Research On Dimensionality Reduction Method Based On Graph Embedding

With the ongoing development of modern information technology,the dimensionality of data has increased dramatically,making it difficult for people to grasp the nature of the data and then utilize it;while in the fields of feature selection and transfer learning,constructed models inspired by the idea of graph embedding are often able to achieve better results.Therefore,based on the idea of graph embedding and combining with other methods,it will be a feasible research idea to mine the underlying geometric structure and obtain the key features of the data,then achieving dimensionality reduction.Specifically,based on two methods of graph embedding,namely adaptive graph embedding and predefine graph embedding,this paper proposes two new unsupervised feature selection models,namely,Unsupervised Feature Selection with Joint Graph Embedding and Feature Weighting(JGEFW)and Dual-Graph Regularized Feature Weighted Regression(NSDFWR).JGEFW model,which utilizes adaptive graph embedding to obtain the similarity matrix,and the pseudo cluster label matrix is captured which then is incorporated into a feature weighted orthogonal regression framework to obtain a weight matrix,and finally the more discriminative and non-redundant features are selected,to reduce the dimensionality of data effectively and preserve the information of data mostly.NSDFWR model,which utilizes predefined graph embedding to learn the data space and feature space,then the manifold structural information are discovered.Based on the abovementioned information,two low-dimensional embedding matrices are obtained,in which the non-negative constraints are introduced to enforce the property of the spaces;meanwhile the embedding of feature space also performs as a projection matrix in a unified feature weighted regression framework with orthogonal constraint,and the feature weight matrix is utilized to form low-dimensional data with discrimination and non-redundancy,realizing the aim of reducing dimensionality finally.In order to verify the effectiveness of the models,we compare these two models with the commonly used unsupervised feature selection algorithms on several data sets,specifically: JGEFW model is compared with LS,MCFS,UDFS DSRMR and Baseline algorithms on YALE,TOX,ISOLET,and COIL data sets;NSDFWR model is compared with LS,MCFS,RSR and Baseline algorithms on the Ionosphere,ISOLET,warp AR10 P and warp PIE10 P data sets.The experimental results show that in most cases,the JGEFW model and the NSDFWR model are better than other comparison algorithms,and the clustering result is improved to a certain extent,indicating that the model s can effectively mine the underlying geometric structure information of the data and select features with abundant information,achieving dimensionality reduction effectively.Finally,the convergence analysis and parameter sensitivity analysis prove that the JGEFW model and the NSDFWR model have good mathematical convergence and certain robustness in some cases.