Research On Class-Preserving Laplacian Eigenmaps For Dimensionality Reduction

With the rapid development of science and technology,the present situation of higher dimensional and massive data makes more and more persons pay close attention to the dimensionality reduction techniques.Laplacian Eigenmaps(LE)is a classical nonlinear dimensionality reduction algorithm,which preserves the local neighborhood structure of samples in the lower dimensional space.Although LE and its modifications have been widely applied in the fields of classification,face recognition and data visualization,they also have lots of deficiencies,including sensitivity to parameters and no capability of unfolding the global structures of data,so cannot well preserve class structures of data in the processing of dimensionality reduction.On the basis of classical LE algorithm and existing modified LE algorithms,two class-preserving Laplacian Eigenmaps algorithms for dimensionality reduction are proposed.The first one is accomplished by adaptively determining the thresholds of homogeneous neighbors and heterogeneous neighbors.Another one incorporates theory of information entropy and rough fuzzy sets in the processing of nonlinear dimensionality reduction.Detailed research contents are as follows.For data sets with class labels information,a supervised class-preserving Laplacian Eigenmaps for dimensionality reduction(SCPLE)is proposed by adaptively determining homogeneous neighbors and heterogeneous neighbors.In SCPLE,two neighbor graphs,intra-class graph and inter-class graph,are adaptively constructed by using the label information of data,the similarity of homogeneous samples and the difference of homogeneous samples.Simultaneously,the weight of each edge of intra-class neighborhood graph is set as a number more than 0.5.By maximizing the weighted neighbor distances between heterogeneous samples and minimizing the weighted neighbor distances between homogeneous samples,SCPLE algorithm can make homogeneous samples be mapped closer and heterogeneous samples be mapped farther in the low dimensional space,and preserves the class characterization of the original data.The proposed SCPLE algorithm is compared with three nonlinear dimensionality reduction algorithms for four face image data sets,and experimental results demonstrate the effectiveness and superiority of the proposed SCPLE algorithm.For data sets with part known class labels information,a semi-supervised Laplacian Eigenmaps for dimensionality reduction is proposed by introducting the information entropy and rough fuzzy sets theory in nonlinear dimensionality reduction,called as SSRFLE.In SSRFLE,the significance of features is assessed based on information entropy,and the weights between samples are evaluated based on neighborhood rough fuzzy set model by constructing a fuzzy matrix of dataset.A weighted neighborhood graph and a weighted class-related graph are constructed to represent topological structures between samples and their prototypes.Minimizing both the weighted distances between samples and the weighted distance between samples and prototypes can ensure homogeneous samples being mapped closer and more compact around the prototypes,so SSRFLE can preserve the class structures of original samples in the lower dimensional space.The proposed SSRFLE is compared against commonly used semi-supervised nonlinear dimensionality reduction algorithms for hybrid data sets.Experimental results show superior performance of SSRFLE in classification accuracy and data visualization.