Reduction of Variables through Nearest Neighbor Relations in Threshold Networks

Abstract

Threshold networks are useful as a fundamental technology in the recent learning and AI domains. Reduction of data variables in threshold networks is an important issue and it is needed for the processing of higher dimensional data in the application domains and AI. Boolean and rough set is fundamental and useful to reduce higher dimensional data to lower one for the classification. We develop a reduction of data variables and classification method based on geometrical reasoning, which is characterized by nearest neighbor relations. In this paper, the nearest neighbor relations are shown to be useful for the reduction of variables and their classification in threshold networks. The Boolean operation and convex cones generated by the nearest neighbor relations derive the reduced variables of data and the classifications using them. Then, the edges of convex cones are compared for the reduction of variables. Further, hyperplanes with reduced variables are generated on the same convex cones for data classification.