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Clustering is an unsupervised machine learning methodology widely used in several sciences to find groups of similar patterns in complex data. The results generated by clustering algorithms generally depend on user-defined input parameters such as the number of expected clusters, which can have a great impact on the homogeneity of the identified clusters. Clustering validity indices (CVIs) are an effective method for determining the optimal number of clusters that best fit the natural partition of a dataset. They do not require any underlying assumption nor a priori knowledge about the true dataset structure. Since 1965, many cluster validity indices have been proposed in the literature and used in several different applications. In this paper, the performance of 68 cluster validity indices was evaluated on 21 real-life research and simulated datasets. CVIs were compared on the same partition for each dataset, which was searched for by the k-means clustering algorithm. Multivariate chemometric methods were applied to disclose mutual relationships among the indices and to select those that are more effective in terms of accuracy and reliability.

The present research aims at expanding the literature on biologization (i.e., a form of dehumanization in which others are perceived as contagious entities) by providing the first empirical evidence of the link between this sociopsychological process and indirect aggression (i.e., behaviours intended to harm someone in a roundabout manner, such as excluding them from a group or society). We first identified the most dehumanized social groups in Italy. Then, by using cluster analysis, we demonstrated that biologized social groups (i.e., drug addicts, homeless people, prostitutes, and sick people) tend especially to be victims of indirect rather than direct aggression tendencies (i.e., intentions against individuals or groups to cause damage through face-to-face confrontation). Furthermore, we found that social groups associated with disease-related metaphors are more likely to be victims of indirect aggression than social groups perceived as animal-like (i.e., immigrants, prisoners, and Roma). These findings enrich our understanding of biological dehumanization and enhance the so far scarce literature on the topic.

AimPatients with heart failure experience multiple co-occurring symptoms that lower their quality of life and increase hospitalization and mortality rates. So far, no heart failure symptom cluster study recruited patients from community settings or focused on symptoms predicting most clinical outcomes. Considering physical and psychological symptoms together allows understanding how they burden patients in different combinations. Moreover, studies predicting symptom cluster membership using variables other than symptoms are lacking. We aimed to (a) cluster heart failure patients based on physical and psychological symptoms and (b) predict symptom cluster membership using sociodemographic/clinical variables.DesignSecondary analysis of MOTIVATE-HF trial, which recruited 510 heart failure patients from a hospital, an outpatient and a community setting in Italy.MethodsCluster analysis was performed based on the two scores of the Hospital Anxiety-Depression scale and two scores of the Heart-Failure Somatic Perception Scale predicting most clinical outcomes. ANOVA and chi-square test were used to compare patients' characteristics among clusters. For the predictive analysis, we split the data into a training set and a test set and trained three classification models on the former to predict patients' symptom cluster membership based on 11 clinical/sociodemographic variables. Permutation analysis investigated which variables best predicted cluster membership.ResultsFour clusters were identified based on the intensity and combination of psychological and physical symptoms: mixed distress (high psychological, low physical symptoms), high distress, low distress and moderate distress. Clinical and sociodemographic differences were found among clusters. NYHA-class (New York Heart Association) and sleep quality were the most important variables in predicting symptom cluster membership.ConclusionsThese results can support the development of tailored symptom management intervention