Feature Selection Based On Latent Representation And Spectral Graph Analysis

With the rapid development of science and technology,massive amounts of data are generated from various industries every day.Moreover,the rapid expansion of data dimensions has caused more and more noise,redundancy,and irrelevant features,which has increased the difficulty of data processing.Therefore,it is necessary to reduce the dimensionality of large-scale high-dimensional data.Feature selection is one of the common dimensionality reduction methods,which selects representative features from the original features according to specific criteria,so as to obtain a compressed data representation.In recent years,many novel feature selection algorithms have been proposed and achieved good results.However,these methods still have some limitations that need to be overcome,such as insufficient utilization of data inherent information,insufficient optimization of the clustering indicator matrix,and ignoring global structure of data.In this thesis,for the problem of unsupervised feature selection,this thesis proposes three new algorithms.The main works of this thesis are as follows:(1)A new algorithm called dual space latent representation learning for unsupervised feature selection(DSLRL)is proposed.First,DSLRL constructs affinity matrices in data space and feature space,which are used to represent the internal relationships between instances and the internal relationships between features,respectively.Secondly,DSLRL uses the affinity matrix to perform latent representation learning in two spaces simultaneously,to obtain low-dimensional latent representations of data and feature.Then,DSLRL uses the latent representation matrix of data to provide clustering indicators,and unifies the latent representation matrix of feature and the sparse transformation matrix,which uses the correlation information between the features and clusters to guide the matching between the data matrix and the clustering indicator matrix.Finally,the sparse transformation matrix is constrained by non-negative and orthogonal conditions to make it more accurately reflect the importance of features.(2)A new algorithm called unsupervised feature selection via discrete spectral clustering and feature weights(FSDSC)is proposed.First,FSDSC integrates regression models and spectral clustering into the framework of feature selection,and introduces a feature weight matrix,which intuitively expresses the importance of each feature with its diagonal elements and simplifies the process of feature evaluation.Secondly,FSDSC improves the spectral clustering method and obtains a discrete clustering indicator matrix,which provides clearer guidance information for feature selection.In addition,FSDSC imposes orthogonal constraints on the transformation matrix to avoid trivial solutions,and the combination of the orthogonal regression model and the spectral clustering method better preserves the local geometric structure of data.(3)A new algorithm called unsupervised feature selection based on graph optimization and global constraints(GOGFS)is proposed.First,GOGFS embeds graph learning in the framework of feature selection and optimizes the similarity graph during the feature search process to obtain a more reliable similarity graph,thereby better retaining local structural information.Secondly,GOGFS imposes constraints on the samples of the low-dimensional space to capture the global structure information of the samples.The local and global geometric structures enhance the performance of feature selection by providing complementary information to each other.In addition,GOGFS uses the l_2,1–norm constraint to select discriminative features.