Research On Unsupervised Feature Selection Based On Low-Rank Constraint And Graph Embedding

In recent years,research on feature selection and dimension reduction has witnessed that several important structures should be preserved by the selected features.These important structures include,but not limited to,the global structure,the local manifold structure.Sparse representation and low rank representation are generally used to reconstruct data which can learn the global structure.The local manifold structure can maintain the local relationship between samples which can be obtained by graph learning.Aforementioned structures can be captured by widely used models in the form of graph,such as the sample pairwise similarity graph,the k-nn graph,the global integration of local discriminant model,the local linear embedding etc.Obviously,many of existing unsupervised feature selection methods rely on the structure characterization through some kind of graph,which can be computed within the original feature space.Once the graph is determined,it can be fixed in the next process and guided to search for informative features,such as sparse spectral regression.Therefore,the performance of feature selection depends on the effectiveness of graph structures to some extent.However,the original data are usually noisy and redundant,which inevitably leads to irrelevant or noisy features,and henceforth degrade the following feature selection performance.Therefore graph structures learned directly from the original feature space may not be appropriate.In this paper,the idea of low-rank representation and adaptive graph embedding is integrated into the unified framework.The global and local structure of data in a transformed space is learned by low rank representation and adaptive graph embedding,which can be reduce the negative effects of noise and redundancy.Based on the aboue ideas,a joint low-rank representation and graph embedding unsupervised feature selection(JLRRGE)method is proposed,which combines feature selection,global structure learning and local manifold structure learning in a unified framework.Meanwhile its optimization algorithm is proposed.Furthermore,we considering the discriminative information of selected features in the reconstruction process,so that the reconstruction not only extracts principle component information,but also preserves the global representation structure of data simultaneously.Based on this idea,a low-rank preserving reconstruction and graph embedding for unsupervised feature selection(LRPRGE)is proposed and it is solved by optimization algorithm.To testify the performance of the proposed models,JLRRGE is experimented on five open datasets such as UMIST,JAFFE,ORL32,MFEA and COIL20 datasets.LRPRGE is experimented on five open datasets such as COIL,LUNG,JAFFE,USPS and MFEA.Experiments show that the proposed models has good convergence,and the accuracy is superior to other similar researches.We are also interested in the sensitivity of the regularization parameters,and the results show that the proposed methods has a certain robustness to the parameters.Accordingly,JLRRGE and LRPRGE not only have good convergence and robustness,but also more accurately capture the intrinsic structure of data.