Efficient neighborhood covering reduction with submodular function optimization

Abstract

Neighborhood Covering Reduction (NCR) methods learn rules for classification through formulating the covering of data space with neighborhoods. NCR method transforms original data into neighborhood systems and facilitates the data generalization. However, the computational complexity of extant NCR methods is which impedes the application of NCR on massive data and the error bound analysis is insufficient. In this paper, we remodel the objective of NCR from the view of Submodular Function Optimization and thereby improve the efficiency of NCR based on submodular optimization strategies. We first optimize the reduction process of neighborhoods with Lazy-Greedy strategy and further extend the serial algorithm to a parallel version according to the parallel optimization strategy of submodular functions. The error bounds of the proposed NCR algorithms are also analyzed. Experimental results validate the efficiency of the proposed NCR algorithms.