Subspace Clustering Based On Low-rank Sparse Hypergraph Learning

With the rapid development of the information age,data acquisition is more and more easy,and the dimension and complexity of data are also increasing exponentially.This brings great challenges to our data processing,but in many cases,the processing of high-dimensional data is traceable.In fact,many high-dimensional data are usually located on the union of several low-dimensional subspaces,such as face data.Subspace clustering uses this property to obtain the internal structure of the data by learning several low dimensional subspaces,and then applies spectral clustering to the low dimensional representation of the data to obtain the clustering results.The existing subspace clustering model mainly uses a certain loss function to describe the noise in the observation data.However,in the actual high-dimensional data,the noise may have a complex and unknown distribution,so it is unreasonable to assume that it is a single noise.The complexity of data is not only reflected in the dimensions,but also in the various forms of data.The data we get often has multiple views.For the problem of multi view clustering,there are many mature methods.However,these methods are based on the assumption that all views exist.In real life,due to sensor failure or human factors and other reasons,there are some samples with missing views.Aiming at the above challenges,this paper studies the problem of subspace clustering in machine learning.For the case of complex noise in single view scene and the problem of missing subspace clustering in multi view scene,we propose an effective algorithm and verify our performance on open data sets:1)Aiming at the complex noise in high-dimensional sample data in single view subspace clustering,a low rank sparse hypergraph model based on Gaussian mixture model is proposed.The model can not only effectively model the complex noise in samples through Gaussian mixture model,but also capture the global and local linear correlation information among samples by using low rank representation and sparse representation.Furthermore,we use hypergraph model instead of traditional graph to model the association information between samples.Finally,we do experiments on several real datasets to show the effectiveness and superiority of our model.2)Aiming at the situation that there may be missing views in multi view scene,a low rank sparse hypergraph model based on hidden space is proposed.Through the existing view data,a complete representation of each sample is learned in the hidden space,and the low rank sparse self representation model is used for clustering.Furthermore,we use hypergraph model instead of traditional graph to model the association information between samples.Finally,we verify the effectiveness and superiority of our model on several public datasets for view missing scenarios.