# Hexadecimal Aggregate Approximation Representation and Classification of Time Series Data
## 4 Experimental Evaluation
### Experimental Results and Analysis  
Four methods, the SAX, SAX_TD, SAX-BD and ED, were the baseline methods, and the classification accuracy of each representation method was calculated based on the 1-NN. Table 4 shows the experimental results. The column ID is the identifier of the data set in Table 3. The columns, ED, PAX, HAX, SAX, SAX-TD and SAX-BD, are the representation methods' names. The values in each column of the methods are the classification accuracy values. Figure 8 shows the results in a plot. Our previous work [62] presented the comparison results among SAX, ESAX, SAX-TD and SAX-BD. Here we will focus on the comparison of HAX, SAX, PAX, SAX-BD and ED. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**ID** & **ED** & **SAX** & **SAX-TD** & **SAX-BD** & **PAX** & **HAX** \\ \hline  
\hline \hline \end{tabular}
\end{table} 
Table 4: Classification accuracy on UCRArchive2018. The results in Table 4 show that the classification accuracy of the PAX is significantly higher than those of the HAX and SAX methods, and the HAX has some advantages over the SAX classification accuracy. Figure 9 makes the comparison between the HAX and SAX methods more obvious. The X-axis value is the accuracy of the SAX, the Y-axis value is the accuracy of the HAX and the scattered points are mostly in the upper triangle (71 points in the upper triangle and 43 points in the lower triangle). This shows that the accuracy of the HAX is larger than the SAX. Figure 10 makes the comparison between the PAX and SAX methods more obvious. Almost all the scattered points in Figure 10 are in the upper triangle, which shows that the accuracy of the PAX is significantly larger than the SAX. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**ID** & **ED** & **SAX** & **SAX-TD** & **SAX-BD** & **PAX** & **HAX** \\ \hline
101 & 0.76 & 0.49 & 0.66 & 0.86 & 0.76 & 0.59 \\
102 & 0.75 & 0.59 & 0.77 & 0.73 & 0.70 & 0.65 \\
103 & 0.91 & 0.78 & 0.88 & 0.83 & 0.91 & 0.51 \\
104 & 0.76 & 0.64 & 0.77 & 0.79 & 0.78 & 0.68 \\
105 & 0.95 & 0.81 & 0.92 & 0.88 & 0.92 & 0.72 \\
106 & 0.74 & 0.66 & 0.72 & 0.71 & 0.73 & 0.61 \\
107 & 0.66 & 0.58 & 0.65 & 0.65 & 0.67 & 0.51 \\
108 & 0.65 & 0.59 & 0.64 & 0.65 & 0.65 & 0.55 \\
109 & 1.00 & 0.98 & 0.99 & 0.99 & 0.99 & 0.98 \\
110 & 0.61 & 0.50 & 0.55 & 0.55 & 0.61 & 0.51 \\
111 & 0.62 & 0.51 & 0.59 & 0.61 & 0.63 & 0.47 \\
112 & 0.45 & 0.47 & 0.50 & 0.5 & 0.52 & 0.40 \\
113 & 0.61 & 0.59 & 0.60 & 0.61 & 0.62 & 0.54 \\
114 & 0.83 & 0.67 & 0.80 & 0.78 & 0.81 & 0.69 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: _Cont._  
Figure 8: Accuracy comparison plot for Table 4.  
The ED is still widely used in equal length time series measurements. In our work, we selected the ED and SAX methods as baselines. Figure 11 shows the accuracy comparison among the HAX, the ED and the SAX. The results show that ED still has higher accuracy when compared with the SAX and HAX methods. Figure 12 shows the accuracy comparison among the PAX, the ED and the SAX. It shows that the accuracy rates of the PAX and ED are very close. Figure 13 makes the comparison between the PAX and ED methods more obvious. About half of the scattered points in Figure 13 are in the upper triangle. Figure 14 makes the comparison between the PAX and SAX-BD methods more obvious. These figures show that the accuracy of PAX is lower than the ED and SAX-BD methods but very close to them. Figure 10: Accuracy comparison between PAX and SAX (111 points in the upper triangle and 3 points in the lower triangle). Figure 9: Accuracy comparison between HAX and SAX (71 points in the upper triangle and 43 points in the lower triangle). In terms of space cost, the HAX realizes the dimensionality reduction of high-dimensional time series by representing a time series as a set of hex strings, reducing the amount of information required for time series storage and making it more convenient to be used in various fields. For a time series with the same parameter \(w\), the length of the hex string is equal to that of the SAX string.