Approximating a Set of Approximate Inclusion Dependencies

Abstract

Approximating a collection of patterns is a new and active area of research in data mining. The main motivation lies in two observations : the number of mined patterns is often too large to be useful for any end-users and user-defined input parameters of many data mining algorithms are most of the time almost arbitrary defined (e.g. the frequency threshold). In this setting, we apply the results given in the seminal paper {[}11] for frequent sets to the problem of approximating a set of approximate inclusion dependencies with k inclusion dependencies. Using the fact that inclusion dependencies are ``representable as sets{''}, we point out how approximation schemes defined in {[}11] for frequent patterns also apply in our context. An heuristic solution is also proposed for this particular problem. Even if the quality of this approximation with respect to the best solution cannot be precisely defined, an interaction property between IND and FD may be used to justify this heuristic. Some interesting perspectives of this work are pointed out from results obtained so far.