# Efficient Time-Series Clustering through Sparse Gaussian Modeling
## 5 Experimental Evaluation
### Dataset Level Assessment
Even though it allows for conclusions that are informative and easy to grasp, averaging ARI results across different datasets (and possibly across different parameter configurations) is inadequate for a comprehensive evaluation of the proposed framework for Sparse Time-Series Clustering. A particularly poor or particularly good performance in specific datasets for certain parameter configurations may significantly affect the average ARI, potentially leading to misleading conclusions (notice also the standard deviations in Table A2). A characteristic example is the TwoPatterns dataset (see the corresponding rows in Tables A1 and A2), where the standard \(k\)-means achieves an average ARI of 0.870, while the average ARI of our framework for different numbers of inducing points (where average is taken across all values of \(\alpha\)) ranges from 0.304 to 0.825 (see the corresponding row in Table A1 and the large standard deviations in the corresponding row of Table A2). \begin{table}
\begin{tabular}{c c c c c c c} \hline  & & \multicolumn{4}{c}{\((\alpha T/m)\)-DTW} \\ \hline
**Parameter \(\alpha\)** & **Baseline** & \(\mathbf{1\cdot log}\,T\) & \(\mathbf{2\cdot log}\,T\) & \(\mathbf{3\cdot log}\,T\) & \(\mathbf{4\cdot log}\,T\) & \(\mathbf{5\cdot log}\,T\) \\ \hline
**0** & 0.249 (2.524) & 0.173 (4.270) & 0.222 (3.683) & 0.217 (3.492) & 0.220 (3.762) & 0.225 (3.270) \\
**10\({}^{-4}\)** & 0.249 (2.587) & 0.175 (4.365) & 0.222 (3.746) & 0.217 (3.635) & 0.220 (3.635) & 0.226 (3.032) \\
**10\({}^{-3}\)** & 0.249 (2.746) & 0.172 (4.508) & 0.213 (3.841) & 0.214 (3.317) & 0.215 (3.444) & 0.224 (3.143) \\
**10\({}^{-2}\)** & 0.249 (2.762) & 0.162 (4.381) & 0.196 (4.127) & 0.210 (3.476) & 0.215 (3.492) & 0.228 (2.762) \\
**best** & 0.249 (3.254) & 0.193 (4.238) & 0.238 (3.810) & 0.238 (3.333) & 0.243 (3.333) & 0.252 (3.032) \\
**mean** & 0.249 (2.556) & 0.171 (4.413) & 0.213 (3.857) & 0.215 (3.556) & 0.217 (3.587) & 0.226 (3.032) \\ \hline \end{tabular}
\end{table} 
Table 3: Summarized ARI averages for different parameter configurations. The average relative order of the results achieved by each algorithm is reported in parentheses. ARI values for each dataset are reported in Table A1 (where \(\alpha=0\)) and in Table A2 (where we report average ARI over all different values of \(\alpha\in\{0,10^{-4},10^{-3},10^{-2}\}\)) in Appendix A. To provide a more detailed picture of the quality of clusterings produced by our framework for different datasets and how they compare against the clustering produced by the standard \(k\)-means, in Appendix A, we present in Table A1 the average ARI for each dataset for the baseline and our framework with \(m=\gamma\log_{2}T\) inducing points, for each value of \(\gamma\in\{1,2,3,4,5\}\) and \(\alpha=0\), where average ARI is taken across all 10 runs for both the standard \(k\)-means and our framework. In Table A2, we present the same information  
Figure 3: Spread diagrams with comparative ARI results of Algorithm 1 against Algorithm 3 with \((10^{-4}T/m)\)-DTW and \(m=\gamma\log_{2}T\) inducing points, for \(\gamma\in\{1,2,3,4,5\}\). The spread and the average loss of the sparse framework are reported in the caption and in the upper left corner. We observe a slight improvement in clustering quality as the number of inducing points increases. We observe a small average gain in (**f**), where we keep the best ARI, and a small average loss in (**g**), where we take the mean ARI in each dataset (both across all values of \(\gamma\in\{1,2,3,4,5\}\)). for all datasets along with the standard deviation computed across all 10 runs (for standard \(k\)-means) and all 10 runs and all different values of \(\alpha\in\{0,10^{-4},10^{-3},10^{-2}\}\). The information in Table 1 demonstrates the importance of careful (and possibly dependent on the parameters of the datasets) tuning.