Back Propagation Approach for Semi-supervised Learning in Granular Computing

Zadeh proposes that there are three basic concepts underlying human cognition: granulation, organization and causation and that a granule is a clump of points (objects) drawn together by indistinguishability, similarity, proximity or functionality. Tolerance relation can describe the concept of Granular systems. In this paper, a novel definition of Granular System(GS), which is described by metric function under the framework of tolerance relation, is presented, concepts are created upon GS, and we introduce semi-supervised learning into the Granular computing for concepts creating. For this purpose, a novel back propagation approach is developed for concepts learning. The experiment shows that the new BP is better than traditional EM algorithm when samples do not come from a random source, which has the density we want to estimate.