# Interval Feature Transformation for Time Series Classification Using Perceptually Important Points
## 4 Experimental Studies
### Results  
Our first objective is to establish that IFT does not reduce classification performance. For comparison purposes, we test the performance of four traditional classifiers on the transformed data constructed by the IFT method and test the performance of 1 NN-DTW on the raw data. Table 2 lists the accuracy results from the four classifiers on the interval feature transformed data. The win-lose-tie results of each IFT classifier compared to the 1 NN-DTW on raw data, and the average rank of each classifier is also calculated. As shown in Table 2, at least one IFT classifier out of four is better than 1 NN-DTW on the raw data in 11/22 data sets. For the transformed data, the random forest classifier is the most sensitive classifiers on average. There are several data sets where the interval feature transformation was detrimental to the accuracy of the classifier. For example, on the data set FaceFour, all the classifiers lose about 25% on accuracy. However, some motion data sets, image data sets and simulated data sets (Worms, ToeSegmentation1, BirdChicken, ShapeletSim) show good improvement with the IFT method implemented. In this step, we confirm that the IFT method can improve the classification performance over several different data sets and is less sensitive to the additive noise. The comparative experiment results are listed in Table 3. The average rank of each classifier is calculated. When the significance level is 0.05 and the degree of freedom is (5, 105), \(F_{F}=9.2269>F_{0.05}(5105)=2.301\). Therefore, at the significant level of 0.05, the six classifiers are significantly different. Then, according to Equation (14), \(CD=1.6076\) for \(\alpha=0.05\). As shown in Table 3, the IFT classifier achieves the best average rank, and best performance in six out of 22 problems. The average rank of IFT is very close to the TSF method, but the TSF has the best performance in more data sets. The critical difference diagram is shown in Figure 5, and it shows that there is an obvious difference between the IFT method and Symbolic Aggregate approXimation and Vector Space Model (SAXVSM) and LS and BOSS, the difference between the IFT method, TSF and 1 NN-DTW is found but not significant. The proposed method is applied to several real-world applications. The ECGFiveDays data set from PhysioNet.Org [39] is a long ECG time series recorded on two different days with the same patient; a copy of this dataset can also be found at [34]. The dataset contains 890 objects, with 23 objects as training data and 861 as test data. As shown in Figure 6, the time series from two different classes are very similar, at least globally. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \# & **1 NN-DTW** & **LS** & **BOSS** & **TSF** & **SAXVSM** & **IFT** \\ \hline
1 & 0.7500 & 0.9000 & 0.9500 & 0.9000 & 0.5000 & 0.9000 \\
2 & 0.9042 & 0.8079 & 0.8242 & 0.9958 & 0.6800 & 0.9035 \\  
An electrocardiogram (ECG) is a test that measures the electrical activity of the heartbeat. With each beat, an electrical impulse (or \"wave\") travels through the heart. This wave causes the muscle to squeeze and pump blood from the heart. A normal heartbeat on ECG will show the timing of the top and lower chambers. The right and left atria or upper chambers make the first wave called a \"P wave\", following a flat line when the electrical impulse goes to the bottom chambers. The right and left bottom chambers or ventricles make the next wave called a \"QRS complex.\" The QRS complex duration is measured from the beginning of the Q wave to the end of the S wave. A complete QRS complex consists of a Q-, R- and S-wave. The final wave or \"T wave\" represents electrical recovery or return to a resting state for the ventricles. A healthy person's electrocardiogram has a certain pattern. The experiment result of the feature extraction with our IFT method from the EEGFiveDays data set is shown in Figure 7. We extract 68 discriminative feature vectors from 14 intervals in each time series as the patterns of time series, as shown in Figure 7a.