Research On Image Clustering And Dimensionality Reduction Method Based On Low-rank And Sparse Representation

In real world,a large number of image data are produced every moment.Due to high-dimensional,massive and noisy of images,labeling these image data is not only time-consuming and labor-intensive,but also has a very serious subjective dependency problem.Therefore,clustering unlabeled images has become a research hotspot and difficulty in the fields of pattern recognition.Meantime,the high-dimensional features of image data not only increase the computational difficulty and storage consumption of the computer,but also bring about the problem of “curse of dimensionality”.Therefore,dimensionality reduction of image data with high-dimensional features has also become one of the hot research points.In recent years,low-rank or sparse representation-based learning methods have been gradually proposed to deal with the problems of high redundancy,high dimensions,and complex data space structures in high-dimensional images.In terms of current research status,research methods based on low-rank or sparse representation can not only solve the bottleneck problems encountered by traditional clustering methods,but also effectively solve the problem that traditional dimensionality reduction algorithms do not have obvious dimensionality reduction effects on large data sets.In view of these two aspects of research,this thesis takes unsupervised learning,graph construction,and subspace learning as carriers,and applies low-rank and sparse representation for the problems of image clustering and dimensionality reduction.The main work and innovations of this thesis are summarized as follows:1.The method based on low-rank or sparse representation has the problem that the local geometric structure and global structure of the data cannot be obtained at the same time.To alleviate the issue,this thesis proposed a novel subspace clustering method termed structure-constrained symmetric low-rank representation.By fusing a weighted sparse constraint and a symmetric constraint into the low-rank representation of highdimensional image data,the developed method can not only reveal the global mixture of subspaces structure and the locally linear structure of the data,but also guarantee the weights of each pair of data points in subspaces are consistent.Extensive experimental results on benchmark datasets show that the proposed method can well reveal the structure of complex subspace and yield promising clustering performance in comparison with several state-of-the-art methods.2.Representation learning based on low-rank or sparse and subspace learning are two independent steps,that is,firstly,a similarity matrix is learned from the data using sparse or low-rank minimization techniques.Secondly,subspace learning is performed based on this similarity matrix.Since representation learning and subspace learning are two independent steps,the constructed similarity matrix may not be suitable for subsequent subspace learning,which also makes it difficult for the subspace learning algorithm based on representation learning to obtain a global optimum.On this problem,this thesis proposed an algorithm based on representation learning and subspace joint learning.By combining low-rank representation,weighted sparse representation,and low-dimensional subspace learning into a unified framework for joint learning and more robust feature extraction.Such a subspace learning method can not only solve problems outside the sample,but also learn the optimal representation matrix and low-dimensional projection matrix.