Research On Graph Regularized Clustering Methods

Massive data is a huge challenge for training traditional supervised learning models,because it is impractical to manually labele the dynamically adding samples.Luckily,the unsupervised learning method can replace the supervised learning method in the data analysis task.In unsupervised learning,clustering can intuitively analyze data,and its goal is to divide unlabeled data into several clusters ensuring that similar samples are clustered into clusters.Given its intuitive practical meaning,clustering algorithms have been widely used in tasks such as image segmentation,pattern recognition,and data mining.Manifold learning believes that high-dimensional data can be regarded as the em-bedding of low-dimensional manifolds in high-dimensional space,so many clustering algorithms project the original high-dimensional data into low-dimensional space to get a simpler representation.Subspace clustering projects each cluster into the corresponding low-dimensional subspace and deep clustering algorithm uses deep network to get deep embedding of data.Traditional clustering algorithm does not use the similarity informa-tion between samples,it can not mine the manifold structure of the data,and it is difficult to obtain the global optimal solution in the complex sample space.The graph regularized clustering algorithm maintains the similarity between samples during the projection of data,thereby retaining the geometric structure of the data in low-dimensional projection.This paper proposes three graph regularized clustering models:1)Graph-Laplacian correlated low-rank representation clustering model.This paper combines a trace loss based on the F norm with Graph-Laplacian regularization to capture the local correlation of the data.Meanwhile,the matrix reconstruction is used to obtain the low-rank representation of the data,which makes the data structure clearer,thereby improving clustering accuracy.Experiments of motion segmentation and image clustering confirm the efficacy of the model.2)Correlation self-expression shrunk clustering model.This paper uses the exact Schatten p norm to approximate the low rank constraint,and the affinity matrix is induced of both sparse and dense representation.Meanwhile,adaptive shrunk pattern is used to reduce the deviation of similar samples.Experiments on four image clustering tasks verify the efficacy of the model.3)Deep clustering on approximate uniform manifolds.This paper designs a two-stage training model to consider manifold structure while clustering.In the first stage,this paper pull similar samples together and push different samples far away under the proposed similarity metric.In the second stage,this paper use the Kullback-Leibler divergence of two proposed distributions to enhance the clustering performance.Experiments on four clustering tasks verify the efficacy of the model.