Geometric lattice structure of covering and its application to attribute reduction through matroids

The reduction of covering decision systems is an important problem in data mining, and covering-based rough sets serve as an efficient technique to process the problem. Geometric lattices have been widely used in many fields, especially greedy algorithm design which plays an important role in the reduction problems. Therefore, it is meaningful to combine coverings with geometric lattices to solve the optimization problems. In this paper, we obtain geometric lattices from coverings through matroids and then apply them to the issue of attribute reduction. First, a geometric lattice structure of a covering is constructed through transversal matroids. Then its atoms are studied and used to describe the lattice. Second, considering that all the closed sets of a finite matroid form a geometric lattice, we propose a dependence space through matroids and study the attribute reduction issues of the space, which realizes the application of geometric lattices to attribute reduction. Furthermore, a special type of information system is taken as an example to illustrate the application. In a word, this work points out an interesting view, namely, geometric lattice to study the attribute reduction issues of information systems

Active Sample Selection Based Incremental Algorithm for Attribute Reduction with Rough Sets

Attribute reduction with rough sets is an effective technique for obtaining a compact and informative attribute set from a given dataset. However, traditional algorithms have no explicit provision for handling dynamic datasets where data present themselves in successive samples. Incremental algorithms for attribute reduction with rough sets have been recently introduced to handle dynamic datasets with large samples, though they have high complexity in time and space. To address the time/space complexity issue of the algorithms, this paper presents a novel incremental algorithm for attribute reduction with rough sets based on the adoption of an active sample selection process and an insight into the attribute reduction process. This algorithm first decides whether each incoming sample is useful with respect to the current dataset by the active sample selection process. A useless sample is discarded while a useful sample is selected to update a reduct. At the arrival of a useful sample, the attribute reduction process is then employed to guide how to add and/or delete attributes in the current reduct. The two processes thus constitute the theoretical framework of our algorithm. The proposed algorithm is finally experimentally shown to be efficient in time and space

An efficient randomised sphere cover classifier

This paper describes an efficient randomised sphere cover classifier(aRSC), that reduces the training data set size without loss of accuracy when compared to nearest neighbour classifiers. The motivation for developing this algorithm is the desire to have a non-deterministic, fast, instance-based classifier that performs well in isolation but is also ideal for use with ensembles. We use 24 benchmark datasets from UCI repository and six gene expression datasets for evaluation. The first set of experiments demonstrate the basic benefits of sphere covering. The second set of experiments demonstrate that when we set the a parameter through cross validation, the resulting aRSC algorithm outperforms several well known classifiers when compared using the Friedman rank sum test. Thirdly, we test the usefulness of aRSC when used with three feature filtering filters on six gene expression datasets. Finally, we highlight the benefits of pruning with a bias/variance decompositio