## 4 Experiments
### Experiments about Influencing Factors  
#### 4.2.1 Experiments Description  
We have an appropriate data selection to facilitate cartographic analysis, for which the number of the classes \(c_{T}\) should be \(5\leq c_{T}\leq 10\), and the length of data time-steps \(l_{T}\) should be \(400\leq l_{T}\leq 600\). The assumption is to bring the fundamental setup of the experiments into this subsection, and ensure fairness among methods.  
According to the criterion above, we use the dataset \"OSU Leaf\" to demonstrate the effectiveness of our approach. This shape-converted time series dataset is generated by radial scanning of the shape profile to convert the image into a one-dimension series. The dataset contains six classes, corresponding to six kinds of leaves with different shapes. Among them, the similarity between the first, second, third, and forth classes is high, and the similarity between the fifth, sixth classes is high [48].  
The experiments follow the principle of controlling variables. We adjust several circumstances: the signal to noise ratio (SNR), truncated length, data missing, and overlapping. We train different  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Dataset**} & \multicolumn{2}{c}{**Distance-Based**} & \multicolumn{2}{c}{**Feature-Based**} & \multicolumn{4}{c}{**ANN-Based**} \\ \cline{2-9}  & **1 NN-ED** & **1 NN-DTW** & **Shapelets** & **Features-RF** & **FNNs** & **RNNs** & **LSTM** & **BICORN-RNNs** \\ \hline
50 Words & 0.369(3) & 0.310(1) & 0.489(6) & 0.333(2) & 0.677(8) & 0.641(7) & 0.425(5) & 0.408(4) \\ ChlorineCon & 0.352(7) & 0.350(6) & 0.417(8) & 0.272(5) & 0.209(3) & 0.174(2) & 0.213(4) & 0.165(1) \\ ECG & 0.232(8) & 0.203(7) & 0.004(1) & 0.158(5) & 0.160(6) & 0.146(4) & 0.120(3) & 0.097(2) \\ Fish & 0.217(6) & 0.177(3) & 0.197(4) & 0.157(2) & 0.302(8) & 0.253(7) & 0.208(5) & 0.154(1) \\ Motefrain & 0.121(4) & 0.165(5) & 0.217(8) & 0.103(2) & 0.194(7) & 0.188(6) & 0.101(1) & 0.114(3) \\ OliveOil & 0.133(3) & 0.167(5) & 0.213(7) & 0.093(1) & 0.302(8) & 0.150(4) & 0.211(6) & 0.102(2) \\ Lightning7 & 0.425(6) & 0.274(1) & 0.403(4) & 0.295(2) & 0.552(8) & 0.545(7) & 0.386(3) & 0.412(5) \\ SwedishLeaf & 0.213(5) & 0.208(4) & 0.269(8) & 0.088(2) & 0.259(7) & 0.248(6) & 0.103(3) & 0.087(1) \\ Symbols & 0.100(7) & 0.050(3) & 0.068(4) & 0.138(8) & 0.091(6) & 0.083(5) & 0.042(2) & 0.023(1) \\ SyntheticControl & 0.120(6) & 0.007(1) & 0.081(4) & 0.017(2) & 0.139(7) & 0.097(5) & 0.156(8) & 0.024(3) \\ Best & 0 & 3 & 1 & 1 & 0 & 0 & 1 & 4 \\ Better-3 & 2 & 5 & 1 & 7 & 1 & 1 & 5 & 8 \\ Mean-ranking & 5.5 & 3.6 & 5.4 & 3.1 & 6.8 & 5.3 & 4.0 & 2.3 \\ \hline \hline \end{tabular}  
* 1 NN-ED: 1-nearest neighbor with Euclidean distance; 1 NN-DTW: 1-nearest neighbor with dynamic time warping; RF: random forests based on features; ANN: artificial neural network; FNNs: feedforward neural networks; RNNs: recurrent neural networks; LSTM: long-short time memory.  
\end{table}
Table 2: Classification error and performance ranking. The values in parentheses indicate the performance ranks of the different methods in three categories, and the optimal result of each dataset is represented as a bold number.  
Figure 8: Critical difference diagram over mean ranks of 8 methods belonging to 3 categories. Each label corresponds to the mean ranking of each classifier; the smaller the value, the better performance of the method. The length of bold lines indicates the critical difference with a confidence level of 0.05, which means that a group of classifiers with a bold line shows no significant difference. The critical difference is 1.25. Our classifier was the most optimal in all eight methods.  
RNNs-based classifiers with the same noise level; some of the basic experimental parameters settings are shown in Table 3.