Research On Clustering Based On Robust Non-negative Matrix Factorization

With the rapid development of information technology,the era of big data has arrived.Facing the massive amount of data,it becomes especially important to extract useful infor-mation from it and use it rationally.Clustering,as an important topic in the fields of machine learning,data mining and computer vision,has been widely studied in recent years.In most cases,the dimensionality of data in real-world clustering tasks is very high,and traditional clustering algorithms and their variants do not perform well in handling high-dimensional data because of the effects of noise and redundancy.Therefore,Non-Negative Matrix Fac-torization（NMF）has become one of the most popular dimensionality reduction algorithms for clustering tasks due to its good interpretability of data representation and its explicit physical meaning.Usually,NMF minimizes the distance between the original data matrix and the re-construction matrix by Euclidean distance,which is sensitive to non-Gaussian noise and outliers.To address the influence of noisy data and outliers on clustering results and to improve clustering performance,the NMF-based task is handled with correntropy.Three robust NMF-based clustering clustering algorithms is proposed:（1）For the image clustering problem,a robust image clustering algorithm based on manifold regularization is proposed.Using NMF based on correntropy is used as the loss function to suppress the influence of non-Gaussian noise and outliers,while the structure information of the data is fully considered by using manifold regularization,and the non-negative matrix is dual sparse coding by7)_2,1-norm.The Half-Quadratic Optimization Tech-nique is used to optimization,and the convergence and computational complexity are ana-lyzed.Testing on a public image dataset.The experimental results show that the proposed algorithm has good effectiveness and robustness in the image clustering task.（2）A robust clustering algorithm based on doubly stochastic matrix regularization is proposed to address the fixed and non-dynamically updatable situation of the manifold regularization construction graph.Most graph construction methods obtain the original data directly from the initial input graph,which may lead to poor quality of the graph.In order to take full advantage of the local structure of the data and to learn high quality graphs,a doubly random matrix is introduced to achieve dynamic updates of the graph.The algorith-m was tested on multiple types of datasets and the experimental results showed significant improvements.（3）For the multi-view clustering task,in order to address the influence of redundant information on the clustering results,a robust multi-view clustering algorithm is proposed based on robust multi-view clustering algorithm based on non-redundant regularization.The Hilbert-Schmidt independence criterion（HSIC）is introduced to generate non-redundant regularization terms to better focus on the differences between views and reduce redun-dant information between different views.The proposed algorithm is tested on a publicly available multi-view dataset and achieves higher clustering performance compared to other related multi-view methods.