Generation of Convex Cones Based on Nearest Neighbor Relations

Dimension reduction of data is an important issue in the data processing and it is needed for the analysis of higher dimensional data in the application domain. Rough set is fundamental and useful to reduce higher dimensional data to lower one for the classification. We develop generation of reducts based on nearest neighbor relation for the classification. In this paper, the nearest neighbor relation is shown to play a fundamental role for the classification from the geometric easoning of reducts by convex cones. Then, it is shown that reducts are generated based on the convex cones construction. Finally, using nearest neighbor relation, algebraic operations are derived on the degenerate convex cones.