# A Novel Approach for Cognitive Clustering of Parkinsonisms through Affinity Propagation
## 4 Discussion
In particular, we calculated the residuals of each MMSE subscale by applying a multiple linear regression with the method ordinary least squares. The application of cluster analysis on regression residuals was previously performed by [PERSON] et al. [16], which used the [PERSON]'s method for investigating the heterogeneity of early-onset Alzheimer's disease patients. However, it has been showed that the application of traditional clustering methods, such as \(K\)-means [25], \(K\)-median and Ward's [5], could not be suitable for every kind of data [8; 49]. More in detail, it has been suggested to privilege the use of AP algorithm in presence of sparse similarity matrix [28], as it could be occurred in the cluster analysis of regression residuals of MMSE subscales, which are discrete variables with a limited range of values (0-5). Another strength of the AP algorithm relies in the automatic detection of the cluster centers [28; 29], the exemplars, which are in our case actual participants. In particular, we found that: one healthy control participant was representative of Cluster #1, the group with almost intact cognitive profile; one PD patient relatively young and with high education level was the center of Cluster #2, the group with the most intact cognitive profile; one PD patient, elder and with low education level, was the exemplar of Cluster #3, the most cognitively impaired group, specifically in TO, OS, AC, Rec, SR, W, CE and D; one PSP patient, elder but with high education level, was the representative participant of Cluster #4, the ensemble with a moderate cognitive deficit. Such an automatic detection of cluster centers by the AP algorithm represents a valuable tool for the exploratory analysis of neuropsychological patterns when no a priori knowledge exists, and a full data-driven investigation is needed [8]. Moreover, the identification of actual participants as representatives of the clusters could provide to the neuropsychologists a more accurate understanding of the natural structure of the collected data. As further novel contribution, our work compared the findings of the cluster analysis by varying the preference value of the AP algorithm as the median and the minimum value of the similarity matrix. Interestingly, we corroborated the literature [8; 46] by finding that the use of the median dramatically overestimated the number of clusters, besides by obtaining poor performance as calculated with the Silhouette index [47; 50]. The present study had two main limitations. The first is related to the specification of the similarity matrix calculated as the negative squared Euclidean distance. Indeed, we did not provide any insight whether the use of different distance metrics could provide different findings. The second limitation of the present work is the absence of the tuning of the damping factor, which could have indeed provided, as in the case of the first limitation, different results. Further work needs to be done on a larger cohort of participants to assess whether our algorithm shows reliability and stability. Furthermore, future studies should include a more extensive battery of neuropsychological tests to confirm or not the heterogeneity of the cognitive profiles in PD and PSP patients. In conclusion, we proposed a novel approach of unsupervised learning based on the application of AP clustering algorithm on the regression residuals of MMSE subscale scores for the exploration of the patterns of cognitive impairment of Parkinson's disease and Progressive Supranuclear Palsy patients. Our findings revealed an intra- and inter-diagnostic heterogeneity never investigated before now among Parkinsonisms. The proposed unsupervised learning method could represent a new promising tool aimed at supporting the neuropsychologists in understanding the natural structure of MMSE performance in the neurodegenerative diseases. Conceptualization, A.S., M.G.V. and A.Q. ([PERSON]); formal analysis, A.S. and M.G.V. ; investigation, A.S., M.G.V. and A.Q. ([PERSON]); methodology, A.S. and M.G.V.