Compstat 2006 - Proceedings in Computational Statistics: by Kaye Basford, Geoff McLachlan, Richard Bean (auth.),

By Kaye Basford, Geoff McLachlan, Richard Bean (auth.), Professor Alfredo Rizzi, Professor Maurizio Vichi (eds.)

International organization for Statistical Computing The overseas organization for Statistical Computing (IASC) is a bit of the overseas Statistical Institute. The goals of the organization are to foster world-wide curiosity in e?ective statistical computing and to - swap technical wisdom via foreign contacts and conferences - tween statisticians, computing execs, corporations, associations, g- ernments and most people. The IASC organises its personal meetings, IASC global meetings, and COMPSTAT in Europe. The seventeenth convention of ERS-IASC, the biennial assembly of eu - gional portion of the IASC was once held in Rome August 28 - September 1, 2006. This convention came about in Rome precisely twenty years after the seventh COMP- STAT symposium which was once held in Rome, in 1986. prior COMPSTAT meetings have been held in: Vienna (Austria, 1974); West-Berlin (Germany, 1976); Leiden (The Netherlands, 1978); Edimbourgh (UK, 1980); Toulouse (France, 1982); Prague (Czechoslovakia, 1984); Rome (Italy, 1986); Copenhagen (Denmark, 1988); Dubrovnik (Yugoslavia, 1990); Neuchˆ atel (Switzerland, 1992); Vienna (Austria,1994); Barcelona (Spain, 1996);Bristol(UK,1998);Utrecht(TheNetherlands,2000);Berlin(Germany, 2002); Prague (Czech Republic, 2004).

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Thus, the aim is to determine a limited number of clusters such that the within cluster dispersion is minimized. The peculiarities of the proposed models are to be found in their capability of coping with the complexity of the data structure. In fact, each observation consists of a set of fuzzy data collected at several time occasions. Therefore, at each time occasion, the available information is uncertain, in particular vague, and is treated from the fuzzy viewpoint, by representing it in the form of fuzzy numbers.

T , with Xi ≡ {xijt : j = 1, . J; t = 1, . . T }, Xj ≡ {xijt : i = 1, . I; t = 1, . . T } and Xt ≡ {xijt : i = 1, . I; j = 1, . . J}. 2 LR fuzzy multivariate time trajectories Let RJ+1 be the vectorial space (space of the observation units), where the axes are referred to the J variables and time. , riJt , t) . ,I , represent the matrix Xt . Letting t vary within its range, the scatters f NI (t) are placed on T hyperplanes parallel to the sub-space RJ . ,T , represent the matrix Xi . ,I represents the set of the LR fuzzy multivariate time trajectories.

As one may expect, the obtained clusters can be ordered according to the levels of the pollutants: in particular, by observing the medoid trajectories and the observations belonging to the clusters involved, the second cluster contains testing stations with the highest recorded levels of pollutants, whereas the opposite holds for the third cluster. This can be highlighted in Fig. 4, where the center values of the medoid trajectories are displayed. In fact, the trajectory pertaining to Libia (Tenuta del Cavaliere) lies above (below) the others at all the time occasions.

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