 clusters, ‘□’ mark) and 30 features (9 clusters, ‘○’ mark).
Fig 5.
Training process of the stepwise cluster analysis: influence of the number of clusters.
The values of Se, PPV, Mean(Se,PPV) are reported at the optimal iteration step (3, 6, 9 clusters are assigned with the same marks as in Fig 4). The best performing solution is defined for 9 clusters (Step 30). The continuous performance graphs are depicted by spline interpolation between the solutions at integer number of clusters.
Fig 6.
Training process of stepwise fuzzy analysis: influence of the number of features entered in the model on the trend of Se, PPV, Mean(Se,PPV).
The optimal iteration step is defined for 72 features at maximal Se during a plateau of Mean(Se,PPV)–see (‘○’ mark).
Fig 7.
Training process of SDA: influence of the number of features entered in the model.
The trend of Se, PPV, Mean(Se,PPV) is reported for different settings of the prior probabilities of SVB vs. VB-class: 50%/50% and 70/30%. The optimal iteration step is defined for 134 features (50%/50%, ‘○’ mark) and 142 features (30%/70%, ‘*’ mark).
Fig 8.
Training process of SDA: influence of the prior probability of SVB vs. VB-class.
The values of Se, PPV, MeanSePPV are reported at the optimal iteration step (50%/50% and 30%/70% are highlighted by the same marks as in Fig 7). The best performing solution is defined for prior probability of 30%/70% (Step 142).
Fig 9.
It shows the trend of performance: Se, PPV, Mean(Se,PPV) in respect of:—left graph: different prior probabilities of SVB vs. VB-class. The optimal setting is defined for equal prior probabilities 50%/50% (‘o’ mark at maximal Se over the Mean(Se,PPV) plateau).—right graph: the number of final decision nodes after pruning of the tree. The solutions with 30, 72, 142 nodes are highlighted (Mean(Se,PPV) = 95.3%, 96.8%, 98.5%; Se = 96.9%, 97.4%, 99%) as they correspond to the number of features in the best performing Cluster, Fuzzy, LDA models, respectively. The maximal CT performance at the final splitting step is also marked–Mean(Se,PPV) = 99.4%, Se = 99.7%.
Fig 10.
Complexity of the CT model evaluated in Fig 9 (right graph).
It shows the relationship between the number of the decision nodes vs. (i) the total number of nodes, (ii) the number of features included in the model, (iii) the error cost function, all marked for the highlighted solutions with 30, 72, 142 and 221 decision nodes.
Table 3.
Test performance of the combined beat classifier (Stage 1 + Stage 2) on MIT-BIH database.
Different Stage 2 classification methods are compared–The maximal performance of stepwise Cluster (step 30), Fuzzy (step 72), LDA (step 142) models with optimal number of steps vs. CT models with an equivalent number of final nodes. The maximal accuracy of the CT final solution (221 nodes) is also reported. Sp is calculated for SVB-class; Se, PPV are calculated for VB-class, as well as only for V-beats (part of VB-class), the latter performance being usually reported in other published heartbeat classifiers.
Table 4.
Statistical distribution of the basic features for SVB and VB-class evaluated for the beats in the training dataset that are supplied to the input of Stage 2.
The discrete features (F1-F5) are reported as frequency of observation; the continuous features (F6-F20) are represented as Mean±Std. The top-10 ranked second-order feature interactions selected by Cluster, Fuzzy, LDA, CT models are denoted in the row of each involved feature, specifying the index of the coupling feature in the interaction. If one feature is involved in several interactions, then the order of their selection in the model is used to list the respective coupling features.
Table 5.
Performance of the combined beat classifier vs. published studies, using the same linear-programming based classification methods as those implemented in Stage 2.
The values of Sp, Se, PPV are shown as reported by the authors, replaced by ‘-‘ mark when not published.