Convex granules and convex covering rough sets

Abstract

Many extensions of rough sets have been trying to seek appropriate granular structures, such as neighborhood systems, disjoint intervals and coverings. However, few of them consider data-driven approaches to generating posets-structured coverings based on granules of irregular shapes and variable sizes. By generalizing norm granules (intervals, δ-neighborhoods and k-nearest neighbors), the present study proposes a tree-structured model whose information granules are obtained through an “onion-peeling” strategy, CrossSift. Two comparative experiments are conducted in this paper. One shows that granules generated by CrossSift are able to achieve a higher dependency degree with fewer numbers than equal width/frequency intervals, δ-neighborhoods and k-nearest neighbors. The other shows the trees output by CrossSift outperform SVC, KNN, AdaBoost, Cart, LDA in the average rank of classification accuracy. The proposed method bridges a gap between rough sets and perceptrons, and is expected to contribute to dimensionality reduction, computer vision and geometry.