Research On Rough Set Method Based On Sample Correlation

With the development of computer technology,we are entering the era of the information explosion,and the massive data brought by it contains lots of uncertain and incomplete information.Rough set theory is an effective mathematical tool for handling fuzzy,uncertain knowledge and inconsistent data.It has great effects on data mining and knowledge recognition.As the foundation and key point in rough set model,inter-sample relationship description and uncertainty measurement are of great significance in the data processing with uncertain information.This thesis proposes a sample correlation measurement method via the quantitative analysis of relationship corresponding with samples and clusters,and applying it into attribute reduction and clustering method.The main contents are as follows:Firstly,a sample correlation-based attribute reduction method.For the moment,most existing attribute reduct definitions are based on the indiscernibility or equivalence relation.The performance of each reduct is determined by the qualitative or quantitative inclusion relationship between the equivalence classes and the decision class.However,these definitions only focus on changes in the size of equivalence classes,but they ignore the changes between samples that do not have equivalence relationships,especially among samples belonging to different decision classes.This is precisely a key factor that affects the classification ability based on the reduct.In views of this,this thesis proposes an improved attribute reduction method.Firstly,the concept of sample correlation in this thesis is introduced.Based on the sample correlation,the intra-class sample correlation for samples in the same decision class and the inter-class correlation for different decision classes are defined.Secondly,a sample correlation-based attribute reduct by maximizing intra-class sample correlation and minimizing inter-class correlation in the rough set model is defined.Thirdly,by considering the heuristic search strategy,this thesis also designs a corresponding reduction method for the proposed attribute reduct.The experimental results indicate that compared with other representative attribute reducts,the attribute reduct proposed in this thesis can significantly improve the classification performance.Secondly,a sample correlation-based three-way cluster method.As for traditional cluster method and three-way decision theory,the number of clusters and the three-way partition threshold are always selected by subjective optimization.However,this fixed number of clusters and partition thresholds can't be adjusted for data sets and clusters with different size and density.It can't choose the appropriate number of clusters and partition threshold while the data sets and clusters are changed.To solve the problems above,an improved three-way cluster method is proposed in this thesis.Firstly,the equal relationship and its corresponding concepts are defined by introducing the sample correlation,and a partition validity measure is defined by the property of rough set and three-way decision theory.Then,the intra-class sample correlation and the inter-class sample correlation are proposed to describe the quantitative relationship of samples in the same decision class or in the different decision class.By the integration of these two concepts,a validity metrics of clustering performance is defined to measure the performance of different cluster number.And finally,an automatic sample correlation-based three-way cluster method is proposed via the integration of clustering validity index and partition validity index.Moreover,the validity of this cluster method is verified by a number of comparative experiments.