Research On Robust Spectral Clustering Algorithm Based On Low-rank Representation And Laplacian Graph Construction

With the rapid development of information technology,massive amounts of data can be generated and stored.How to dig out useful information from these data has become a research hotspot in recent years.Spectral clustering algorithm is a classic clustering algorithm in the field of data mining,which has a good performance on data with complex structure.However,data in actual production and life inevitably have noise,occlusion and information redundancy,which greatly affects the performance of traditional spectral clustering.In order to solve the above problems,we propose a robust spectral clustering algorithm based on low-rank representation and Laplacian graph construction on the basis of traditional spectral clustering.Specifically,the main work of this article is as follows:1.In order to improve the robustness of traditional spectral clustering algorithms,we propose a robust spectral clustering algorithm based on low-rank sample expression.Different from the traditional method,we use a combination of sample low-rank representation and Laplacian graph learning for cluster structure learning.Because the low-rank representation can well capture the global structure of the data,it can resist the interference of noise.The noise-removing structure obtained by the lowrank representation is embedded in the process of Laplacian graph learning.The sample affinity graph allows the algorithm not only to obtain the global structure of the data but also to consider the local structure between data samples.The clustering performance of our algorithm on several public data sets with different noises is higher than that of the comparison algorithm.The experimental results prove that our algorithm is robust to noisy data and has good clustering performance.2.Considering that the performance of the clustering performance of the spectral clustering algorithm largely depends on the quality of the affinity graph,and the sample affinity graph is usually pre-constructed,and the clustering process and the construction of the affinity graph are step-by-step.The sample affinity maps of existing methods are mostly constructed based on Euclidean distance,and outliers or noise will weaken the ability of the affinity map to reveal the manifold structure of the sample.Therefore,we propose a robust spectral clustering algorithm for lowrank sample expression and adaptive graph construction,which specifically puts the construction of affinity graphs and the learning of clustering structures into the same framework.And because of the low-rank representation of the sample,the robust affinity graph is no longer severely affected by noise.The clustering performance on several well-known public data sets with different noises has proved the effectiveness of the algorithm.3.Based on the robust spectral clustering algorithm constructed by the abovementioned low-rank sample expression and adaptive graph,we developed a damaged image recovery system.The operating results of the system are good,and the interface of the system is friendly,which can meet the task of picture restoration in the presence of different types of picture damage or noise.The good performance of the system also proves the actual effectiveness of our proposed algorithm.