## 2 Methods
### Clustering Algorithms  
Clustering techniques seek to automatically detect sets of points that are similar among themselves (thus forming a cluster) and different from the rest [34]. For instance, three common clustering techniques (K-means, SC and Gaussian Mixture) are shown within Figure 1 on six different two-dimensional datasets. Points with the same color have been assigned to the same cluster by the algorithm. Visually, SC seems to be the best able to find the correct groupings in all the datasets.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & **MEAN** & **SD** & **MIN** & **25\%** & **50\%** & **75\%** & **MAX** & **MISSING** \\ \hline Age (years) & 44.7 & 14.4 & 18.0 & 33.0 & 45.0 & 53.5 & 83.0 & 0.5\% \\ Headache & & & & & & & & \\ frequency & 16.8 & 9.45 & 1.0 & 8.0 & 16.0 & 28.0 & 30.0 & 2.4\% \\ (days/month) & & & & & & & & \\ Headache & & & & & & & & \\ duration & 7.4 & 4.35 & 0.5 & 3.5 & 6.85 & 12.0 & 24.0 & 7.7\% \\ (hours/attack) & & & & & & & & \\ Headache & & & & & & & & \\ intensity (nps & 6.1 & 2.65 & 0.0 & 5.0 & 6.0 & 7.6 & 31.0 & 0.0\% \\ 0-10) & & & & & & & & \\ Years with & & & & & & & & \\ headache & 10.3 & 11.25 & 0.0 & 2.0 & 5.5 & 15.0 & 60.0 & 3.85\% \\ HADS-A (0–21) & 9.9 & 4.7 & 0.0 & 6.0 & 10.0 & 14.0 & 19.0 & 18.75\% \\ HADS-D (0–21) & 7.9 & 4.45 & 1.0 & 4.0 & 7.0 & 11.0 & 20.0 & 18.75\% \\ HDI-E (0–52) & 19.1 & 13.2 & 0.0 & 8.0 & 16.0 & 26.0 & 52.0 & 18.75\% \\ HDI-P (0–48) & 22.8 & 12.3 & 0.0 & 14.0 & 22.0 & 32.0 & 52.0 & 18.75\% \\ PPT temporalis & & & & & & & & \\ (kpa) & 213.3 & 94.5 & 0.0 & 140.9 & 201.75 & 267.0 & 537.0 & 0.0\% \\ PPT cervical spine & & & & & & & & \\ (kpa) & 227.9 & 136.6 & 0.0 & 139.25 & 193.5 & 273.75 & 784.0 & 0.0\% \\ PPT second & & & & & & & & \\ metacarpal (kpa) & 258.7 & 105.9 & 0.0 & 179.9 & 253.0 & 320.0 & 629.5 & 0.0\% \\ PPT tibialis & & & & & & & & \\ anterior (kpa) & 423.65 & 211.3 & 0.0 & 296.9 & 381.75 & 512.6 & 1233.0 & 0.0\% \\ Pain-evoked DPT & & & & & & & & \\ (nps, 0–10) & 2.95 & 1.7 & 0.5 & 1.5 & 2.5 & 4.0 & 8.5 & 3.85\% \\ DPT (grammes) & 1170.4 & 756.8 & 450.0 & 600.0 & 850.0 & 1450.0 & 4325.0 & 3.85\% \\ Active TrPs & 4.6 & 3.0 & 0.0 & 2.0 & 5.0 & 7.0 & 11.0 & 1.4\% \\ Latent TrPs & 1.5 & 2.3 & 0.0 & 0.0 & 0.0 & 2.0 & 11.0 & 1.4\% \\ Sleep quality & & & & & & & & \\ (0–21) & 8.0 & 4.4 & 0.0 & 4.0 & 8.0 & 11.0 & 20.0 & 10.1\% \\ Vitality (0–100) & 48.55 & 22.3 & 0.0 & 30.0 & 50.0 & 65.0 & 100.0 & 1.0\% \\ Social function & 66.3 & 25.4 & 0.0 & 50.0 & 63.0 & 88.0 & 100.0 & 1.0\% \\ (0–100) & & & & & & & & & \\ Physical function & & & & & & & & \\ (0–100) & & 78.9 & 24.2 & 0.0 & 70.0 & 85.0 & 100.0 & 100.0 & 1.0\% \\ Bodily pain & & & & & & & & & \\ (0–100) & 50.6 & 23.3 & 0.0 & 32.0 & 51.0 & 62.0 & 100.0 & 1.0\% \\ Emotional role & & & & & & & & \\ (0–100) & & & & & & & & & \\ Physical role & & & & & & & & & \\ (0–100) & & & & & & & & & \\ General health & & & & & & & & & \\ (0–100) & & & & & & & & \\ Mental health & & & & & & & & & \\ (0–100) & & & & & & & & \\ \end{tabular}
\end{table}
Table 1: Summary statistics for the dataset (\(n=208\)).  
In the above-mentioned example, it is possible to visually assess the results of each algorithm, since the data is two-dimensional, and the clusters are clearly separated. However, for general N-dimensional problems (as is our sample of TTH patients), it is extremely difficult to evaluate the performances. Even if several metrics exist for that matter, such as the Silhouette Score or the Davies Bouldin Score [35], for our particular problem their values were similar among the algorithms and inconsistent among metrics (e.g., an algorithm deemed good by one metric would be bad by others). Hence, the decision to use SC over competing techniques was qualitative, based on its reported advantages and its perceived improved performance on our data.