Research On Robust Clustering Algorithm Based On Symmetric Nonnegative Matrix Factorization

As a graph-based clustering algorithm,symmetric nonnegative matrix factorization（SNMF）can capture the clustering structure embedded in graph representation more naturally,and get better clustering results on linear and nonlinear data,but it is sensitive to the initialization of variables.In addition,the standard SNMF algorithm uses the sum of squares of errors to measure the quality of decomposition,which is sensitive to noise and outliers.In order to solve these problems,a robust adaptive symmetric nonnegative matrix factorization clustering algorithm（RS³NMF）is proposed from the perspective of ensemble learning.Furthermore,the discriminant ability of projection matrix is enhanced by combining the label information of training set,and a robust adaptive learning discriminant symmetric nonnegative matrix decomposition algorithm（RADS³NMF）is proposed by integrating robustness、adaptive graph learning and label information into SNMF framework.The main research contents of this paper include the following two parts:Inspired by robust nonnegative matrix factorization,adaptive methods and ensemble learning,a robust adaptive symmetric nonnegative matrix factorization clustering algorithm（RS³NMF）is constructed,which integrates robustness into the SNMF framework.The norm-based RS³NMF model alleviates the influence of noise and outliers,maintains the invariance of feature rotation and improves the robustness of the model.At the same time,without any additional information,the clustering performance is gradually enhanced by using the sensitivity of SNMF to initialization features.The alternating iteration method is used to optimize and ensure the convergence of the objective function value.A large number of experimental results show that the proposed RS³NMF algorithm is superior to other advanced algorithms and has strong robustness.In addition,the application of GDP data of 31 provinces and cities in China shows that the robust clustering algorithm can judge the development differences among provinces and has good practical application value.Inspired by the spatial clustering self-expression learning method,a robust adaptive learning discriminant symmetric nonnegative matrix factorization algorithm（RADS³NMF）is constructed by introducingnorm、adaptive learning and label information.Specifically,firstly,the affinity matrix is represented by the obtained self-representation coefficient,and the discrimination ability of the projection matrix is enhanced by using the label information of the training set;Secondly,the model is optimized,the auxiliary function is constructed,the convergence of the model is proved,and the algorithm complexity of the model is given.Finally,using the hourly concentration data of nitrogen dioxide（NO₂）pollutants in Beijing in a certain period of time,the algorithm is applied to the cluster analysis of air quality monitoring stations in Beijing.The results show that RADS³NMF algorithm can better identify the spatial layout of air quality monitoring stations and has good applicability.