In this paper we focus on the identification of discrete-time hybrid systems in the Piece-Wise Affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multi-dimensional domain. In order to achieve our goal, we propose an algorithm that exploits the combined use of clustering, linear identification, and classification techniques. This allows to identify both the affine submodels and the polyhedral partition of the domain on which each submodel is valid.