Riccardo Massari

Robust fuzzy regression analysis

In this paper we propose a robust fuzzy linear regression model based on the Least Median Squares-Weighted Least Squares (LMS-WLS) estimation procedure. The proposed model is general enough to deal with data contaminated by outliers due to measurement errors or extracted from highly skewed or heavy tailed distributions. We also define suitable goodness of fit indices useful to evaluate the performances of the proposed model. The effectiveness of our model in reducing the outliers influence is shown by using applicative examples, based both on simulated and real data, and by a simulation study.

Fuzzy clustering of human activity patterns

In the context of human activity pattern analysis, we adopt a fuzzy clustering around medoids approach to classify ordered sequences (paths). These sequences represent patterns of individual behavior in an actual or virtual space-time domain. A fuzzy approach is suitable for path data, since sequences of human activities are typically characterized by switching behaviors, which are likely to produce overlapping clusters. We adopt a partitioning around medoids strategy since in human activity patterns analysis it is useful to represent each cluster by means of an observed (not fictitious) prototype (medoid). To measure pairwise distances among all sequence pairs we make use of the Levenshtein distance, which allows for the comparison between sequences of different length and explicitly takes into account the sequential nature of the data. We also consider two robust versions of the fuzzy clustering algorithm based, respectively, on the noise cluster and on the trimming technique. Robust algorithms deal with noisy observations, which are likely to occur in this framework and could provide an improvement to the standard model. We show several applications on sequence data, regarding different research areas, like Web usage mining, travel behavior, tourists and shopping paths.

Bagged Clustering and its application to tourism market segmentation

Aim of the paper is to propose a segmentation technique based on the Bagged Clustering (BC) method. In the partitioning step of the BC method, B bootstrap samples with replacement are generated by drawing from the original sample. The fuzzy C-medoids Clustering (FCMdC) method is run on each bootstrap sample, obtaining (BxC) medoids and the membership degrees of each unit to the different clusters. The second step consists in running a hierarchical clustering algorithm on the (BxC) medoids. The best partition of the medoids is obtained investigating properly the dendrogram. Then each unit is assigned to each cluster based on the membership degrees observed in the partitioning step. The effectiveness of the suggested procedure has been shown analyzing a suggestive tourism segmentation problem. We analyze two sample of tourists, each one attending a different cultural attraction, enlightening differences among clusters in socio-economic characteristics and in the motivational reasons behind visit behavior.

Poverty and inequality in European regions

The European Union Statistics on Income and Living Conditions (EU-SILC) is the main source of information about poverty and economic inequality in the member states of the European Union. The sample sizes of its annual national surveys are sufficient for reliable estimation at the national level but not for inferences at the sub-national level, failing to respond to a rising demand from policy-makers and local authorities. We provide a comprehensive map of median income, inequality (Gini coefficient and Lorenz curve) and poverty (poverty rates) based on the equivalised household income in the countries in which the EU-SILC is conducted. We study the distribution of income of households (pro-rated to its members), not merely its median (or mean), because we regard its dispersion and frequency of lower extremes (relative poverty) as important characteristics. The estimation for the regions with small sample sizes is improved by the small-area methods. The uncertainty of complex nonlinear statistics is assessed by bootstrap. Household-level sampling weights are taken into account in both the estimates and the associated bootstrap standard errors.

Hierarchical Modelling of Disparities in Preferences for Redistribution

We evaluate the magnitude of the disparities in the demand for redistribution across European countries and American states during the 2000s. Modelling the demand for redistribution in a multilevel framework, we identify the determinants that contribute the most in predicting support for redistribution. We observe that individual characteristics and contextual variables are associated with demand for redistribution in the same way in Europe and in the US, whereas others exert different influences on the probability of supporting redistribution. We find important differences from some well-established evidence obtained from data collected for the 1980s and the 1990s.

Trimmed fuzzy clustering for interval-valued data

In this paper, following a partitioning around medoids approach, a fuzzy clustering model for interval-valued data, i.e., FCMd-ID, is introduced. Successively, for avoiding the disruptive effects of possible outlier interval-valued data in the clustering process, a robust fuzzy clustering model with a trimming rule, called Trimmed Fuzzy

Exponential distance-based fuzzy clustering for interval-valued data

C

GARCH-based robust clustering of time series

C-medoids for interval-valued data (TrFCMd-ID), is proposed. In order to show the good performances of the robust clustering model, a simulation study and two applications are provided.