Research On Data Dimensionality Reduction And Clustering Based On Low Rank Laplacian Graph Learning

Spectral graph learning method models the relationships between data objects in the form of a graph to reveal the intrinsic structural information of a dataset.It has been widely used in various fields,such as data dimensionality reduction and clustering analysis.However,the presence of noise in the data can greatly affect the quality of the constructed graph,thereby reducing the effectiveness of graph-based methods for data dimensionality reduction and clustering analysis.To address this issue,this paper proposes a robust dimensionality reduction method based on low-rank Laplacian graph and a clustering method based on multi-view consensus and uniqueness.The main research work and innovations of this paper are as follows:1.In response to the problem of reduced performance of graph-based data dimensionality reduction algorithms due to hidden noise in the data,this paper proposes a robust data dimensionality reduction method based on low-rank Laplacian graph learning(LRLGL)to better acquire the intrinsic structural information of the data and achieve robust data dimensionality reduction.The low-rank Laplacian graph is a graph structure that combines a Laplacian regularization term that represents the sample distance and a low-rank representation that represents the data subspace structure.Its integrated low-rank representation can robustly separate real data from noise in the data to reduce the interference of noise in obtaining the structural information of the data.Moreover,the graph structure is more discriminative under the constraint of graph Laplacian rank,implicitly dividing the data objects into connected components,further improving the data dimensionality reduction performance of the algorithm.In a series of noise and occlusion experiments on synthetic data and multiple public datasets,the proposed algorithm demonstrates excellent robust data dimensionality reduction performance.2.In response to the problem that existing graph-based multi-view clustering algorithms cannot fully acquire the internal information of each view of the data and do not properly address the inconsistent information among multiple views,this paper proposes a multi-view clustering method based on low-rank Laplacian graph consensus and distinctiveness(GMCFC).This method is based on the previously proposed low-rank Laplacian graph learning,which properly addresses the problem that the view structure information cannot be fully and robustly acquired when noise exists in the data.Moreover,it uses the sparsity of noise in inconsistent information among views to extract irrelevant information,such as noise,from the inconsistent information among views using the residual product regularization term between views,which preserves unique and useful information in the structure information obtained from each view.The proposed algorithm is validated on synthetic data and multiple public multi-view datasets,and the results show that it is robust in multi-view clustering and has high clustering accuracy.3.Based on the previously proposed multi-view clustering algorithm,this paper has developed an image clustering system.The system is designed to meet people’s needs for storing and clustering images,using mainstream technology architecture and reasonable design of system functions.The system’s performance verifies the effectiveness of the proposed algorithm and demonstrates its practical value for real-world applications.