Hypergraph Low-rank Feature Selection Algorithms With Application

In the data growing increasing time,all kinds of electronic equipment will produce more or less the data in every moment,sometimes the data have very high dimensions,which is called high dimensional data.However,the high dimension data often contain redundant features in data mining,and cannot be directly used to real applications.Feature selection plays an indispensable role in machine learning,and is often used in engineering and academic research.It can eliminate unnecessary features in high dimensional data.Using feature reduction can select the most significant features,and reduce the dimension of high dimensional data,so as to improve the efficiency of data mining algorithm without changing its learning effect.The existing method of feature reduction can be divided into two categories:subspace learning and feature selection.Subspace learning projects high dimensional data to low dimensional space,which keeps the related structure between the data.Feature selection method can sort features by some integrating ranking criteria,and select the most significant features.It is a way to improve the performance of algorithms,so it can be widely applied in pattern recognition and machine learning.In this paper,feature selection and subspace learning are applied simultaneously in the model,and hypergraph regularization term is used to keep the local structure between the data,low-rank constraint is used to maintain the global structure of the different data for applying to classification and regression data sets.The core contents and advantages of this paper are as follows:?1?This paper puts forward an“Unsupervised Spectral Feature Selection with local structure learning”,abbreviated as LSL_FS.This method combines feature selection and local structure learning,and it can learn local manifold structure of high-dimensional data adaptively,and learn more valuable features.This method introduces a reasonable constraint condition,the graph matrix dynamically obtained by local and global structure correlations from the low dimensional space with noise and redundancy as less as possible.Thus,the graph matrix will be more reliable.In our framework,we integrate the?_2,1-norm regularization term into the least square loss function to seek the correlation of the samples.It can effectively exclude the interference of the outliers and select many more useful samples to enhance the capability of feature selection model.?2?This paper puts forward a“Based on hypergraph expressing low-rank feature selection algorithm for regression analysis”,LHSL_FS for short.The LHSL_FS algorithm takes into account the relationship between class labels in feature selection,and considers data sparsity for feature selection via utilizing the double sparse expressing norm,that is,using?_2,1-norm and?_2,p-norm to select significant samples for loss function and punish the coefficient matrix,respectively.By adjusting the parameter p?0<p<2?,the more spare the coefficient matrix,the more important the selected features.Thus,the model can accurately select the important features,and the algorithm has better robustness and generalization.In order to consider the relationship between the various types of data,using hypergraph instead of the ordinary graph.The algorithm avoids using the common graph to find the complex relationship between the data.However,the hypergraph regularization can be used to preserve local structure of data,the hypergraph makes the neighborhood structure of the sample data invariant after the spatial projection.Using the low-rank constraint to maintain the global structure of different data.It is the fact that the low-rank constraint equals using LDA subspace learning,subspace learning tries to ensure that the information of data is intact and reduce the dimension of data.The sparse representation makes the most of elements of coefficient matrix be zero,the nonzero elements corresponding coefficient in the matrix has been maintained for feature selection.Meanwhile,in order to make the feature selection model is more robust,this paper effectively combines the LDA subspace learning algorithm to tune the results in the feature selection model.Therefore,the algorithm can greatly deal with the multiple output regression analysis problem of high dimensional data.This paper proposes a way to solve the objective function of LHSL_FS algorithm,which is different from alternating direction multiplier method?ADMM?.Firstly,we fix the result of low-rank feature selection to enhance the ability of subspace learning.Then,the result of the fixed subspace learning ensures that the low-rank feature selection outputs a more discriminant feature set.The optimization algorithm makes the target value gradually close to the global optimal solution in each iteration process,and finally obtains the global optimal solution.In this paper,using the high dimensional data sets about classification and regression to analyze and design experiments,and the performance of the feature selection algorithms proposed are fully verified.Specifically,this paper uses hypergraph,low-rank and sparse technology to run the experiments of feature selection for classification and regression task.Our algorithms performance are more excellent than other features selection algorithms in most public data sets.In the future work,we will consider combining the deep learning framework with feature selection for data preparation,and apply it to all kinds of practical applications.