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Title: A novel bi-clustering algorithm for Hilbert data Authors:  Agostino Torti - Politecnico di Milano (Italy) [presenting]
marta galvani - politecnico di milano (Italy)
Alessandra Menafoglio - Politecnico di Milano (Italy)
Piercesare Secchi - Politecnico di Milano (Italy)
Simone Vantini - Politecnico di Milano (Italy)
Abstract: The problem of bi-clustering for the analysis of Hilbert data is considered with the aim of simultaneously clustering the rows and columns of a data matrix whose entries are objects for which a meaningful Hilbert space structure can be identified. A definition of ideal bi-cluster for Hilbert data is given and a novel bi-clustering algorithm - called HC2 (i.e, Hilbert Cheng and Church) - is developed. The HC2 relies on a non-parametric deterministic iterative procedure capable of finding bi-clusters in a data matrix where each cell contains an object, possibly belonging to a multidimensional space. The introduced algorithm is very flexible and allows one to discover different types of bi-clusters depending on the model chosen to define the concept of ideal bi-cluster for the problem at hand. Simulation studies are performed to show the potentials of the introduced method. The HC2 algorithm is finally applied to the analysis of the regional railway service in the Lombardy region with the aim of identifying recurrent patterns in the passengers' daily access to trains and/or stations, thus supporting correct management of the service.