| Image clustering has always been a hot research topic in the field of machine learning.Its main task is to divide the data into many different categories.In the past 20 years,non-negative matrix factorization(NMF)algorithm has attracted extensive attention due to its good performance in data clustering applications.Non-negative matrix factorization is mainly to decompose the original data matrix into two subfactor matrices with non-negative constraints,it can extract local image features and has a good clustering interpretation.However,with the advent of the era of big data,the image data collected in real life is more and more complex,which usually contains a lot of hidden hierarchical information,and is difficult to be processed by the traditional single-layer NMF algorithm.With the development of deep learning,researchers found that the deep model with multi-layer structure has the ability to extract the hidden hierarchical information of data,which is mainly reflected in the fact that different layers can extract different data features.And deep model can learn the low-rank representation of data with more representation ability,which has a significant improvement in the processing of clustering tasks.Therefore,the deep structure of the matrix factorization algorithm and its application have become a new research hotspot in recent years.Firstly,this paper describes the research background and significance of non-negative matrix factorization algorithm and image clustering,then comprehensively analyzes the research status of deep matrix factorization model and image clustering,after that points out the existing problems of deep matrix factorization model,and designs corresponding solutions.The main contributions of this paper are as follows:(1)In order to solve the problem that the existing deep semi-non-negative matrix factorization algorithms can not make use of the manifold structure information of data,we consider the graph constrained regularization technique.By using the k-nearest neighbor method,we construct the graph Laplacian matrix for the input data matrix,and apply the graph matrix to the learning process of low-rank representation matrix,so that the learned low-rank representation matrix can effectively retain the original data manifold structure information.Secondly,to solve the problem that the existing deep matrix factorization algorithms are difficult to guarantee the convergence,we use the forward-backward splitting algorithm to solve the graph constrained deep semi-non-negative matrix factorization model.At the same time,we analyze its convergence and prove that the sequence generated by the proposed algorithm can steadily descend and converge to a critical point.Through the experiments on four image datasets,we compare five matrix factorization methods,and our method can achieve the best clustering performance.(2)Aiming at the problem that the existing deep matrix factorization methods can not make full use of the characteristics of data in processing multi-view image clustering tasks,we propose a deep matrix factorization framework based on partially shared structure,which divides the representation matrix into common part and independent part.It can mine the consistency and complementarity information of multi-view data at the same time,enrich the information of low-rank representation matrix,and improve the clustering performance.Secondly,in view of the problem that the existing deep matrix factorization multi-view methods are unsupervised models and can not consider the prior label information,we add the label regression technology to make full use of the prior label information and construct a semi-supervised deep matrix decomposition model.In addition,we also introduce self-weight and graph constraint technology to further improve the clustering performance of the model.On four classic multi-view image datasets,we compare the unsupervised and semi-supervised classical clustering algorithms,and our methods have achieved better performance in most cases... |
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