Research On Clustering Algorithm Based On Adaptive Graph Regularization

Cluster analysis,an important data analysis method in modern machine learning research,which has a wide range of applications in data mining,pattern recognition and other fields.In order to make up for some shortcomings of the original clustering method and improve the performance of the clustering method,many scholars have proposed related improvement methods.Among many improved algorithms,graph regularization-based clustering algorithms have gained widespread attention due to their superior clustering performance,which improves the performance of the original clustering algorithm by exploiting the hidden manifold structure information in the data.Especifically,the clustering algorithm based on graph regularization uses the Laplacian graph to construct the manifold structure in the original data,and then integrates the Laplacian graph into the objective function to improve its performance.Obviously,it is too important to construct a high quality for impacting on the performance of graph regularization-based clustering algorithms.However,in the process of constructing graphs in existing algorithms,the graph construction is prespecified,and the graph construction and the objective function of the original clustering algorithm is independent.Usually these algorithms require multiple tunings to find a good graph.Therefore,a further research on the clustering algorithm based on graph regularization has been conducted in this paper,and further improves the performance of the algorithm by constructing an adaptive graph.The main contribution of this paper can be summarized as follows:(1)This paper elaborates the relevant knowledge of clustering methods,introduces how graph regularized methods improves the performance of the original one,and introduces two improvement directions,namely graph regularization and sparseness.The coding algorithm(graph regularization sparse coding,Graph SC)and the graph regularization nonnegative matrix factorization(GNMF)algorithm are described in detail;at the same time,this paper also summarizes some classic graph regularization-based clustering algorithm,and analyze the performance of the method through experiments on real databases.(2)The Graph SC algorithm is further studied.Since Graph SC uses the K nearest neighbor method(KNN)to construct the Laplacian graph,the graph constructed by KNN cannot completely fit the data.Therefore,this paper proposes an adaptive regularization sparse coding algorithm(graph regularization sparse coding with adaptive neighbour,Graph SCAN).The algorithm first uses an adaptive method to construct a suitable local Laplacian graph,and then adds it to the objective function of sparse coding,so that the graph construction and sparse coding are incorporated into a unified framework,so that the graph construction and sparse coding operations are performed simultaneously.At the same time,an effective algorithm for solving Graph SCAN is also given,and the effectiveness of the algorithm is verified by experiments on two image datasets.(3)In view of the shortcomings of the existing GNMF algorithm: first,the GNMF algorithm does not consider the low-rank structure of the data;second,in the GNMF algorithm,its Laplacian graph is predefined using the KNN method,However,the KNN method cannot always obtain the optimal graph,so that the performance of the GNMF algorithm cannot be optimal.To address these problems in GNMF,this paper proposes a nonnegative low-rank matrix factorization with adaptive graph neighbors(NLMFAN)algorithm for adaptive graph regularization.On the one hand,by introducing low-rank constraints,NLMFAN can obtain the effective low-rank structure of the original data set;The results of matrix factorization are integrated into an overall framework,so that the similarity of nodes in the graph is automatically learned from the data.In addition,the solution framework of the algorithm is also given.Experimental results on eight text datasets demonstrate the superiority of the algorithm.(4)GNMF only constructs a single Laplacian graph to approximate the manifold structure of the data,making it unable to accurately capture the geometric structure hidden in the data;in addition,its Laplacian graph is usually constructed using the k NN method,which may destroy the original data.local connectivity,and the best neighbors cannot be obtained.To address these issues,we propose a new algorithmic model which called multiple graph regularized nonnegative matrix factorization with adaptive neighbors(MGNMFAN).MGNMFAN not only uses adaptive methods to construct a single Laplacian graph,but also uses a linear combination of multiple Laplacian graphs with automatic weight parameters to better fit the inherent manifold structure of the original data.This paper also presents an effective algorithm for solving MGNMFAN.The algorithm comparison experiments on various image data sets verify the clustering ability of the algorithm.