Research Of Clustering Algorithm For Adaptive Graph Regularized Non-negative Matrix Factorization

With the advent of the big data era,the data information generated and transmitted by people is getting bigger and bigger,and its dimensions are getting higher and higher.How to deal with massive high-dimensional data and find a suitable low-dimensional data representation has become an important topic in data mining,pattern recognition and computer vision.In practical applications,the initial dimensionality of data is often very high,leading to many bottlenecks in processing them,so the problem of dimensionality reduction arises.The Non-negative Matrix Factorization algorithm is a popular dimensionality reduction method.It decomposes the original input high-dimensional output data matrix into a base matrix and a representation matrix,which can effectively express the relationship between the part and the whole.Although nonnegative matrix factorization model is currently an important direction in the field of machine learning research,and has in the image,face recognition,text mining,clustering has been widely used in such fields as computer vision,but the existing nonnegative matrix decomposition model still faces the following questions:(1)Faced with the problem of the finitude of the representation of single class center by the existing clustering methods,the existing clustering center representation methods will lead to the degradation of clustering performance.(2)Faced with the low-rank problem of category representation matrix in clustering,the existing methods fail to consider that the category structure attributes of the original data are all hidden in its low-rank part,thus affecting the clustering performance.(3)Faced with the noise problem of unknown linear subspace in clustering,most existing methods ignore the noise influence of original data,thus affecting the performance.Based on different clustering scenarios and problems,we mainly study the non-negative matrix factorization algorithm based on adaptive graph regularization to solve the above three problems.The main research work and results are as follows:(1)The Manifold Peaks Adaptive Graph regularized Non-negative Matrix Factorization algorithm is proposed to solve the finiteness of single class center point representation in the composition problem.Each category of general data is represented by one or more central points,and this representation often depends on whether the chosen central point can better describe the characteristics and structure of the data,so this representation is vague and crude.In order to solve the problems,we use the Geodesic Density Peaks algorithm to find multiple peak points from the data,then use the manifold structure of peak points to construct the graph smoothness regularization term,and finally use the low-dimensional embedded manifold structure to construct the spectral cluster graph regularization term to complete the clustering.Clustering experiments on a large number of real data sets show that our algorithm can make better use of the data structure information,so as to improve the clustering performance(2)The Low-rank Adaptive Graph regularized Non-negative Matrix Factorization algorithm is proposed to deal with the low-rank problem of category representation matrices.In practice,the common basic information of an image category is hidden in its low rank.In order to obtain an effective low-rank data representation,the low-rank approximation of the original data matrix is obtained by the low-rank matrix restoration algorithm,and then the low-rank approximation is obtained by the non-negative matrix decomposition.Finally,the spectral graph is constructed by the coefficient matrix.Clustering experiments on multiple face images and handwritten digital datasets show that the proposed model can better mine low-rank representations of raw data.(3)The Adaptive Neighborhood Projection Graph regularized Non-negative Matrix Factorization algorithm is proposed to deal with the noise problem of unknown linear subspace.In the face of unknown data sampled in different linear subspaces,and many of the data contain noise,performance will be affected.In order to solve this problem,we first decompose the original data by projecting the projection matrix into the subspace to reduce the influence of noise in the input space,and then use the data point adaptive learning to construct the similarity matrix,the spectral clustering term and self-adaptive learning.Experiments on datasets show that our model is effective in mitigating the effects of original spatial noise on clustering performance.