Pierpaolo D’ Urso

In this paper we extend the Exploratory Graph Analysis (EGA) framework by replacing the Pearson correlation matrix with a Nonparanormal (NPN) estimator derived from Spearman rank correlations, which recovers the latent Gaussian dependence under a broader model that accomodates for skewed and heavy-tailed marginals. We further enhance robustness and interpretability by combining bootstrap EGA with Non-Euclidean Fuzzy Relational Clustering on a dissimilarity matrix derived from consensus over output partitions, producing fuzzy rather than crisp assignments that capture overlaps and ambiguity. We apply the full pipeline to 37 indicators from the Varieties of Democracy (V-Dem) dataset covering 179 countries in 2024, coming from five different theoretical democracy indices. The recovered structure validates the theoretical indices while revealing some meaningful discrepancies.

In this paper, we propose a novel clustering method based on three-way distances. We define a fuzzy c -medoid algorithm based on the semi-perimeter three-way distance, which can be derived from any classical (two-way) distance. This algorithm minimizes an objective function defined as a linear combination of the three-way distances between the medoid of each cluster and call couples of members of the cluster, and an entropic regularization term. We test its effectiveness, applying it both to simulated data and data from the Italian census, showing how it outperforms the standard fuzzy c -medoids algorithm.

The methodological objective of the present study is to extend Rothman’s additive interaction framework from two factors to three or more factors considered simultaneously, while preserving its original causal interpretation and operational simplicity. we propose a generalized Synergy Index ( S _p ) that retains the additive logic of Rothman’s original formulation while extending it to an arbitrary number of dichotomous factors. For the analysis we used a database of a previous work in which the synergistic factor was calculated for each couples of two factors (alcohol, tobacco smoke and other risk factors) for age-related macular degeneration. The proposed three-factor S _p is sensitive to the underlying structure of the risk factors considered. When a strong susceptibility component such as family history is included, the combined exposure exhibits clear super-additive behavior ( S _p = 1.783). Conversely, when hypercholesterolemia replaces family history, the joint effect remains substantial but does not exceed additivity ( S _p = 0.756). The generalized multi-factor Synergy Index represents a valuable conceptual and analytical tool for investigating higher-order interactions. It is particularly well suited for the study of complex diseases, where multiple exposures co-occur and interact. It enables the identification of exposure constellations characterized by true superadditivity, with potential implications for etiological research, risk stratification, and targeted prevention strategies.

This paper proposes clustering methods for large-scale stationary time series using a fuzzy approach. Adopting partitioning around centroids (PAC) and partitioning around medoids (PAM), and focusing on distributional properties of individual series, we classify a large set of time series by transforming the series into probability density functions via nonparametric density estimation, such as the kernel estimation, and using a proper distance measure, such as the Hellinger distance, between density functions. We use simulations and two real applications to demonstrate the good performance and effectiveness of the proposed clustering methods in finite samples. The proposed methods are also applicable to the spectral density functions if one focuses on the serial dependence of individual series.

As an ordered extension of evidence theory, Random permutation set (RPS) theory has received increasing attention due to its advantage in dealing with order-structured uncertain information. However, a significant research gap remains in the current literature concerning the construction of RPS. Building on the interpretation of RPS as a layer-2 belief structure, this paper proposes a data-driven hierarchical method for generating RPS, called DDHRPS. Specifically, DDHRPS first generates BPA from statistical features of data on the layer-1 belief structure, and then refines them with propensity information derived from distance analysis between samples to single classes, ultimately forming RPS on the layer-2 belief structure. Moreover, a DDHRPS-based classification algorithm (DDHRPSCA) is presented. Experimental comparisons involving two kinds of classifiers, namely, two uncertainty-based classifiers and seven machine learning classifiers validate the effectiveness and superiority of DDHRPSCA in handling uncertain information in classification tasks.

Clustering categorical data presents unique challenges that traditional techniques do not adequately address. This paper proposes an extension of the fuzzy C-modes algorithm. By incorporating a noise cluster and integrating spatial contiguity relationships among units, the algorithm’s robustness is significantly enhanced. Performance evaluations using synthetic data demonstrate the efficacy of the proposed algorithm in handling both global and local outliers. Furthermore, the paper discusses the application of the algorithm to real-world data on sustainable urban mobility in the Italian provincial capitals during 2021, highlighting its practical relevance and potential impact in real-world scenarios.

This paper addresses the ambitious goal of merging two different approaches to group detection in complex domains: one based on fuzzy clustering and the other on community detection theory. To achieve this, two clustering algorithms are proposed: fuzzy C-medoids clustering with modularity spatial correction and fuzzy C-modes clustering with modularity spatial correction. The former is designed for quantitative data, while the latter is intended for qualitative data. The concept of fuzzy modularity is introduced into the standard objective function of fuzzy clustering algorithms as a spatial regularization term, whose contribution to the clustering criterion based on attributes is controlled by an exogenous parameter. An extensive simulation study is conducted to support the theoretical framework, complemented by two applications to real-world data related to the theme of sustainability. The first application involves data from the 2030 Agenda for Sustainable Development, while the second focuses on urban green spaces in Italian provincial capitals and metropolitan cities. Both the simulation results and the applications demonstrate the advantages of this new methodological proposal.