Stefano Rovetta

The paper addresses the issue of assessing the importance of input variables with respect to a given dichotomic classification problem. Both linear and non-linear cases are considered. In the linear case, the application of derivative-based saliency yields a commonly adopted ranking criterion. In the non-linear case, the method is extended by introducing a resampling technique and by clustering the obtained results for stability of the estimate. The work is preliminary, and many properties and options are to be investigated in future research.

We discuss the graded possibilistic model. We review some clustering algorithms derived from the basic c-Means and introduce a formalism to provide an alternative, unified perspective on these clustering algorithms, focused on the memberships rather than on the cost function. An interesting case is the concept of graded possibility. Its formulation includes as the two extreme cases the "probabilistic" assumption and the "possibilistic" assumption. A possible formulation can be stated as an interval equality constraint enforcing both the normality condition and the required graded possibilistic condition. We outline a basic example of graded possibilistic clustering algorithm. The experimental demonstrations presented aim at highlighting the different properties attainable through appropriate implementation of a suitable graded possibilistic model.