# Similarity Measurement and Classification of Temporal Data Based on Double Mean Representation
## 4 Experimental Validation
### Experimental Results and Analysis  
We compared the classification accuracy and error rate of SAX-DM with those of ED, SAX, SAX-TD, and SAX-BD. The experimental results show that in most of the datasets, SAX-DM achieved comparable accuracy to SAX-TD and SAX-BD, with the additional advantage of lower classification error rates. Figure 5 presents the comparison results between the SAX-DM and ED methods. Each point in the graph represents a dataset, where the x-axis represents the classification accuracy using the ED method, and the y-axis represents the classification accuracy using the SAX-DM method. Intuitively, the more points above the diagonal line, the more datasets in which the SAX-DM achieved higher accuracy compared to the ED method. After statistical analysis, it was found that SAX-DM had a slightly lower classification accuracy than ED in 67% of the datasets. This is because the Euclidean distance, which directly measures similarity on the original time series data without compression and dimension reduction, achieves high accuracy but puts a significant burden on computer memory and has lower computational efficiency. It is typically used as a comparative method to assess the viability of an approach and is not directly used for data mining tasks. Subsequent experiments on the data compression ratio did not require a comparison with the ED method. Although the SAX-DM may perform worse or on par with the Euclidean distance method in most datasets, the accuracy gap is within 0.1 for 80% of the datasets, indicating that it achieves effective data dimension reduction while maintaining a reasonably close accuracy level compared to the Euclidean distance method. The comparison results between the SAX-DM and SAX methods in terms of classification accuracy are shown in Figure 6. The x-axis represents the classification accuracy using the SAX method, while the y-axis represents the classification accuracy using the SAX-DM method. The results represent the average classification accuracy for both representation methods under all \(\alpha\) and w parameters, reflecting the overall classification performance. The results are evident, as using the SAX-DM method for approximate representation and similarity measurement in classification tasks yielded a higher accuracy in 98% of the datasets. \begin{table}
\begin{tabular}{c c} \hline \hline
**Method** & **Parameter** \\ \hline ED & null \\ SAX-DM & \(w\in[5,20]\)\(\alpha\in[3,16]\) \\ SAX & \(w\in[5,20]\)\(\alpha\in[3,16]\) \\ SAX-TD & \(w\in[5,20]\)\(\alpha\in[3,16]\) \\ SAX-BD & \(w\in[5,20]\)\(\alpha\in[3,16]\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Approximate expression method parameters. Compared to SAX, the SAX-DM further incorporates trend distance expression, allowing for better representation of the trend characteristics in time series data. However, this comes at the cost of sacrificing some data compression and dimension reduction rates. In practical usage, different methods can be chosen based on the application's requirements for similarity accuracy in queries. Figure 7 presents the comparison results between the SAX-DM and SAX-TD representation methods. From the figure, it can be observed that the two methods achieved similar accuracy in the classification task. When considering the reasons behind this, SAX-TD introduces a representation approach for capturing the trend by measuring the distance between the left and right endpoint values and the overall mean of the time series data. It combines this trend information with the mean value for symbolization. This approach is almost identical to the feature extraction methodology used in this paper, but it has certain limitations in practical applications. As the right endpoint value of one segment in time series data can be used as the left endpoint value of the next segment, when the number of segments is large, it is possible to approximate two symbols representing one segment. Figure 5: Comparison results of SAX-DM and ED. Figure 6: Comparison results of SAX-DM and SAX.