Discrete Optimal Graph Clustering

Co-Clustering by Directly Solving Bipartite Spectral Graph Partitioning

Bipartite spectral graph partitioning (BSGP) method as a co-clustering method, has been widely used in document clustering, which simultaneously clusters documents and words by making full use of the duality between documents and words. It consists of two steps: 1) graph construction and 2) singular value decomposition on the bipartite graph to compute a continuous cluster assignment matrix, followed by post-processing to get the discrete solution. However, the generated graph is unstructured and fixed. It heavily relies on the quality of the graph construction. Moreover, the two-stage process may deviate from directly solving the primal problem. In order to tackle these defects, a novel bipartite graph partitioning method is proposed to learn a bipartite graph with exactly c connected components (c is the number of clusters), which can obtain clustering results directly. Furthermore, it is experimentally and theoretically proved that the solution of the proposed model is the discrete solution of the primal BSGP problem for a special situation. Experimental results on synthetic and real-world datasets exhibit the superiority of the proposed method.

A Review of Convex Clustering From Multiple Perspectives: Models, Optimizations, Statistical Properties, Applications, and Connections

Traditional partition-based clustering is very sensitive to the initialized centroids, which are easily stuck in the local minimum due to their nonconvex objectives. To this end, convex clustering is proposed by relaxing K -means clustering or hierarchical clustering. As an emerging and excellent clustering technology, convex clustering can solve the instability problems of partition-based clustering methods. Generally, convex clustering objective consists of the fidelity and the shrinkage terms. The fidelity term encourages the cluster centroids to estimate the observations and the shrinkage term shrinks the cluster centroids matrix so that their observations share the same cluster centroid in the same category. Regularized by the lpn -norm ( pn ∈ {1,2,+∞} ), the convex objective guarantees the global optimal solution of the cluster centroids. This survey conducts a comprehensive review of convex clustering. It starts with the convex clustering as well as its nonconvex variants and then concentrates on the optimization algorithms and the hyperparameters setting. In particular, the statistical properties, the applications, and the connections of convex clustering with other methods are reviewed and discussed thoroughly for a better understanding the convex clustering. Finally, we briefly summarize the development of convex clustering and present some potential directions for future research.

Multi-View Discrete Clustering: A Concise Model

In most existing graph-based multi-view clustering methods, the eigen-decomposition of the graph Laplacian matrix followed by a post-processing step is a standard configuration to obtain the target discrete cluster indicator matrix. However, we can naturally realize that the results obtained by the two-stage process will deviate from that obtained by directly solving the primal clustering problem. In addition, it is essential to properly integrate the information from different views for the enhancement of the performance of multi-view clustering. To this end, we propose a concise model referred to as Multi-view Discrete Clustering (MDC), aiming at directly solving the primal problem of multi-view graph clustering. We automatically weigh the view-specific similarity matrix, and the discrete indicator matrix is directly obtained by performing clustering on the aggregated similarity matrix without any post-processing to best serve graph clustering. More importantly, our model does not introduce an additive, nor does it has any hyper-parameters to be tuned. An efficient optimization algorithm is designed to solve the resultant objective problem. Extensive experimental results on both synthetic and real benchmark datasets verify the superiority of the proposed model.

Low-rank discrete multi-view spectral clustering

Spectral clustering has attracted intensive attention in multimedia applications due to its good performance on arbitrary shaped clusters and well-defined mathematical framework. However, most existing multi-view spectral clustering methods still have the following demerits: (1) They ignore useful complementary information embedded in indicator matrices of different views. (2) The conventional post-processing methods based on the relax and discrete strategy inevitably result in the sub-optimal discrete solution. To tackle the aforementioned drawbacks, we propose a low-rank discrete multi-view spectral clustering model. Drawing inspiration from the fact that the difference between indicator matrices of different views provides useful complementary information for clustering, our model exploits the complementary information embedded in indicator matrices with tensor Schatten p-norm constraint. Further, we integrate low-rank tensor learning and discrete label recovering into a uniform framework, which avoids the uncertainty of the relaxed and discrete strategy. Extensive experiments on benchmark datasets have demonstrated the effectiveness and superiority of the proposed method.

Flexible Multiview Spectral Clustering With Self-Adaptation

Multiview spectral clustering (MVSC) has achieved state-of-the-art clustering performance on multiview data. Most existing approaches first simply concatenate multiview features or combine multiple view-specific graphs to construct a unified fusion graph and then perform spectral embedding and cluster label discretization with k -means to obtain the final clustering results. They suffer from an important drawback: all views are treated as fixed when fusing multiple graphs and equal when handling the out-of-sample extension. They cannot adaptively differentiate the discriminative capabilities of multiview features. To alleviate these problems, we propose a flexible MVSC with self-adaptation (FMSCS) method in this article. A self-adaptive learning scheme is designed for structured graph construction, multiview graph fusion, and out-of-sample extension. Specifically, we learn a fusion graph with a desirable clustering structure by adaptively exploiting the complementarity of different view features under the guidance of a proper rank constraint. Meanwhile, we flexibly learn multiple projection matrices to handle the out-of-sample extension by adaptively adjusting the view combination weights according to the specific contents of unseen data. Finally, we derive an alternate optimization strategy that guarantees desirable convergence to iteratively solve the formulated unified learning model. Extensive experiments demonstrate the superiority of our proposed method compared with state-of-the-art MVSC approaches. For the purpose of reproducibility, we provide the code and testing datasets at https://github.com/shidan0122/FMICS.

Unsupervised Feature Selection With Weighted and Projected Adaptive Neighbors

In the field of data mining, how to deal with high-dimensional data is a fundamental problem. If they are used directly, it is not only computationally expensive but also difficult to obtain satisfactory results. Unsupervised feature selection is designed to reduce the dimension of data by finding a subset of features in the absence of labels. Many unsupervised methods perform feature selection by exploring spectral analysis and manifold learning, such that the intrinsic structure of data can be preserved. However, most of these methods ignore a fact: due to the existence of noise features, the intrinsic structure directly built from original data may be unreliable. To solve this problem, a new unsupervised feature selection model is proposed. The graph structure, feature weights, and projection matrix are learned simultaneously, such that the intrinsic structure is constructed by the data that have been feature weighted and projected. For each data point, its nearest neighbors are acquired in the process of graph construction. Therefore, we call them adaptive neighbors. Besides, an additional constraint is added to the proposed model. It requires that a graph, corresponding to a similarity matrix, should contain exactly c connected components. Then, we present an optimization algorithm to solve the proposed model. Next, we discuss the method of determining the regularization parameter γ in our proposed method and analyze the computational complexity of the optimization algorithm. Finally, experiments are implemented on both synthetic and real-world datasets to demonstrate the effectiveness of the proposed method.

Smoothness Sensor: Adaptive Smoothness-Transition Graph Convolutions for Attributed Graph Clustering

Clustering techniques attempt to group objects with similar properties into a cluster. Clustering the nodes of an attributed graph, in which each node is associated with a set of feature attributes, has attracted significant attention. Graph convolutional networks (GCNs) represent an effective approach for integrating the two complementary factors of node attributes and structural information for attributed graph clustering. Smoothness is an indicator for assessing the degree of similarity of feature representations among nearby nodes in a graph. Oversmoothing in GCNs, caused by unnecessarily high orders of graph convolution, produces indistinguishable representations of nodes, such that the nodes in a graph tend to be grouped into fewer clusters, and pose a challenge due to the resulting performance drop. In this study, we propose a smoothness sensor for attributed graph clustering based on adaptive smoothness-transition graph convolutions, which senses the smoothness of a graph and adaptively terminates the current convolution once the smoothness is saturated to prevent oversmoothing. Furthermore, as an alternative to graph-level smoothness, a novel fine-grained nodewise-level assessment of smoothness is proposed, in which smoothness is computed in accordance with the neighborhood conditions of a given node at a certain order of graph convolution. In addition, a self-supervision criterion is designed considering both the tightness within clusters and the separation between clusters to guide the entire neural network training process. The experiments show that the proposed methods significantly outperform 13 other state-of-the-art baselines in terms of different metrics across five benchmark datasets. In addition, an extensive study reveals the reasons for their effectiveness and efficiency.

Progressive Self-Supervised Clustering With Novel Category Discovery

These days, clustering is one of the most classical themes to analyze data structures in machine learning and pattern recognition. Recently, the anchor-based graph has been widely adopted to promote the clustering accuracy of plentiful graph-based clustering techniques. In order to achieve more satisfying clustering performance, we propose a novel clustering approach referred to as the progressive self-supervised clustering method with novel category discovery (PSSCNCD), which consists of three separate procedures specifically. First, we propose a new semisupervised framework with novel category discovery to guide label propagation processing, which is reinforced by the parameter-insensitive anchor-based graph obtained from balanced K -means and hierarchical K -means (BKHK). Second, we design a novel representative point selected strategy based on our semisupervised framework to discover each representative point and endow pseudolabel progressively, where every pseudolabel hypothetically corresponds to a real category in each self-supervised label propagation. Third, when sufficient representative points have been found, the labels of all samples will be finally predicted to obtain terminal clustering results. In addition, the experimental results on several toy examples and benchmark data sets comprehensively demonstrate that our method outperforms other clustering approaches.

A Differential Evolution Algorithm With Adaptive Niching and K-Means Operation for Data Clustering

Clustering, as an important part of data mining, is inherently a challenging problem. This article proposes a differential evolution algorithm with adaptive niching and k -means operation (denoted as DE_ANS_AKO) for partitional data clustering. Within the proposed algorithm, an adaptive niching scheme, which can dynamically adjust the size of each niche in the population, is devised and integrated to prevent premature convergence of evolutionary search, thus appropriately searching the space to identify the optimal or near-optimal solution. Furthermore, to improve the search efficiency, an adaptive k -means operation has been designed and employed at the niche level of population. The performance of the proposed algorithm has been evaluated on synthetic as well as real datasets and compared with related methods. The experimental results reveal that the proposed algorithm is able to reliably and efficiently deliver high quality clustering solutions and generally outperforms related methods implemented for comparisons.

miRCom: Tensor Completion Integrating Multi-View Information to Deduce the Potential Disease-Related miRNA-miRNA Pairs

MicroRNAs (miRNAs) are consistently capable of regulating gene expression synergistically in a combination mode and play a key role in various biological processes associated with the initiation and development of human diseases, which indicate that comprehending the synergistic molecular mechanism of miRNAs may facilitate understanding the pathogenesis of diseases or even overcome it. However, most existing computational methods had an incomprehensive acknowledge of the miRNA synergistic effect on the pathogenesis of complex diseases, or were hard to be extended to a large-scale prediction task of miRNA synergistic combinations for different diseases. In this article, we propose a novel tensor completion framework integrating multi-view miRNAs and diseases information, called miRCom, for the discovery of potential disease-associated miRNA-miRNA pairs. We first construct an incomplete three-order association tensor and several types of similarity matrices based on existing biological knowledge. Then, we formulate an objective function via performing the factorizations of coupled tensor and matrices simultaneously. Finally, we build an optimization schema by adopting the ADMM algorithm. After that, we obtain the prediction of miRNA-miRNA pairs for different diseases from the full tensor. The contrastive experimental results with other approaches verified that miRCom effectively identify the potential disease-related miRNA-miRNA pairs. Moreover, case study results further illustrated that miRNA-miRNA pairs have more biologically significance and prognostic value than single miRNAs.

Robust Structured Graph Clustering

Graph-based clustering methods have achieved remarkable performance by partitioning the data samples into disjoint groups with the similarity graph that characterizes the sample relations. Nevertheless, their learning scheme still suffers from two important problems: 1) the similarity graph directly constructed from the raw features may be unreliable as real-world data always involves adverse noises, outliers, and irrelevant information and 2) most graph-based clustering methods adopt two-step learning strategy that separates the similarity graph construction and clustering into two independent processes. Under such circumstance, the generated graph is unstructured and fixed. It may suffer from a low-quality clustering structure and thus lead to suboptimal clustering performance. To alleviate these limitations, in this article we propose a robust structured graph clustering (RSGC) model. We formulate a novel learning framework to simultaneously learn a robust structured similarity graph and perform clustering. Specifically, the structured graph with proper probabilistic neighborhood assignment is adaptively learned on a robust latent representation that resists the noises and outliers. Furthermore, an explicit rank constraint is imposed on the Laplacian matrix to structurize the graph such that the number of the connected components is exactly equal to the ground-truth cluster number. To solve the challenging objective formulation, we propose to first transform it into an equivalent one that can be tackled more easily. An iterative solution based on the augmented Lagrangian multiplier is then derived to solve the model. In RSGC, the discrete cluster labels can be directly obtained by partitioning the learned similarity graph without reliance on label discretization strategy as most graph-based clustering methods. Experiments on both synthetic and real data sets demonstrate the superiority of the proposed method compared with the state-of-the-art clustering techniques.

A physical model inspired density peak clustering

Clustering is an important technology of data mining, which plays a vital role in bioscience, social network and network analysis. As a clustering algorithm based on density and distance, density peak clustering is extensively used to solve practical problems. The algorithm assumes that the clustering center has a larger local density and is farther away from the higher density points. However, the density peak clustering algorithm is highly sensitive to density and distance and cannot accurately identify clusters in a dataset having significant differences in cluster structure. In addition, the density peak clustering algorithm's allocation strategy can easily cause attached allocation errors in data point allocation. To solve these problems, this study proposes a potential-field-diffusion-based density peak clustering. As compared to existing clustering algorithms, the advantages of the potential-field-diffusion-based density peak clustering algorithm is three-fold: 1) The potential field concept is introduced in the proposed algorithm, and a density measure based on the potential field's diffusion is proposed. The cluster center can be accurately selected using this measure. 2) The potential-field-diffusion-based density peak clustering algorithm defines the judgment conditions of similar points and adopts different allocation strategies for dissimilar points to avoid attached errors in data point allocation. 3) This study conducted many experiments on synthetic and real-world datasets. Results demonstrate that the proposed potential-field-diffusion-based density peak clustering algorithm achieves excellent clustering effect and is suitable for complex datasets of different sizes, dimensions, and shapes. Besides, the proposed potential-field-diffusion-based density peak clustering algorithm shows particularly excellent performance on variable density and nonconvex datasets.

Multiview Consensus Graph Learning for lncRNA-Disease Association Prediction

Long noncoding RNAs (lncRNAs) are a class of noncoding RNA molecules longer than 200 nucleotides. Recent studies have uncovered their functional roles in diverse cellular processes and tumorigenesis. Therefore, identifying novel disease-related lncRNAs might deepen our understanding of disease etiology. However, due to the relatively small number of verified associations between lncRNAs and diseases, it remains a challenging task to reliably and effectively predict the associated lncRNAs for given diseases. In this paper, we propose a novel multiview consensus graph learning method to infer potential disease-related lncRNAs. Specifically, we first construct a set of similarity matrices for lncRNAs and diseases by taking advantage of the known associations. We then iteratively learn a consensus graph from the multiple input matrices and simultaneously optimize the predicted association probability based on a multi-label learning framework. To convey the utility of our method, three state-of-the-art methods are compared with our method on three widely used datasets. The experiment results illustrate that our method could obtain the best prediction performance under different cross validation schemes. The case study analysis implemented for uterine cervical neoplasms further confirmed the utility of our method in identifying lncRNAs as potential prognostic biomarkers in practice.

Model Update Strategies about Object Tracking: A State of the Art Review

Object tracking has always been an interesting and essential research topic in the domain of computer vision, of which the model update mechanism is an essential work, therefore the robustness of it has become a crucial factor influencing the quality of tracking of a sequence. This review analyses on recent tracking model update strategies, where target model update occasion is first discussed, then we give a detailed discussion on update strategies of the target model based on the mainstream tracking frameworks, and the background update frameworks are discussed afterwards. The experimental performances of the trackers in recent researches acting on specific sequences are listed in this review, where the superiority and some failure cases on each of them are discussed, and conclusions based on those performances are then drawn. It is a crucial point that design of a proper background model as well as its update strategy ought to be put into consideration. A cascade update of the template corresponding to each deep network layer based on the contributions of them to the target recognition can also help with more accurate target location, where target saliency information can be utilized as a tool for state estimation.