Research On Graph Construction Algorithm Based On Low Rank Representation In Graph Based Semi Supervised Learning

In practical classification applications,obtaining labeled samples can be costly and difficult.Semi-supervised learning utilizes the ability to classify unlabeled samples with a small number of labeled samples,and has significant practical value.Graph-based semi-supervised learning methods have gained attention due to their superior classification accuracy.However,constructing a graph that reveals the underlying relationships between data is challenging due to the large amount of data and complex connections between them.Therefore,this thesis proposes a low-rank local manifold information graph construction method to facilitate label propagation.Specifically,the proposed method captures the global subspace structure of the data by adopting low-rank representation on the overall structure,and improves the method further by introducing local constraints to capture the local structure of the data.Additionally,a regularization term based on the k-nearest neighbor approach is used to capture the manifold information between data,leading to a more discriminative graph structure.The proposed method is experimentally demonstrated to achieve high classification accuracy.To address the high computational complexity of graph construction,an accelerated graph construction method is proposed based on the low-rank local manifold information graph.Specifically,the optimization problem is solved using the adaptive penalty alternating direction method,which involves multiple singular value decompositions,leading to high computational complexity.To overcome this,the proposed method combines matrix factorization with kernel norm optimization to perform singular value decomposition on the data matrix,resulting in a smaller target matrix.The resulting coefficient matrix is used for graph construction.Experimental results demonstrate that the proposed method reduces computational complexity and achieves fast graph construction.To avoid suboptimal solutions resulting from separate graph construction and inference algorithms,this thesis proposes a unified optimization framework based on pseudo label constraints.The proposed method integrates the local manifold information graph construction and label propagation stages into a unified optimization framework to simultaneously learn the graph structure and unknown labels.To improve the effectiveness of the estimated labels,a k-nearest neighbor-based pseudo label selection algorithm is proposed to obtain higher classification accuracy with a small number of labeled samples.Experimental results demonstrate the effectiveness of the proposed method in classification applications and show that it significantly reduces the number of required labeled samples while maintaining classification accuracy.In summary,the proposed graph construction method can be effectively applied to label propagation algorithms to improve classification accuracy.The proposed accelerated graph construction method addresses the problem of low efficiency of graph construction,improving the efficiency of the classification task.Moreover,the proposed unified optimization framework overcomes the limitation of independent graph construction and inference algorithms,and the integration of pseudo label information helps to overcome the problem of insufficient label information.Experimental results on several datasets demonstrate the effectiveness of the proposed method.