Semi-supervised rough fuzzy Laplacian Eigenmaps for dimensionality reduction

Laplacian Eigenmaps is a popular nonlinear dimensionality reduction technique and there exist various scenarios of its extensions. In this paper, a semi-supervised rough fuzzy Laplacian Eigenmaps (SSRFLE) approach is developed for dimensionality reduction of high dimensional hybrid data. In the proposed method, a set of semi-supervised fuzzy similarity granules are constructed to characterize the similarity between samples according to the principle that homogeneous samples have higher similarity degrees than heterogeneous samples. A neighborhood rough fuzzy set model of such fuzzy similarity granules is built to assess the degrees two samples belong to the same class. A Laplacian nearest neighborhood graph and a class-related neighborhood graph are constructed to characterize the topological structure between samples and between each sample and its prototype to ensure homogeneous samples being mapped closer to and more compact around the prototypes in a lower dimensional space. In view of the fact that different features bring out distinct impacts on performances of feature extraction and clustering, the significance of each feature is assessed by designing an information entropy measure and the weighted distance between samples is incorporated into the proposed technique. A series of simulation experiments on real world hybrid datasets are carried out. Experimental results show superior performance of the proposed method in classification accuracy and data visualization compared with other state of the art semi-supervised methods.