Research On Graph Embedded Clustering Models

With the development of science and technology and the arrival of the era of big data,clustering,as a typical unsupervised machine learning method,has received great attention of researchers and engineers in recent years.From the perspective of the number of views in the data,existing clustering methods can be simply divided into two categories,i.e.,single-view clustering and multi-view clustering.Graph embedding based method is one of the mainstream methods in the field of clustering.Although researchers have proposed a large number of graph embedding based single-view clustering and multi-view clustering methods in the past decades,these methods still have some shortcomings.For example,the existing graph embedding based single-view clustering methods mainly have the following defects: 1)These methods cannot obtain the affine graph that captures the intrinsic structure of data.2)These methods are not robust to noise and their performance generally decreases significantly on noisy data.For the existing multi-view clustering methods,especially the graph embedding based multi-view clustering methods,due to the defect of their models,these methods fail to deal with the multi-view clustering tasks with missing views.This dissertation mainly studies the graph embedding based clustering methods,and focus on designing more robust and flexible graph embedded clustering models to solve the above problems and improve the clustering performance.Specifically,the following clustering methods are proposed in this dissertation:(1)To address the problem of traditional graph embedding methods that cannot capture the essential structure of data,we propose an affine graph learning method based on low-rank representation and adaptive graph regularization.The proposed method introduces a distance based regularization term and a nonnegative graph constraint to the low-rank representation framework,which makes the model sufficiently exploit the global representation information and local distance information for affine graph construction.To guarantee the exact connection components of the learned affine graph,the proposed method further introduces a Laplacian graph based rank constraint to the model.By integrating the above constraints and low-rank representation into a unified optimization framework,the proposed method can adaptively learn the affine graph that captures the essential structure of data,such that a better clustering performance can be obtained.Experimental results on a synthetic database and many real-world databases verify the effectiveness of the proposed method.(2)To address the problem that most graph embedding based single-view clustering methods are not robust to noise,we propose a robust affine graph learning method based on adaptive weighted nonnegative low-rank representation.By analyzing the existing representation based affine graph learning methods,we find that these methods treat all features equally during the affine graph learning,which will make the noises and outliers interfere or even dominate the self-representation based affine graph learning.Based on this finding,the proposed method introduces a weighted matrix constraint to the selfrepresentation based affine graph learning model.This approach not only can adaptively enhance the contribution of the important features during the representation,but also can reduce the negative influence of noise,and thus can enhance the robustness to noise.In addition,the proposed method also introduces a distance based regularization term and a nonnegative constraint,which not only enables the model to exploit the global and local information of data for affine graph construction,but also enhances the interpretability of the affine graph.We have compared many state-of-the-art clustering methods on several noisy databases and real-world databases.Experimental results show that the proposed method not only obtains the best clustering performance,but also improves the robustness to noise.(3)To solve the view missing problem of multi-view clustering,we propose a graph embedding based incomplete multi-view clustering method.Based on the low-rank representation model,the proposed method adaptively learns some affine graphs from the available instances of all views,then it expands the graphs to the same dimension by using the technique of matrix elementary transformation.To achieve a consensus representation of all views,the proposed method further introduces a spectral clustering based constraint and a co-regularization constraint.By jointly optimizing the model,the proposed method can effectively reduce the negative influence caused by the incomplete views,and sufficiently exploits the diversity information and complementary information among all views to guide the consensus representation learning,and thus can obtain a better clustering performance.Experimental results conducted on several incomplete multi-view databases validate the effectiveness of the proposed method on incomplete multi-view clustering tasks.(4)Existing incomplete multi-view clustering methods suffer from the following two issues which restrict their performance: 1)ignoring the imbalance property of the discriminant information of all views;2)cannot fully explore the complementary information among all views.To address the above problems and improve the clustering performance,we propose a graph embedding and views inferring based incomplete multi-view clustering method.To recover the missing views,a feature based Laplacian constraint is introduced to the matrix factorization model.This approach not only ensures all views to be naturally aligned and allows the model to make better use of the complementary information of multiple views,but also enables the model to use the recovered missing views for model training.To explore the local information of data,a reverse graph constraint is introduced to the model.This approach is beneficial to obtain more reasonable missing views.Considering that all views may have different degrees of discriminant information,the proposed method further introduces an adaptive weighted constraint to balance the importance of different views during the model training phase,which is beneficial to make full use of the diversity information of multiple views.Experimental results on two incomplete clustering tasks(i.e.,views are absent under special condition and arbitrary condition)show that the proposed method can improve the clustering performance effectively.In summary,some more robust and flexible graph embedded clustering models are proposed to address the shortcomings of the traditional graph embedding based clustering methods in this dissertation.In addition,we deeply analyze the reasonability of the proposed method from the theoretical view.We have compared many state-of-the-art methods on several datasets and the experimental results prove the effectiveness of the proposed clustering models.