# Weighted \(z\)-Distance-Based Clustering and Its Application to Time-Series Data
## 4 Experimental Results
### Non Time-Series Datasets  
To illustrate the effectiveness of SCC-I, fourteen benchmark non-time-series datasets are selected from the UCI repository [61] for the experiments. The characteristics of these datasets are shown in Table 1. For example, there are 569 instances in the Breast dataset. Each instance has 30 features or dimensions, and belongs to one of 2 classes. For each dataset, an instance belongs to one and only one class. We compare SCC-I with Kmeans [62], DSKmeans [59], Fuzzy C-means (FCM) [63], Gaussian mixture model (Gmm) [64], DBSCAN [65], and SCC [20]. The codes for K-means, DBSCAN, and FCM are adopted from Matlab [66], and the code for Gmm is adopted from [67]. We wrote the codes for DSKmeans, SCC, and SCC-I in Matlab. Table 2 shows comparisons of Fscore, RI, and NMI among different methods for each dataset. To have fair comparisons among different methods, the number of clusters are tuned to be identical to the number of classes for each dataset. For K-means, the number of clusters, \(k\), is set to be equal to the number of classes. For DSKmeans, the parameter \(\gamma\) is set to be a value between 0.01 and 5, and \(\eta\) is between 0.01 and 0.3. For SCC and SCC-I, \(\sigma_{0}\) and \(\rho\) are set to be values between 0.1 and 0.95. Also, each method performed 25 runs on a dataset and the averaged result is shown. For K-means and DSKmeans, each run started with a different set of initial seeds. For SCC and SCC-I, each run was given a different feeding order of the training instances. For FCM, the maximum number of iterations is set to be 50. For DBSCAN, \(\varepsilon\) is set to be a value between 0.1 and 3, while the minimum number of neighbors, _minpts_, required for a core point, is set to be between 1 and 10. In addition to the values of the measures, performance ranking is also indicated at the right side of '/' for each dataset in Table 2. For example, consider the Breast dataset. The Fscore values are 0.9270, 0.8710, 0.9274, 0.7470, 0.7983, and 0.9264 by K-means, DSKmeans, FCM, Gmm, DBSCAN, SCC, and SCC-I, respectively. FCM has the best value, 0.9274, so it ranks as the first place, indicated by 1 at the right side of '/'; K-means has the second best value, 0.9270, so it ranks as the second place, indicated by 2 at the right side of '/'; etc. From this table, we can see that (1) SCC-I outperforms SCC significantly, and (2) SCC-I is no less effective than the other methods. Table 3 shows the averaged ranking of all the 14 datasets for each method. As can be seen, SCC-I is the best in Fscore and NMI, indicated by boldfaced numbers, and is the second best in RI. \begin{table}
\begin{tabular}{l c c c} \hline \hline
**Dataset** & **\#Instances** & **\#Features** & **\#Classes** \\ \hline Breast & 569 & 30 & 2 \\ Ecoli & 336 & 7 & 8 \\ Ionophere & 351 & 33 & 2 \\ Breast\_Tissue & 106 & 9 & 6 \\ SPECT Heart & 267 & 44 & 2 \\ Seeds & 210 & 7 & 3 \\ Sonar & 208 & 60 & 2 \\ User\_Knowledge & 403 & 5 & 4 \\ Musk & 476 & 166 & 2 \\ Vehicle & 846 & 18 & 4 \\ Glass & 214 & 9 & 6 \\ Heart & 270 & 12 & 2 \\ Iris & 150 & 4 & 3 \\ Yeast & 1484 & 8 & 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Characteristics of 14 non-time-series datasets.