Efficient Attribute Reduction with Submodular Function Optimization Attribute Reduction problem is an important content in Rough Set theory, which has been proven to be NPhard. 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 positiveregionbased, discernibilitymatrixbased and mutualinformationbased 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(n2), 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 LazyGreedy 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.

A neighborhood rough set model with nominal metric embedding Abstract   Rough set theory is an essential tool for measuring uncertainty, which has been widely applied in attribute reduction algorithms. Most of the related researches focus on how to update the lower and the upper approximation operator to match data characteristics or how to improve the efficiency of the attribute reduction algorithm. However, in the nominal data environment, existing rough set models that use the Hamming metric and its variants to evaluate the relations between nominal objects can not capture the inherent ordered relationships and statistic information from nominal values due to the complexity of data. The missing information will affect the accuracy and validity of the data representation, thereby reducing the reliability of rough set models. To overcome this challenge, we propose a novel object dissimilarity measure, i.e., relative object dissimilarity metric(RODM) that learned from nominal data to replace the Hamming metric and then construct a xcfx88neighborhood rough set model. It extends the classical rough set model to a robust, representative, and effective model which is close to the characteristics of nominal data. Based on the xcfx88neighborhood rough set model, we propose a heuristic twostage attribute reduction algorithm(HTSAR) to perform the feature selection task. Experiments show that the xcfx88neighborhood rough set model can take advantage of more potential knowledge in nominal data and achieve better performance for attribute reduction than the existing rough set model.