Structured Graph Learning for Clustering and Semi-supervised Classification

Graphs have become increasingly popular in modeling structures and interactions in a wide variety of problems during the last decade. Graph-based clustering and semi-supervised classification techniques have shown impressive performance. This paper proposes a graph learning framework to preserve both the local and global structure of data. Specifically, our method uses the self-expressiveness of samples to capture the global structure and adaptive neighbor approach to respect the local structure. Furthermore, most existing graph-based methods conduct clustering and semi-supervised classification on the graph learned from the original data matrix, which doesn't have explicit cluster structure, thus they might not achieve the optimal performance. By considering rank constraint, the achieved graph will have exactly $c$ connected components if there are $c$ clusters or classes. As a byproduct of this, graph learning and label inference are jointly and iteratively implemented in a principled way. Theoretically, we show that our model is equivalent to a combination of kernel k-means and k-means methods under certain condition. Extensive experiments on clustering and semi-supervised classification demonstrate that the proposed method outperforms other state-of-the-art methods.

On Deep Unsupervised Active Learning

Unsupervised active learning has attracted increasing attention in recent years, where its goal is to select representative samples in an unsupervised setting for human annotating. Most existing works are based on shallow linear models by assuming that each sample can be well approximated by the span (i.e., the set of all linear combinations) of certain selected samples, and then take these selected samples as representative ones to label. However, in practice, the data do not necessarily conform to linear models, and how to model nonlinearity of data often becomes the key point to success. In this paper, we present a novel Deep neural network framework for Unsupervised Active Learning, called DUAL. DUAL can explicitly learn a nonlinear embedding to map each input into a latent space through an encoder-decoder architecture, and introduce a selection block to select representative samples in the the learnt latent space. In the selection block, DUAL considers to simultaneously preserve the whole input patterns as well as the cluster structure of data. Extensive experiments are performed on six publicly available datasets, and experimental results clearly demonstrate the efficacy of our method, compared with state-of-the-arts.

Relation-Guided Representation Learning

Deep auto-encoders (DAEs) have achieved great success in learning data representations via the powerful representability of neural networks. But most DAEs only focus on the most dominant structures which are able to reconstruct the data from a latent space and neglect rich latent structural information. In this work, we propose a new representation learning method that explicitly models and leverages sample relations, which in turn is used as supervision to guide the representation learning. Different from previous work, our framework well preserves the relations between samples. Since the prediction of pairwise relations themselves is a fundamental problem, our model adaptively learns them from data. This provides much flexibility to encode real data manifold. The important role of relation and representation learning is evaluated on the clustering task. Extensive experiments on benchmark data sets demonstrate the superiority of our approach. By seeking to embed samples into subspace, we further show that our method can address the large-scale and out-of-sample problem.

Two-Dimensional Semi-Nonnegative Matrix Factorization for Clustering

In this paper, we propose a new Semi-Nonnegative Matrix Factorization method for 2-dimensional (2D) data, named TS-NMF. It overcomes the drawback of existing methods that seriously damage the spatial information of the data by converting 2D data to vectors in a preprocessing step. In particular, projection matrices are sought under the guidance of building new data representations, such that the spatial information is retained and projections are enhanced by the goal of clustering, which helps construct optimal projection directions. Moreover, to exploit nonlinear structures of the data, manifold is constructed in the projected subspace, which is adaptively updated according to the projections and less afflicted with noise and outliers of the data and thus more representative in the projected space. Hence, seeking projections, building new data representations, and learning manifold are seamlessly integrated in a single model, which mutually enhance other and lead to a powerful data representation. Comprehensive experimental results verify the effectiveness of TS-NMF in comparison with several state-of-the-art algorithms, which suggests high potential of the proposed method for real world applications.

Multi-view Subspace Clustering via Partition Fusion

Multi-view clustering is an important approach to analyze multi-view data in an unsupervised way. Among various methods, the multi-view subspace clustering approach has gained increasing attention due to its encouraging performance. Basically, it integrates multi-view information into graphs, which are then fed into spectral clustering algorithm for final result. However, its performance may degrade due to noises existing in each individual view or inconsistency between heterogeneous features. Orthogonal to current work, we propose to fuse multi-view information in a partition space, which enhances the robustness of Multi-view clustering. Specifically, we generate multiple partitions and integrate them to find the shared partition. The proposed model unifies graph learning, generation of basic partitions, and view weight learning. These three components co-evolve towards better quality outputs. We have conducted comprehensive experiments on benchmark datasets and our empirical results verify the effectiveness and robustness of our approach.

Structure Learning with Similarity Preserving

Leveraging on the underlying low-dimensional structure of data, low-rank and sparse modeling approaches have achieved great success in a wide range of applications. However, in many applications the data can display structures beyond simply being low-rank or sparse. Fully extracting and exploiting hidden structure information in the data is always desirable and favorable. To reveal more underlying effective manifold structure, in this paper, we explicitly model the data relation. Specifically, we propose a structure learning framework that retains the pairwise similarities between the data points. Rather than just trying to reconstruct the original data based on self-expression, we also manage to reconstruct the kernel matrix, which functions as similarity preserving. Consequently, this technique is particularly suitable for the class of learning problems that are sensitive to sample similarity, e.g., clustering and semisupervised classification. To take advantage of representation power of deep neural network, a deep auto-encoder architecture is further designed to implement our model. Extensive experiments on benchmark data sets demonstrate that our proposed framework can consistently and significantly improve performance on both evaluation tasks. We conclude that the quality of structure learning can be enhanced if similarity information is incorporated.

Large-scale Multi-view Subspace Clustering in Linear Time

A plethora of multi-view subspace clustering (MVSC) methods have been proposed over the past few years. Researchers manage to boost clustering accuracy from different points of view. However, many state-of-the-art MVSC algorithms, typically have a quadratic or even cubic complexity, are inefficient and inherently difficult to apply at large scales. In the era of big data, the computational issue becomes critical. To fill this gap, we propose a large-scale MVSC (LMVSC) algorithm with linear order complexity. Inspired by the idea of anchor graph, we first learn a smaller graph for each view. Then, a novel approach is designed to integrate those graphs so that we can implement spectral clustering on a smaller graph. Interestingly, it turns out that our model also applies to single-view scenario. Extensive experiments on various large-scale benchmark data sets validate the effectiveness and efficiency of our approach with respect to state-of-the-art clustering methods.

Multi-graph Fusion for Multi-view Spectral Clustering

A panoply of multi-view clustering algorithms has been developed to deal with prevalent multi-view data. Among them, spectral clustering-based methods have drawn much attention and demonstrated promising results recently. Despite progress, there are still two fundamental questions that stay unanswered to date. First, how to fuse different views into one graph. More often than not, the similarities between samples may be manifested differently by different views. Many existing algorithms either simply take the average of multiple views or just learn a common graph. These simple approaches fail to consider the flexible local manifold structures of all views. Hence, the rich heterogeneous information is not fully exploited. Second, how to learn the explicit cluster structure. Most existing methods don't pay attention to the quality of the graphs and perform graph learning and spectral clustering separately. Those unreliable graphs might lead to suboptimal clustering results. To fill these gaps, in this paper, we propose a novel multi-view spectral clustering model which performs graph fusion and spectral clustering simultaneously. The fusion graph approximates the original graph of each individual view but maintains an explicit cluster structure. Experiments on four widely used data sets confirm the superiority of the proposed method.

Multiple Partitions Aligned Clustering

Multi-view clustering is an important yet challenging task due to the difficulty of integrating the information from multiple representations. Most existing multi-view clustering methods explore the heterogeneous information in the space where the data points lie. Such common practice may cause significant information loss because of unavoidable noise or inconsistency among views. Since different views admit the same cluster structure, the natural space should be all partitions. Orthogonal to existing techniques, in this paper, we propose to leverage the multi-view information by fusing partitions. Specifically, we align each partition to form a consensus cluster indicator matrix through a distinct rotation matrix. Moreover, a weight is assigned for each view to account for the clustering capacity differences of views. Finally, the basic partitions, weights, and consensus clustering are jointly learned in a unified framework. We demonstrate the effectiveness of our approach on several real datasets, where significant improvement is found over other state-of-the-art multi-view clustering methods.

Latent Multi-view Semi-Supervised Classification

To explore underlying complementary information from multiple views, in this paper, we propose a novel Latent Multi-view Semi-Supervised Classification (LMSSC) method. Unlike most existing multi-view semi-supervised classification methods that learn the graph using original features, our method seeks an underlying latent representation and performs graph learning and label propagation based on the learned latent representation. With the complementarity of multiple views, the latent representation could depict the data more comprehensively than every single view individually, accordingly making the graph more accurate and robust as well. Finally, LMSSC integrates latent representation learning, graph construction, and label propagation into a unified framework, which makes each subtask optimized. Experimental results on real-world benchmark datasets validate the effectiveness of our proposed method.