# A Novel Approach for Cognitive Clustering of Parkinsonisms through Affinity Propagation
## 1 Introduction  
Cluster analysis is an unsupervised learning technique introduced by [PERSON] [1], which has an aim to partition objects into homogenous groups for detecting the natural structure as well as the underlying patterns of a dataset according to a measure of similarity, for example geometrical distance. Unlike supervised learning [2, 3], clustering is totally data-driven and clustering methods such as traditional hierarchical [4, 5] and non-hierarchical [6, 7] represent a valuable support to the neuopsychologists [8, 9, 10] for clustering patients and discovering different patterns of cognitive impairment or multiple cognitive profiles within diagnostic groups [11, 12, 13, 14, 15]. Moreover, cluster analysis resulted to be a powerful tool for finding the intra- and inter-diagnostic heterogeneity of psychological and cognitive performance of participants with bipolar disorder or depression syndrome [11, 12, 13, 14] or of patients with Mild Cognitive Impairment [15]. The clustering was also recently applied for exploring patterns of cognitive impairment in Alzheimer's disease (AD) patients [16], where different cognitive subtypes in the early onset AD subjects were found using the Ward's method [5] on the regression residuals of the cognitive scores. Together with the wide application of cluster analysis for the cognitive clustering of the AD [17], also the Parkinson's disease was largely investigated with this technique [18], focusing the attention both on the motor and non-motor symptoms [19, 20, 21, 22, 23, 24]. However, the vast majority of clustering approaches for understanding the natural structure of cognitive performance in the neurodegenerative diseases [17; 18] are traditional methods such as \(K\)-means [25], \(K\)-median and Ward's [5], which are less effective, or even inapplicable, on certain kind of cognitive data [8]. Moreover, a crucial issue of these clustering algorithms is the initial choice of the optimum number of clusters for the specific dataset [26; 27], which choice, in most applications, could not be based on a priori knowledge [8]. [PERSON] and [PERSON] [28] proposed in 2007 a clustering algorithm, called affinity propagation (AP), which does not explicitly require to provide the number of clusters, while it identifies an ensemble of representative samples in the dataset to serve as clusters centers. Once these special points, called exemplars, are found, the other data points are connected to the exemplar which has the maximum similarity value [29]. More in detail, the AP algorithm is based on passing messages between data points, where the value of the messages measures the current eligibility of a candidate point to serve as exemplar for another data point [28]. The AP algorithm showed efficiency in handling high dimensional problems [8; 28; 29; 30] and it was applied widely in the physical sciences, especially for the clustering of gene expression. Given the three main advantages, that is (i) the ability of handling different type of similarity measures, (ii) the automatic discovery of the number of clusters and (iii) the computational efficiency [8], the AP algorithm resulted to be the best candidate approach for exploring, for the first time here, the natural structure of cognitive deficits in Parkinsonisms patients. In the present work, Parkinson's disease and Progressive Supranuclear Palsy subjects, together with healthy control participants, were evaluated with the Mini Mental State Examination (MMSE) [23; 24; 25], which is the most widely used cognitive screening tool. In particular, we wanted to evaluate whether an intra- and inter-diagnostic heterogeneity exists in the altered cognitive functioning of Parkinsonisms and whether the eleven MMSE subscales could capture this possible heterogeneity.