Research On Robust Subspace Clustering Method Based On Low Rank Representation

In machine learning,computer vision,pattern recognition and other fields,how to deal with high-dimensional data effectively is a problem that researchers often face.The highdimensional data not only increases the computation time and memory requirement of the algorithm,but also adversely affects the performance of the algorithm due to the existence of high-dimensional noise.Subspace clustering,as a powerful method for processing highdimensional data,divides data from different classes into subspaces to which they belong essentially.Ideally,each class corresponds to a subspace.Subspace clustering can not only efficiently reduce the dimension of data,but also complete the clustering of different categories of data.As the most popular algorithm model for subspace clustering in the past decade,low-rank representation(LRR)has won wide attention due to its advantages of easy operation,good robustness to noise and remarkable clustering effect.Algorithm models based on low-rank representation are emerging one after another,constantly updating the upper limit of clustering performance.Based on this,this paper proposes new subspace clustering algorithm models based on low-rank representation to improve the clustering performance by solving the defects of traditional low-rank representation.The main research contents of this paper are as follows:1.Robust subspace clustering based on latent low rank representation with non-negative sparse Laplacian constraintsAiming at the defects of traditional low-rank representation algorithm,such as directly using original data as the dictionary,only considering the global structure of data but ignoring the local geometric structure of data and the possibility of negative values of representation matrix,this paper proposes a new subspace clustering algorithm model named non-negative sparse Laplacian constrained latent low rank representation(NNSLLatLRR).By using the framework of latent low-rank representation(LatLRR)model to replace the original low-rank representation model,the problem of severe decline in clustering effect caused by directly using the original data matrix as the dictionary when the data pollution is very serious and the data sampling is insufficient is overcome.Meanwhile,three effective constraints-sparse,Laplacian and non-negative constraints are imposed on the representation matrix,which introduce rich structural information to the representation matrix.This not only helps to obtain the local geometric structure of the data,but also improves the interpretability of the algorithm model.The representation matrix can more accurately reflect the real similarity relationship between data samples,greatly improving the representation ability of the model,so as to achieve the purpose of improving the clustering accuracy of the algorithm model.2.Subspace clustering based on non-negative Laplacian constrained Frobenius norm minimization based latent low rank representationFor the traditional low-rank representation algorithm based on nuclear norm minimization optimization,it is necessary to perform many singular value decomposition operations,and singular value decomposition is very time-consuming and labor-intensive.Therefore,this paper proposes a new subspace clustering algorithm model named nonnegative Laplacian constrained Frobenius norm minimization based latent low rank representation(NLFLatLRR).The latent low-rank representation model framework is also used to replace the original low-rank representation model,and non-negative constraint together with Laplacian constraint are imposed on the representation matrix to improve the robustness of the model against noise and representation ability.Besides,by using Frobenius norm minimization instead of nuclear norm minimization,the computational complexity of the algorithm is greatly reduced and the running time is largely reduced on the premise of ensuring the clustering accuracy,thus greatly improving the clustering performance of the model.3.Subspace clustering based on Frobenius norm constrained non-negative Laplacian based latent low rank representationIn view of the problem that the representation coefficients of the representation matrix obtained by the traditional low-rank representation algorithm cannot accurately reflect the true similarity relation between data samples and thus affect the clustering accuracy,we are committed to constructing a representation matrix with good structural properties which is dense within classes and sparse between classes.For this reason,this paper proposes a new subspace clustering algorithm model named Frobenius norm constrained non-negative Laplacian based latent low rank representation(FNLLatLRR).In order to encourage denser connections between data samples belonging to the same class,we use Frobenius norm regularizer to make the intra-class representation denser.Besides,based on the model framework of latent low-rank representation,non-negative and Laplacian constraints are applied to the representation matrix,which reduces the false connections between unrelated data points and promotes the inter-class sparsity of the representation matrix.The representation matrix obtained by this algorithm has excellent structure and is conducive to clustering.The representation coefficients can reflect the true similarity relationship between data samples as accurately as possible,and the final clustering accuracy is improved on this basis.