# A Novel Approach for Cognitive Clustering of Parkinsonisms through Affinity Propagation
## 3 Results
### Cluster Analysis  
We first applied our proposed algorithm separately on the MMSE scores of the healthy controls group, PD patients and PSP patients for investigating the natural structure of the intra-diagnostic cognitive profiles and then on the whole cohort of CTRL, PD and PSP participants. The comparison of the performance--calculated with the Silhouette index--of each clustering experiment by varying the preference value was reported in Table 2.  
We found an overestimate of the number of clusters (8 clusters) and a poor Silhouette value (0.302) when the proposed algorithm was applied on the control group with the preference value equal to the median of the similarity matrix. In particular, the bigger cluster was comprised of 26 participants, three clusters were comprised of only 1 subject, two clusters were comprised of 3 subjects, one cluster comprised of 4 subjects and the last one was comprised of 5 subjects. On the contrary, the algorithm with the preference value equal to the minimum of the similarity matrix found only 1 cluster, thus comprising all the healthy control participants. The only exemplar's demographic values and eleven MMSE scores (as a vector: [TO, OS, Reg, AC, Rec, N, SR, P, W, CE, D]) were:  
* Cluster #1 CTRL: male, age 62, education 16, MMSE subscales = [5, 5, 3, 5, 3, 2, 1, 3, 1, 1, 1];  
Regarding the PD participants group, we found 7 clusters and a poor value of the Silhouette index (0.375) when the proposed algorithm was applied with the preference value equal to the median of the similarity matrix. In particular, the two biggest clusters were comprised of 13 and 11 PD participants, two clusters were comprised of 7 PD patients, one cluster was comprised of 6 PD patients, one cluster comprised of 3 PD patients and the last one was comprised of 2 PD patients. A significant improvement of the Silhouette index (0.675) and 2 clusters were found with the preference value equal to the minimum value of the similarity matrix. The exemplars' demographic values and eleven MMSE subscale scores (as a vector: [TO, OS, Reg, AC, Rec, N, SR, P, W, CE, D]) were:  
* Cluster #1 PD: male, age 43, education 13, MMSE subscales = [5, 5, 3, 4, 3, 2, 1, 3, 1, 1, 1];
* Cluster #2 PD: female, age 61, education 8, MMSE subscales = [5, 5, 3, 5, 3, 2, 1, 3, 1, 1, 1];  
The first cluster was comprised of 29 PD patients (13 females) with a mean age of 66.4 \(\pm\) 10.7, a mean education level of 9.14 \(\pm\) 4.98 and a total MMSE mean score of 22.3 \(\pm\) 5.09 (TO 4.14\(\pm\), OS 3.97 \(\pm\) 1.35, Reg 2.97 \(\pm\) 0.19, AC 2.07 \(\pm\) 1.71, Rec 1.62 \(\pm\) 1.12, N 2 \(\pm\) 0, SR 0.83 \(\pm\) 0.38, P 2.97 \(\pm\) 0.19, W 0.55 \(\pm\) 0.51, CE 0.72 \(\pm\) 0.45, D 0.52 \(\pm\) 0.51). The second cluster was comprised of 20 PD patients (9 females) with a mean age of 67.3 \(\pm\) 7.09, a mean education level of 9.45 \(\pm\) 4.50 and a total MMSE mean score of 28.4 \(\pm\) 1.79 (TO 50\(\pm\), OS 4.75 \(\pm\) 0.55, Reg 3 \(\pm\) 0, AC 4.70 \(\pm\) 0.73, Rec 2.45 \(\pm\) 0.83, N 2 \(\pm\) 0, SR 0.80 \(\pm\) 0.41, P 3 \(\pm\) 0, W 0.85 \(\pm\) 0.37, CE 1 \(\pm\) 0, D 0.85 \(\pm\) 0.37). See Figure 3 for the radar plots of the mean values of MMSE subscales of each of the two clusters of PD patients found. The \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{2}{c}{**Median Preference**} & \multicolumn{2}{c}{**Minimum Preference**} \\ \hline
**Group** & **\#Clusters** & **Silhouette Index** & **\#Clusters** & **Silhouette Index** \\ \hline CTRL & 8 & 0.302 & 1 & N.A. \\ PD & 7 & 0.375 & 2 & 0.675 \\ PSP & 6 & 0.387 & 2 & 0.677 \\ CTRL + PD + PSP & 16 & 0.237 & 4 & 0.601 \\ \hline \hline \end{tabular}  
* Abbreviation: N.A. = not applicable; CTRL = healthy control; PD = Parkinson’s disease patients; PSP = Progressive Supranuclear Palsy patients.  
\end{table} 
Table 2: Performance—evaluated with the Silhouette index—of the proposed algorithm by varying the preference value of the affinity propagation (AP) clustering.