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

A Convex Formulation for Spectral Shrunk Clustering

Spectral clustering is a fundamental technique in the field of data mining and information processing. Most existing spectral clustering algorithms integrate dimensionality reduction into the clustering process assisted by manifold learning in the original space. However, the manifold in reduced-dimensional subspace is likely to exhibit altered properties in contrast with the original space. Thus, applying manifold information obtained from the original space to the clustering process in a low-dimensional subspace is prone to inferior performance. Aiming to address this issue, we propose a novel convex algorithm that mines the manifold structure in the low-dimensional subspace. In addition, our unified learning process makes the manifold learning particularly tailored for the clustering. Compared with other related methods, the proposed algorithm results in more structured clustering result. To validate the efficacy of the proposed algorithm, we perform extensive experiments on several benchmark datasets in comparison with some state-of-the-art clustering approaches. The experimental results demonstrate that the proposed algorithm has quite promising clustering performance.Comment: AAAI201

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

An Attention-based Collaboration Framework for Multi-View Network Representation Learning

Learning distributed node representations in networks has been attracting increasing attention recently due to its effectiveness in a variety of applications. Existing approaches usually study networks with a single type of proximity between nodes, which defines a single view of a network. However, in reality there usually exists multiple types of proximities between nodes, yielding networks with multiple views. This paper studies learning node representations for networks with multiple views, which aims to infer robust node representations across different views. We propose a multi-view representation learning approach, which promotes the collaboration of different views and lets them vote for the robust representations. During the voting process, an attention mechanism is introduced, which enables each node to focus on the most informative views. Experimental results on real-world networks show that the proposed approach outperforms existing state-of-the-art approaches for network representation learning with a single view and other competitive approaches with multiple views.Comment: CIKM 201

Similarity Learning via Kernel Preserving Embedding

Data similarity is a key concept in many data-driven applications. Many algorithms are sensitive to similarity measures. To tackle this fundamental problem, automatically learning of similarity information from data via self-expression has been developed and successfully applied in various models, such as low-rank representation, sparse subspace learning, semi-supervised learning. However, it just tries to reconstruct the original data and some valuable information, e.g., the manifold structure, is largely ignored. In this paper, we argue that it is beneficial to preserve the overall relations when we extract similarity information. Specifically, we propose a novel similarity learning framework by minimizing the reconstruction error of kernel matrices, rather than the reconstruction error of original data adopted by existing work. Taking the clustering task as an example to evaluate our method, we observe considerable improvements compared to other state-of-the-art methods. More importantly, our proposed framework is very general and provides a novel and fundamental building block for many other similarity-based tasks. Besides, our proposed kernel preserving opens up a large number of possibilities to embed high-dimensional data into low-dimensional space.Comment: Published in AAAI 201