Low-Rank and Sparse Decomposition for Hyperspectral Image Enhancement and Clustering

In this dissertation, some new algorithms are developed for hyperspectral imaging analysis enhancement. Tensor data format is applied in hyperspectral dataset sparse and low-rank decomposition, which could enhance the classification and detection performance. And multi-view learning technique is applied in hyperspectral imaging clustering. Furthermore, kernel version of multi-view learning technique has been proposed, which could improve clustering performance. Most of low-rank and sparse decomposition algorithms are based on matrix data format for HSI analysis. As HSI contains high spectral dimensions, tensor based extended low-rank and sparse decomposition (TELRSD) is proposed in this dissertation for better performance of HSI classification with low-rank tensor part, and HSI detection with sparse tensor part. With this tensor based method, HSI is processed in 3D data format, and information between spectral bands and pixels maintain integrated during decomposition process. This proposed algorithm is compared with other state-of-art methods. And the experiment results show that TELRSD has the best performance among all those comparison algorithms. HSI clustering is an unsupervised task, which aims to group pixels into different groups without labeled information. Low-rank sparse subspace clustering (LRSSC) is the most popular algorithms for this clustering task. The spatial-spectral based multi-view low-rank sparse subspace clustering (SSMLC) algorithms is proposed in this dissertation, which extended LRSSC with multi-view learning technique. In this algorithm, spectral and spatial views are created to generate multi-view dataset of HSI, where spectral partition, morphological component analysis (MCA) and principle component analysis (PCA) are applied to create others views. Furthermore, kernel version of SSMLC (k-SSMLC) also has been investigated. The performance of SSMLC and k-SSMLC are compared with sparse subspace clustering (SSC), low-rank sparse subspace clustering (LRSSC), and spectral-spatial sparse subspace clustering (S4C). It has shown that SSMLC could improve the performance of LRSSC, and k-SSMLC has the best performance. The spectral clustering has been proved that it equivalent to non-negative matrix factorization (NMF) problem. In this case, NMF could be applied to the clustering problem. In order to include local and nonlinear features in data source, orthogonal NMF (ONMF), graph-regularized NMF (GNMF) and kernel NMF (k-NMF) has been proposed for better clustering performance. The non-linear orthogonal graph NMF combine both kernel, orthogonal and graph constraints in NMF (k-OGNMF), which push up the clustering performance further. In the HSI domain, kernel multi-view based orthogonal graph NMF (k-MOGNMF) is applied for subspace clustering, where k-OGNMF is extended with multi-view algorithm, and it has better performance and computation efficiency

Contribution to Graph-based Multi-view Clustering: Algorithms and Applications

185 p.In this thesis, we study unsupervised learning, specifically, clustering methods for dividing data into meaningful groups. One major challenge is how to find an efficient algorithm with low computational complexity to deal with different types and sizes of datasets.For this purpose, we propose two approaches. The first approach is named "Multi-view Clustering via Kernelized Graph and Nonnegative Embedding" (MKGNE), and the second approach is called "Multi-view Clustering via Consensus Graph Learning and Nonnegative Embedding" (MVCGE). These two approaches jointly solve four tasks. They jointly estimate the unified similarity matrix over all views using the kernel tricks, the unified spectral projection of the data, the clusterindicator matrix, and the weight of each view without additional parameters. With these two approaches, there is no need for any postprocessing such as k-means clustering.In a further study, we propose a method named "Multi-view Spectral Clustering via Constrained Nonnegative Embedding" (CNESE). This method can overcome the drawbacks of the spectral clustering approaches, since they only provide a nonlinear projection of the data, on which an additional step of clustering is required. This can degrade the quality of the final clustering due to various factors such as the initialization process or outliers. Overcoming these drawbacks can be done by introducing a nonnegative embedding matrix which gives the final clustering assignment. In addition, some constraints are added to the targeted matrix to enhance the clustering performance.In accordance with the above methods, a new method called "Multi-view Spectral Clustering with a self-taught Robust Graph Learning" (MCSRGL) has been developed. Different from other approaches, this method integrates two main paradigms into the one-step multi-view clustering model. First, we construct an additional graph by using the cluster label space in addition to the graphs associated with the data space. Second, a smoothness constraint is exploited to constrain the cluster-label matrix and make it more consistent with the data views and the label view.Moreover, we propose two unified frameworks for multi-view clustering in Chapter 9. In these frameworks, we attempt to determine a view-based graphs, the consensus graph, the consensus spectral representation, and the soft clustering assignments. These methods retain the main advantages of the aforementioned methods and integrate the concepts of consensus and unified matrices. By using the unified matrices, we enforce the matrices of different views to be similar, and thus the problem of noise and inconsistency between different views will be reduced.Extensive experiments were conducted on several public datasets with different types and sizes, varying from face image datasets, to document datasets, handwritten datasets, and synthetics datasets. We provide several analyses of the proposed algorithms, including ablation studies, hyper-parameter sensitivity analyses, and computational costs. The experimental results show that the developed algorithms through this thesis are relevant and outperform several competing methods

Consensus graph and spectral representation for one-step multi-view kernel based clustering

Recently, multi-view clustering has received much attention in the fields of machine learning and pattern recognition. Spectral clustering for single and multiple views has been the common solution. Despite its good clustering performance, it has a major limitation: it requires an extra step of clustering. This extra step, which could be the famous k-means clustering, depends heavily on initialization, which may affect the quality of the clustering result. To overcome this problem, a new method called Multiview Clustering via Consensus Graph Learning and Nonnegative Embedding (MVCGE) is presented in this paper. In the proposed approach, the consensus affinity matrix (graph matrix), consensus representation and cluster index matrix (nonnegative embedding) are learned simultaneously in a unified framework. Our proposed method takes as input the different kernel matrices corresponding to the different views. The proposed learning model integrates two interesting constraints: (i) the cluster indices should be as smooth as possible over the consensus graph and (ii) the cluster indices are set to be as close as possible to the graph convolution of the consensus representation. In this approach, no post-processing such as k-means or spectral rotation is required. Our approach is tested with real and synthetic datasets. The experiments performed show that the proposed method performs well compared to many state-of-the-art approaches