Neighborhood rough set reduction based on power set tree and A* search

Rough set reduction has been used as a momentous preprocessing tool for machine learning, pattern recognition, and big data analysis. It is well known that the traditional rough set theory can only handle features with categorical values. Therefore, a neighborhood rough set model is introduced to deal with numerical data sets. Classical greedy search strategies to neighborhood rough set reduction have often failed to achieve optimal reducts. Many researchers shift to swarm intelligence algorithms, such as particle swarm optimization, ant colony optimization and fish swarm algorithm, giving a better solution but with a large cost of computational complexity. It is beneficial for exploring fast and effective feature reduction algorithms. In this paper, we firstly introduce a knowledge representation, named power set tree (PS-tree). It is an order tree enumerating all the subsets of a feature set. Each node of the PS-tree is a possible feature reduct. Furthermore, we develop a tree search framework for reduction question solving by the PS-tree. We present four tree search methods based on PS-tree, which are depth-first, breadth-first, uniform-cost and A* search methods. The effectiveness of these four proposed tree search methods are tested on some UCI data sets. Finally, we compare the A* search with traditional greedy search and swarm intelligence methods. The comparisons show that the selected features by A* search attain good reduction rates and simultaneously maintain the classification accuracy of whole features.