Research On Attribute Reduction Based On Multi-scales Singular Value Decomposition Entropy And Its Applicat Ions

The Real world is big material and colorful.The real world has too much uncertainty,which leads to the human imperfect cognition of the world.Rough set,as an effective tool to solve the uncertain problem,has been widely studied in recent years and applied to deal with uncertain problems in real life.Attribute reduction as the main direction of rough set research has been widely concerned by scholars.In this paper,the concept of singular value decomposition partial entropy and relative entropy are proposed,furthermore,the concept of relative entropy coefficient is deduced.By comparing the relative entropy coefficient attribute can be reduced.The experiments prove the effectiveness of the methods.The main work of this paper is as follows:(1)Singular values can fully reflect the singularity of a trajectory matrix,and a relative entropy coefficient can better describe the correlation between the data.An attribute reduction algorithm based on singular value decomposition entropy is proposed by this paper.The algorithm obtains the relative entropy coefficient between two time series by singular value decomposition of their trajectory matrix.After excluding the attributes having smaller relative entropy coefficients with decision attribute values,condition attributes can finish reduction.Compared with the conditional information entropy algorithm,the concrete examples show that the singular value decomposition method has the advantages whether in the reduction results or in the recognition accuracy.(2)By dividing the whole sequence into several sub-sequences,and by means of sliding window method,we obtain the relative entropy coefficient spectrum of two sequences.Experiments show that the relative entropy coefficient spectrum can describe the degree of correlation between data more accurately,so the method is more effective for data reduction.Furthermore,the relative entropy coefficient spectrum based on multi-scales singular value decomposition partial entropy and relative entropy is proposed.Through that scales change from the positive number to the negative number,the different singular values under the different scales can have an influence on the relative entropy coefficient.The experiments show that the method can describe the stability of the relative entropy coefficient more finely,so as to describe the correlation between condition attributes and decision attributes more accurately.