# Weighted \(z\)-Distance-Based Clustering and Its Application to Time-Series Data
## 4 Experimental Results
### Time-Series Datasets  
Next, we show the effectiveness of SCC-IW in clustering time series data. Ten benchmark time series datasets are taken from the UCR repository [70] for the experiments. The characteristics of these datasets are shown in Table 6. In addition to the previous methods, we also compare with TSKmeans [56] here. We wrote the code for TSKmeans in Matlab. Tables 7 and 8 show the Fscore, RI, and NMI obtained by different methods for each dataset. Again, each method performed 25 runs on a dataset and the averaged result is shown. From these two tables, we can see that (1) SCC-IW outperforms both SCC and SCC-I significantly, and (2) SCC-IW is no less effective th.an the other methods. Table 8 shows the averaged ranking of all the 10 time series datasets for each method. As can be seen, SCC-IW is the best in Fscore, RI, and NMI. However, SCC-IW runs slower than SCC and SCC-I, since weights are involved in SCC-IW and they have to be optimally updated in each training cycle. Comparisons of DBI, DI, and SI among different methods for each dataset are shown in Table 9. As can be seen from the table, SCC-I is better than other methods. SCC-I gets the lowest DBI for 8 out of 10 datasets, the highest DI for 5 out of 10 datasets, and the highest SI for 4 out of 10 datasets. The main reason that SCCIW outperforms all the other competing classifiers in Table 10 is the consideration of both weights and deviations in SCC-IW. Gmm, SCC and SCC-I do not use weights. K-means, DSKmeans, and FCM do not use deviations nor weights in the clustering process. TSKmeans considers weights, but deviations are not involved. Now we use the paired \(t\)-test [68] to test the real significant differences between SCC-IW and other methods. Table 11 shows the t-values based on the values of Fscore, RI, and DBI, respectively, at the 90% confidence level. Note that we have 10 datasets involved. So the degree of freedom is 9 and the corresponding threshold is 1.833. From the above table, we can see that all the t-values are greater than 1.833, except for DSKmeans and FCM with RI. Therefore, by statistical test we observe that SCC-IW shows significantly better performance than other methods. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Dataset** & **\#Instances** & **\#Features** & **\#Classes** \\ \hline SynControl & 600 & 60 & 6 \\ Coffee & 56 & 286 & 2 \\ Light7 & 143 & 319 & 7 \\ OSU\_Leaf & 442 & 427 & 6 \\ Sony\_Surface & 621 & 70 & 2 \\ Trace & 200 & 275 & 4 \\ CBF & 930 & 128 & 3 \\ ECGFiveDays & 884 & 136 & 2 \\ FaceFour & 350 & 112 & 4 \\ OliveOil & 60 & 570 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Characteristics of 10 time-series datasets. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**SCC-I vs** & **K-Means** & **DSKmeans** & **FCM** & **Gmm** & **DBSCAN** \\ \hline Fscore & 3.3559 & 2.5383 & 2.7673 & 2.7686 & 3.9622 \\ NMI & 2.6634 & 2.3637 & 2.4157 & 1.7677 & 2.2601 \\ DBI & 3.3703 & 3.6033 & 4.4584 & 3.3139 & 2.5186 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Pairwise comparisons by \(t\)-test for non-time-series datasets.