Subspace Clustering Algorithm On Manifolds And Its Applications

Clustering is a fundamental research topic in computer vision and machine learning.However,with the continuous changes in the application environment,especially entering the "big data" era,the sheer size of data and the complexity of the structure pose more and more severe challenges to cluster analysis,especially the higher dimensions of data.Traditional clustering algorithms are usually designed and developed for low-dimensional data.When analyzing and processing high-dimensional data,they usually encounter serious bottlenecks,which cannot meet the sparsity of high-dimensional data and avoid the impact of "Curse of Dimensionality".How to design and develop high-dimensional data clustering algorithms to meet the increasing demand is becoming an important research topic in the fields of data mining and pattern recognition.The representation of high-dimensional nonlinear data has always been a problem that plagues clustering tasks.Although existing clustering algorithms can alleviate this problem through convex relaxation,there is no doubt that this is not the optimal solu-tion to the original problem.In recent years,manifold learning theory has revealed the potential nonlinear low-dimensional manifold structure of image and video data,which has become an effective theory and technical tool for processing and representing high-dimensional data such as image and video.Based on self-expressive-based subspace clus-tering,for image and video clustering task,this dissertation propose several kinds of manifolds subspace clustering method,and give the corresponding optimization solution method.The main work of this paper is summarized as follows:(1)A subspace clustering representation model using multi-order statistical features is proposed.For unsupervised tasks,it is important to make full use of prior information.Based on this,we use multi-order statistical features to describe the dataset from different perspectives and propose Multi-geometric sparse subspace clustering(MGSSC).From the experimental results on datasets such as faces,objects,textures,etc.,it can be seen that the proposed method is feasible and effective.(2)A representation model based on low-rank kernel subspace clustering on SPD manifold is proposed.Experiments have found that constructing the covariance matrix of the sample as the second-order feature of the sample can obtain better clustering performance.This is because the SPD manifold representation of high-dimensional image data has the ability to capture the inherent distribution characteristics of the nonlinear manifold structure of the data.Using the kernel method to map the SPD manifold data to the Reproducing Kernel Hilbert Space(RKHS)may not form a linear subspace structure,which is not conducive to the use of self-expressive methods to obtain a better coefficient matrix.We propose a subspace clustering scheme for SPD manifold data.By introducing a low-rank replacement of the kernel matrix,Low-rank Kernel Subspace Clustering on the SPD Riemannian manifold(LKSCR)can encourage SPD manifold data to form a linear subspace structure in the feature space.This is the first time that a multiple kernel clustering model for SPD manifold data has been proposed.Compared with LKSCR,Multiple Kernel Subspace Clustering via A Low-Rank Consensus Kernel Learning on Symmetric Positive Definite Manifolds(LMKSCR)can automatically learn the most suitable consensus core from a set of predefined SPD candidate kernels,and can well adapt to SPD manifold data.In addition,we find that both the LKSCR and LMKSCR introduce an error matrix,which can reduce the negative impact of polluting data points.(3)A new sparse representation method based on Grassmann manifold namely One-step Kernelized Sparse Clustering on Grassmann Manifolds(G-OKSC).First of all,the image set and video data are constructed by using the orthogonal subspace-based manifold representation method to construct the Grassmann manifold representation of the data.In order to further explore the inherent geometric distance between the data on the Grassmann manifold,we use the kernel method to map the Grassmann manifold data into the Reproducing Kernel Hilbert Space(RKHS).In addition,we introduce a low-rank replacement of the kernel matrix to encourage the manifold data to form a linear subspace structure in the high-dimensional feature space,which will help us to use the self-expressive property to obtain a better coefficient matrix.Moreover,applying low-rank constraints to the Laplacian matrix of the learned similarity matrix can prompt us to learn the coefficient matrix and the clustering index at the same time.(4)A multi-manifold subspace clustering representation model for behavior-recognition video data is proposed.For video data,especially behavioral datasets,temporal informa-tion may help the clustering performance.In addition,the sound information correspond-ing to different behavior videos is often very discriminative.Based on this observation,we use the image information in the original video data as the basis,by extracting the optical flow characteristics of the video and the corresponding sound information of the video,and modeling it into the manifold space,and propose Multiple-Manifold Learning by Cross-Modal Audio-Video Subspace Clustering(M-AVSC).By learning the differences between multi-manifold representations,multiple-manifold representations can complement each other,thereby enhancing the clustering performance for video data.