Efficient Attribute Reduction with Submodular Function Optimization

Xuxia Zhang, Xiaodong Yue, Zhikang Xu

Abstract: Attribute Reduction problem is an important content in Rough Set theory, which has been proven to be NP-hard. It tends to find a subset of attributes that preserve the same discriminatory power as the entire attributes. Heuristics methods are used to find the minimum attribute subset. In this paper, we use three typical heuristic methods to do Attribute Reduction. They are positive-region-based, discernibility-matrix-based and mutual-information-based Attribute Reduction algorithm. Experimental results validate that all the three algorithms have good performance on classification for symbolic data. However, the computational complexity of the three Attribute Reduction algorithms are all O(n^2), so it s hard to apply them to massive data. In order to improve the efficiency of the three Attribute Reduction algorithms, we remodel the objective of them from the perspective of Submodular Function Optimization with submodular optimization strategies. We first optimize the attribute selection process with Lazy-Greedy strategy and then extend the serial algorithm to a parallel version according to the parallel optimization strategy of submodular functions. Experimental results validate that the efficiency of the proposed Attribute Reduction algorithms.