Numerical attribute reduction based on neighborhood granulation and rough approximation

To deal with numerical features, a neighborhood rough set model is proposed based on the definitions of δ neighborhood and neighborhood relations in metric spaces. Each object in the universe is assigned with a neighborhood subset, called neighborhood granule. The family of neighborhood granules forms a concept system to approximate an arbitrary subset in the universe with two unions of neighborhood granules: lower approximation and upper approximation. Thereby, the concepts of neighborhood information systems and neighborhood decision tables are introduced. The properties of the model are discussed. Furthermore, the dependency function is used to evaluate the significance of numerical attributes and a forward greedy numerical attribute reduction algorithm is constructed. Experimental results with UCI data sets show that the neighborhood model can select a few attributes but keep, even improve classification power.