Spatial transcriptomics (ST) enables the simultaneous measurement of gene expression and spatial context, offering unprecedented insights into tissue architecture and cellular communication. However, existing approaches often fail to jointly capture spatial topology and transcriptional heterogeneity, leading to suboptimal representations and limited biological interpretability. To address this limitation, we propose stCAMBL, a biased multi-view contrastive framework that integrates spatial graph structure modeling with attentive feature masking and partial contrastive regularization. Built upon a variational graph autoencoder backbone, stCAMBL learns biologically informed and noise-robust embeddings by adaptively emphasizing informative molecular features while mitigating confounding patterns across spatial domains. Comprehensive evaluations on multiple 10$\times$ Visium datasets demonstrate that stCAMBL substantially improves clustering accuracy, gene ontology enrichment, and signal restoration, demonstrating strong generalizability for high-fidelity ST analysis.

Recently, Multi-View Graph Clustering (MVGC) methods have achieved significant progress, leading to their wide adoption in various applications. However, most MVGC methods merely pursue consistent information by simply fusing multi-view graphs, ignoring the cross-view interactions among them, which limits the ceiling of their performance. To make up for this deficiency, we design a credible cross-view graph enhancement module to explore the credible topological structure, while accomplishing cross-view interactions, to boost clustering performance in multi-view graph scenarios. Besides, we reconsider the graph clustering task from the perspective of graph signal processing. From this novel perspective, we adapt the high-order Graph Trend Filter to reveal the inhomogeneities in graph smoothness levels and further consider the brand-new local preference in MVGC, which provides theoretical guidance for graph clustering. Building on these insights, we propose the Enhanced Graph Trend Filter Clustering (EGTFC) method and present an effective algorithm accompanied by corresponding theoretical analyses to tackle the optimization problem inherent in EGTFC. Finally, substantial experimental results on twelve benchmark datasets demonstrate the effectiveness of our proposals and the superiority over thirteen state-of-the-art MVGC methods.

Multi-view Graph Clustering (MGC) is a crucial approach for uncovering complex data structures by leveraging multiple perspectives of data. However, existing MGC methods face two key challenges: (1) limitations in graph structure that neglect long-range dependencies, and (2) overlooking the view-cluster local structure when mining view discrepancies. To address these issues, we propose a Multi-view Graph Clustering approach based on Dual View-Cluster-Order Interactivity (DVCOI-MGC). This approach consists of three modules: (1) Multi-View Multi-Order Graph Construction, where high-order graphs are generated using matrix exponentiation to capture long-range dependencies; (2) Dual View-Cluster-Order Interactivity, which utilizes a discrete graph cut model to separately learn order-specific and view-specific clustering results from the sets of order-specific multi-view graphs and view-specific multi-order graphs, with a separate View-Cluster-Order tensor weight for each learning direction; and (3) Bidirectional Truncation Consistency Learning, which applies a sparse boolean weight vector to locally select and integrate clustering results while preserving both the view-cluster and order-cluster local structures. Additionally, we introduce an efficient iterative optimization method to solve the discrete graph cut problem and provide a theoretical analysis of its convergence and computational complexity. Extensive experiments on 8 real-world datasets demonstrate that our approach significantly improves clustering performance over 11 state-of-the-art methods.

K-means algorithm divides samples into c classes based on their structural characteristics. However, due to the non convex nature of the clustering problem, algorithms are prone to converge to poor local minima. To address the aforementioned issues, we propose the Local Structure Preserving Clustering with Learnable Anchors (LSPC-LA) method. We assume that with a well-designed anchor selection strategy, samples near the same anchor tend to belong to the same cluster, which reveal high confidence Must-Link local structural information for clustering. Based on this observation, we first construct an anchor-based bipartite graph, transforming the sample clustering problem into anchor clustering problem by local structural information, thus reducing the solution space and minimizing the risk of poor local minima. Then we create an anchor guiding matrix to allow anchors to learn the sample structure, improving clustering performance. Subsequently, an alternating iterative algorithm is proposed to optimize the LSPC-LA model. Finally, extensive experiments demonstrate the accuracy of the local structural information and the effectiveness of LSPC-LA.

In recent years, multi-view graph clustering (MVGC) has attracted increasing attention from researchers. However, many existing MVGC methods focus on view-level integration through strategies like assigning weights to different views, for example, ignoring cross-view interactions between nodes. In fact, cross-view interactions at node level are crucial for extraction and fusion of semantic information. Additionally, some methods separate representation learning from clustering, which results in suboptimal clustering performance. To address these problems, we propose a novel unsupervised cross-view message passing method for MVGC. The kernel of our method is the cross-view interaction mechanism, which dynamically constructs node-specific cross-view edges based on node features and structural information. The mechanism enables adaptive interactions of informative nodes from different views, which promotes the extraction and propagation of complementary information. Besides, our method unifies representation learning and hyperspherical clustering in an end-to-end framework, which projects node representations into a hypersphere space, thereby enabling direct acquisition of balanced clustering results without dependence on external clustering methods. We provide comprehensive analyses on our method, and evaluate our method on six multi-view datasets. The results show that our method consistently achieves superior performance than existing state-of-the-art multi-view clustering methods.

In this paper, we present a novel Self-Supervised Learning (SSL) framework tailored for Multi-View Clustering (MVC), which learns cross-view semantic representations with clear clustering boundaries and derives balanced clustering in an end-to-end manner. Concretely, we propose a generative SSL module that learns high-level semantic representations by recovering randomly masked views from observed views. Then the extracted representations are unified via a sample-level local fusion mechanism and projected into a unit-hypersphere space with evenly distributed cluster prototypes such that the pseudo labels can be directly retrieved using cosine similarity. For each sample, we define highly credible positive pairs of the same cluster and negative pairs of different clusters and design a contrastive SSL module to force the sample to move toward its cluster prototype while farther from the other prototypes in the embedding space. Consequently, the representations exhibit clearer clustering boundaries, and the two SSL modules benefit each other. Finally, we further introduce a clustering regularizer to prevent trivial solutions and derive balanced clustering with theoretical guarantees. Comprehensive evaluations over eight benchmark datasets validate the effectiveness of our proposals against ten state-of-the-art MVC methods.

Deep Multi-View Clustering (MVC) methods partition multi-view data into disjoint clusters in an unsupervised manner, showing significant promise across various domains. However, current MVC methods primarily focus on capturing the consistency information shared across all views and undervalue the specificity information inherent in each view that reflects its unique characteristics. Furthermore, the underexploration of the separability of learned representations limits the overall clustering performance of existing MVC methods and leads to undesirable clustering results. In this paper, we propose a fully differentiable and end-to-end deep MVC framework, named Comprehensive Information Extraction with Separable Representation Learning (CIRSEL), to address these issues. CIRSEL recasts specificity information extraction as a high-order graph pooling process to capture the view-specific characteristics of individual views. Utilizing the cross-attention mechanism, CIRSEL adaptively fuses the consistent and view-specific representations to achieve comprehensive information extraction. Subsequently, CIRSEL maps representations into a unit hypersphere space with evenly distributed prototypes and maximizes the variational estimation of Mutual Information, which enhances the inter-cluster separability and intra-cluster compactness in the embedding space and further benefits the following clustering learning. Finally, CIRSEL introduces a nuclear norm-based balance regularization, which ensures balanced clustering results can be directly retrieved by the cosine similarity between the representations and prototypes. Extensive experiments on ten benchmark datasets demonstrate the effectiveness of CIRSEL compared to sixteen current MVC methods.

Clustering based on structured graph learning involves acquiring a proximity matrix with an explicit clustering structure from the original one. However, the original proximity matrix often lacks some must-links compared to the groundtruth, constraining the upper bound of clustering performance. High-order proximity information can mitigate this limitation, yet traditional high-order proximity matrix-based methods are time-intensive. To tackle this, we propose the Tensorized High-order Bipartite Graphs-based structured proximity matrix learning method (THBG). Firstly, we introduce a high-order bipartite graph proximity matrix with a swift computation method, incorporating high-order information and significantly reducing computational overhead. Secondly, we apply tensor nuclear norm minimization to the tensor composed of high-order bipartite graphs, learning a low-rank tensor representation that effectively harnesses the consistency of high-order information. Concurrently, a structured bipartite graph proximity matrix with an explicit clustering structure is adaptively learned based on the low-rank tensor representation and Laplace rank constraint. Experimental results demonstrate the superiority and great potential of this method. Code available:https://anonymous.4open.science/r/THBG-D10D.

Most existing multi-view graph clustering models focus on integrating the topological structure of different views directly, which cannot efficiently stimulate the collaboration between multiple views. To alleviate this problem, this paper proposes a Triangle Topology Enhancement (T2E) module, which expands two topological structures based on the raw topology of each view, including the self-triangle enhanced topology that highlights the local view information and the cross-view triangle enhanced topology containing the global-local view information. Afterward, this paper designs a novel multi-view graph clustering model, named MGC-T2E, to integrate both the raw and derived topological structures and directly induce consistent clustering indicators based on a self-supervised clustering module. In the simulation, the experimental results demonstrate that MGC-T2E achieves state-of-the-art performances compared with a mass of current competitors.

Structured proximity matrix learning, one of the mainstream directions in clustering research, refers to learning a proximity matrix with an explicit clustering structure from the original first-order proximity matrix. Due to the complexity of the data structure, the original first-order proximity matrix always lacks some must-links compared to the groundtruth proximity matrix. It is worth noting that high-order proximity matrices can provide missed must-link information. However, the computation of high-order proximity matrices and clustering based on them are expensive. To solve the above problem, inspired by the anchor bipartite graph, we present a novel high-order bipartite graph proximity matrix and a fast method to compute it. This proposed high-order bipartite graph proximity matrix contains high-order proximity information and can significantly reduce the computational complexity of the whole clustering process. Furthermore, we introduce an efficient and simple high-order bipartite graph fusion framework that can adaptively assign weights to each order of the high-order bipartite graph matrices. Finally, under the Laplace rank constraint, a consensus structured bipartite graph proximity matrix is obtained. At the same time, an efficient solution algorithm is proposed for this model. The model's efficacy is underscored through rigorous experiments, highlighting its superior clustering performance and time efficiency. Code available:https://anonymous.4open.science/r/HBGC-F6C4.

Feature selection plays an important role in data analysis, yet traditional graph-based methods often produce suboptimal results. These methods typically follow a two-stage process: constructing a graph with data-to-data affinities or a bipartite graph with data-to-anchor affinities and independently selecting features based on their scores. In this article, a large-scale feature selection approach based on structured bipartite graph and row-sparse projection (RS2BLFS) is proposed to overcome this limitation. RS2BLFS integrates the construction of a structured bipartite graph consisting of c connected components into row-sparse projection learning with k nonzero rows. This integration allows for the joint selection of an optimal feature subset in an unsupervised manner. Notably, the c connected components of the structured bipartite graph correspond to c clusters, each with multiple subcluster centers. This feature makes RS2BLFS particularly effective for feature selection and clustering on nonspherical large-scale data. An algorithm with theoretical analysis is developed to solve the optimization problem involved in RS2BLFS. Experimental results on synthetic and real-world datasets confirm its effectiveness in feature selection tasks.

In existing multiview clustering research, the comprehensive learning from multiview graph and feature spaces simultaneously remains insufficient when achieving a consistent clustering structure. In addition, a postprocessing step is often required. In light of these considerations, a cross-view approximation on Grassman manifold (CAGM) model is proposed to address inconsistencies within multiview adjacency matrices, feature matrices, and cross-view combinations from the two sources. The model uses a ratio-formed objective function, enabling parameter-free bidirectional fusion. Furthermore, the CAGM model incorporates a paired encoding mechanism to generate low-dimensional and orthogonal cross-view embeddings. Through the approximation of two measurable subspaces on the Grassmann manifold, the direct acquisition of the indicator matrix is realized. Furthermore, an effective optimization algorithm corresponding to the CAGM model is derived. Comprehensive experiments on four real-world datasets are conducted to substantiate the effectiveness of our proposed method.

Graph-based multiview clustering methods have gained significant attention in recent years. In particular, incorporating graph filtering into these methods allows for the exploration and utilization of both feature and topological information, resulting in a commendable improvement in clustering accuracy. However, these methods still exhibit several limitations: 1) the graph filters are predetermined, which disconnects the link with subsequent clustering tasks and 2) the separability of the filtered features is poor, which may not be suitable for the clustering. To mitigate these aforementioned issues, we propose Multiview Clustering via Block Diagonal Graph Filtering (MvC-BDGF), which can learn cluster-friendly graph filters. Specifically, the block diagonal graph filter with localized characteristics, which could make the filtered features very discriminating, is innovatively designed. The MvC-BDGF model seamlessly integrates the learning of graph filters with the acquisition of consensus graphs, forming a unified framework. This integration allows the model to obtain optimal filters and simultaneously acquire corresponding clustering labels. To solve the optimization problem in the MvC-BDGF model, an iterative solver based on the coordinate descent method is devised. Finally, a large number of experiments on benchmark datasets fully demonstrate the effectiveness and superiority of the proposed model. The code is available at https://github.com/haonanxin/MvC-BDGF_code.

Normalized-Cut (N-Cut) is a famous model of spectral clustering. The traditional N-Cut solvers are two-stage: 1) calculating the continuous spectral embedding of normalized Laplacian matrix; 2) discretization via$K$-means or spectral rotation. However, this paradigm brings two vital problems: 1) two-stage methods solve a relaxed version of the original problem, so they cannot obtain good solutions for the original N-Cut problem; 2) solving the relaxed problem requires eigenvalue decomposition, which has${\mathcal {O}}(n^{3})$time complexity ($n$is the number of nodes). To address the problems, we propose a novel N-Cut solver designed based on the famous coordinate descent method. Since the vanilla coordinate descent method also has${\mathcal {O}}(n^{3})$time complexity, we design various accelerating strategies to reduce the time complexity to${\mathcal {O}}(|E|)$($|E|$is the number of edges). To avoid reliance on random initialization which brings uncertainties to clustering, we propose an efficient initialization method that gives deterministic outputs. Extensive experiments on several benchmark datasets demonstrate that the proposed solver can obtain larger objective values of N-Cut, meanwhile achieving better clustering performance compared to traditional solvers.

Exploiting consistent structure from multiple graphs is vital for multi-view graph clustering. To achieve this goal, we propose an Efficient Balanced Multi-view Graph Clustering via Good Neighbor Fusion (EBMGC-GNF) model which comprehensively extracts credible consistent neighbor information from multiple views by designing a Cross-view Good Neighbors Voting module. Moreover, a novel balanced regularization term based on p-power function is introduced to adjust the balance property of clusters, which helps the model adapt to data with different distributions. To solve the optimization problem of EBMGC-GNF, we transform EBMGC-GNF into an efficient form with graph coarsening method and optimize it based on accelareted coordinate descent algorithm. In experiments, extensive results demonstrate that, in the majority of scenarios, our proposals outperform state-of-the-art methods in terms of both effectiveness and efficiency.

Classification is a fundamental task in the field of data mining. Unfortunately, high-dimensional data often degrade the performance of classification. To solve this problem, dimensionality reduction is usually adopted as an essential preprocessing technique, which can be divided into feature extraction and feature selection. Due to the ability to obtain category discrimination, linear discriminant analysis (LDA) is recognized as a classic feature extraction method for classification. Compared with feature extraction, feature selection has plenty of advantages in many applications. If we can integrate the discrimination of LDA and the advantages of feature selection, it is bound to play an important role in the classification of high-dimensional data. Motivated by the idea, we propose a supervised feature selection method for classification. It combines trace ratio LDA with$\ell _{2,p}$-norm regularization and imposes the orthogonal constraint on the projection matrix. The learned row-sparse projection matrix can be used to select discriminative features. Then, we present an optimization algorithm to solve the proposed method. Finally, the extensive experiments on both synthetic and real-world datasets indicate the effectiveness of the proposed method.

Most existing multi-view graph clustering models either seek consistent clustering results from similarity matrices and spectral embeddings respectively or follow direct bidirectional integration of them, which ignores the interaction between them. To make up for this flaw, this paper designs a novel multi-view clustering model that performsBidirectionalFusion withCross-viewGraphFilter (BF-CGF). To be specific, BF-CGF first learns a consistent graph embedding via performing the interaction between multi-view graphs and spectral embeddings with the perspective of the graph spectral domain and then considers seeking a consistent indicator matrix via the graph cut model from the consistent graph embedding and the similarity matrices. To solve the optimization problem of BF-CGF, we propose an efficient iterative algorithm and provide the corresponding convergence and complexity analyses. Extensive experimental results demonstrate that the proposed BF-CGF outperforms state-of-the-art competitors in most benchmark datasets.

Recently, graph-based multi-view clustering (GMC) has attracted extensive attention from researchers, in which multi-view clustering based on structured graph learning (SGL) can be considered as one of the most interesting branches, achieving promising performance. However, most of the existing SGL methods suffer from sparse graphs lacking useful information, which normally appears in practice. To alleviate this problem, we propose a novel multi-view and multi-order SGL ( [Formula: see text]SGL) model which introduces multiple different orders (multi-order) graphs into the SGL procedure reasonably. To be more specific, [Formula: see text]SGL designs a two-layer weighted-learning mechanism, in which the first layer truncatedly selects part of views in different orders to retain the most useful information, and the second layer assigns smooth weights into retained multi-order graphs to fuse them attentively. Moreover, an iterative optimization algorithm is derived to solve the optimization problem involved in [Formula: see text]SGL, and the corresponding theoretical analyses are provided. In experiments, extensive empirical results demonstrate that the proposed [Formula: see text]SGL model achieves the state-of-the-art performance in several benchmarks.

The existing multiview clustering models learn a consistent low-dimensional embedding either from multiple feature matrices or multiple similarity matrices, which ignores the interaction between the two procedures and limits the improvement of clustering performance on multiview data. To address this issue, a bidirectional probabilistic subspaces approximation (BPSA) model is developed in this article to learn a consistently orthogonal embedding from multiple feature matrices and multiple similarity matrices simultaneously via the disturbed probabilistic subspace modeling and approximation. A skillful bidirectional fusion strategy is designed to guarantee the parameter-free property of the BPSA model. Two adaptively weighted learning mechanisms are introduced to ensure the inconsistencies among multiple views and the inconsistencies between bidirectional learning processes. To solve the optimization problem involved in the BPSA model, an iterative solver is derived, and a rigorous convergence guarantee is provided. Extensive experimental results on both toy and real-world datasets demonstrate that our BPSA model achieves state-of-the-art performance even if it is parameter-free.

With the proliferation of multimedia applications, data is frequently derived from multiple sources, leading to the accelerated advancement of multi-view clustering (MVC) methods. In this paper, we propose a novel MVC method, termed GLSEF, to handle the inconsistency existing in multiple spectral embeddings. To this end, GLSEF contains a two-level learning mechanism. Specifically, on the global level, GLSEF considers the diversity of features and selectively assigns smooth weights to partial more discriminative features that are conducive to clustering. On the local level, GLSEF resorts to the Grassmann manifold to maintain spatial and topological information and local structure in each view, thereby enhancing its suitability and accuracy for clustering. Moreover, unlike most previous methods that learn a low-dimension embedding and perform the k-means algorithm to obtain the final cluster labels, GLSEF directly acquires the discrete indicator matrix to prevent potential information loss during post-processing. To address the optimization involved in GLSEF, we present an efficient alternating optimization algorithm accompanied by convergence and time complexity analyses. Extensive empirical results on nine real-world datasets demonstrate the effectiveness and efficiency of GLSEF compared to existing state-of-the-art MVC methods.

Deep clustering seeks to group data into distinct clusters using deep learning techniques . Existing approaches of deep clustering can be broadly categorized into two groups: offline clustering based on unsupervised representation learning and online clustering based on unsupervised classification . While both groups have demonstrated impressive performance in deep clustering, no study has explored the integration of their respective strengths. To this end, we propose Mutual-Taught Deep Clustering (MTDC), which unifies unsupervised representation learning and unsupervised classification into a framework while realizing mutual promotion using a novel mutual-taught mechanism . Specifically, MTDC alternates between predicting pseudolabels in label space and estimating semantic similarity in feature space during training. Moreover, pseudolabels provide weakly-supervised information to enhance unsupervised representation learning, while semantic similarities function as structural priors that regularize unsupervised classification. Consequently, unsupervised classification and unsupervised representation learning can mutually benefit from one another. MTDC is decoupled from prevailing deep clustering methods . For the sake of clarity, we build upon a straightforward baseline in this paper. Despite its simplicity, we demonstrate that MTDC is exceedingly efficacious and consistently enhances the baseline results by substantial margins. For example, MTDC achieves 2.5 % ∼ 7.9 % (NMI), 3.0 % ∼ 13.9 % (ACC), and 3.1 % ∼ 16.7 % (ARI) gains over the baseline on six widely used image datasets. Source code is available at:https://github.com/yichenwang231/MTDC.

In the field of data mining, how to deal with high-dimensional data is an inevitable topic. Since it does not rely on labels, unsupervised feature selection has attracted a lot of attention. The performance of spectral-based unsupervised methods depends on the quality of the constructed similarity matrix, which is used to depict the intrinsic structure of data. However, real-world data often contain plenty of noise features, making the similarity matrix constructed by original data cannot be completely reliable. Worse still, the size of a similarity matrix expands rapidly as the number of samples rises, making the computational cost increase significantly. To solve this problem, a simple and efficient unsupervised model is proposed to perform feature selection. We formulate PCA as a reconstruction error minimization problem, and incorporate a L2,p-norm regularization term to make the projection matrix sparse. The learned row-sparse and orthogonal projection matrix is used to select discriminative features. Then, we present an efficient optimization algorithm to solve the proposed unsupervised model, and analyse the convergence and computational complexity of the algorithm theoretically. Finally, experiments on both synthetic and real-world data sets demonstrate the effectiveness of our proposed method.

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.

Given an affinity graph of data samples, graph-based clustering aims to partition these samples into disjoint groups based on the affinities, and most previous works are based on spectral clustering. However, two problems among spectral-based methods heavily affect the clustering performance. Firstly, the randomness of post-processing procedures, such as$K$-means, affects the stability of clustering. Secondly, the separated stages of spectral-based methods, including graph construction, spectral embedding learning, and clustering decision, lead to mismatched problems. In this paper, we explore a structured graph learning (SGL) framework that aims to fuse these stages to improve clustering stability. Specifically, SGL adaptively learns a structured affinity graph that contains exact$k$connected components. Each connected component corresponds to a cluster so clustering assignments can be directly obtained according to the connectivity of the learned graph. In this way, SGL avoids the randomness brought by reliance on traditional post-processing procedures. Meanwhile, the graph construction and structured graph learning procedures happen simultaneously, which alleviates the mismatched problem effectively. Moreover, we propose an efficient algorithm to solve the involved optimization problems and discuss the connections between this work and previous works. Numerical experiments on several synthetic and real datasets demonstrate the effectiveness of our methods.

This paper proposes an Efficient Multi-view Graph Clustering with Comprehensive Fusion (EMGC²F) model and a corresponding efficient optimization algorithm to address multi-view graph clustering tasks effectively and efficiently. Compared to existing works, our proposals have the following highlights: 1) EMGC²F directly finds a consistent cluster indicator matrix with a Super Nodes Similarity Minimization module from multiple views, which avoids time-consuming spectral decomposition in previous works. 2) EMGC²F comprehensively mines information from multiple views. More formally, it captures the consistency of multiple views via a Cross-view Nearest Neighbors Voting (CN²V) mechanism, meanwhile capturing the importance of multiple views via an adaptive weighted-learning mechanism. 3) EMGC²F is a parameter-free model and the time complexity of the proposed algorithm is far less than existing works, demonstrating the practicability. Empirical results on several benchmark datasets demonstrate that our proposals outperform SOTA competitors both in effectiveness and efficiency.

Recently, several robust principle component analysis (RPCA) models have been proposed to improve the robustness of principle component analysis (PCA). But an important problem that the robustness to outliers affects the discrimination of correct samples has not been solved yet. To solve this problem, we propose a truncated robust principle component analysis (T-RPCA) model which treats correct samples and outliers separately. In fact, the proposed model performs an implicitly truncated weighted learning scheme which is more reasonable for robustness learning respective to previous works. Moreover, we propose a re-weighted (RW) optimization framework to solve a general problem and generalize two sub-frameworks upon it. To be specific, the first sub-framework orients a general truncated loss optimization problem which contains the objective problem of T-RPCA, and the second one focuses on a general singular-value based optimization problem. Besides, we provide rigorously theoretical guarantees for the proposed model, RW framework and sub-frameworks. Empirical studies demonstrate that the proposed T-RPCA model outperforms previous RPCA models on reconstruction and classification tasks.

k-means method using Lloyd heuristic is a traditional clustering method which has played a key role in multiple downstream tasks of machine learning because of its simplicity. However, Lloyd heuristic always finds a bad local minimum, i.e., the bad local minimum makes objective function value not small enough, which limits the performance of k-means. In this paper, we use coordinate descent (CD) method to solve the problem. First, we show that the k-means minimization problem can be reformulated as a trace maximization problem, then a simple and efficient coordinate descent scheme is proposed to solve the maximization problem. Two interesting findings through theory are that Lloyd cannot decrease the objective function value of k-means produced by our CD further, and our proposed method CD to solve k-means problem can avoid produce empty clusters. In addition, according to the computational complexity analysis, it is verified CD has the same time complexity with original k-means method. Extensive experiments including statistical hypothesis testing, on several real-world datasets with varying number of clusters, varying number of samples and varying number of dimensions show that CD performs better compared to Lloyd, i.e., lower objective value, better local minimum and fewer iterations. And CD is more robust to initialization than Lloyd whether the initialization strategy is random or initialization of k-means++.

Finding a consensus embedding from multiple views is the mainstream task in multiview graph-based clustering, in which the key problem is to handle the inconsistence among multiple views. In this article, we consider clustering effectiveness and practical applicability collectively, and propose a parameter-free model to alleviate the inconsistence of multiple views cleverly. To be specific, the proposed model considers the diversities of multiple views as two-layers. The first layer considers the inconsistence among different features of each view and the second layer considers linking the preembeddings of multiple views attentively. By this way, a consensus embedding can be learned via kernel method effectively and the whole learning procedure is parameter-free. To solve the optimization problem involved in the proposed model, we propose an alternative algorithm which is efficient and easy to implement in practice. In the experiments, we evaluate the proposed model on synthetic and real datasets and the experimental results demonstrate its effectiveness.

In this paper, we propose a novel approach called dependence-guided multi-view clustering (DGMC). Our model enhances the dependence between unified embedding learning and clustering, as well as promotes the dependence between unified embedding and embedding of each view. Specifically, DGMC learns a unified embedding and partitions data in a joint fashion, thus the clustering results can be directly obtained. A kernel dependence measure is employed to learn a unified embedding by forcing it to be close to different views, thus the complex dependence among different views can be captured. Moreover, an implicit-weight learning mechanism is provided to ensure the diversity of different views. An efficient algorithm with rigorous convergence analysis is derived to solve the proposed model. Experimental results demonstrate the advantages of the proposed method over the state of the arts on real-world datasets.

This paper explores a succinct kernel model for Group-Sparse Projections Learning (GSPL), to handle multiview feature selection task completely. Compared to previous works, our model has the following useful properties: 1) Strictness: GSPL innovatively learns group-sparse projections strictly on multiview data via ‘2;0-norm constraint, which is different with previous works that encourage group-sparse projections softly. 2) Adaptivity: In GSPL model, when the total number of selected features is given, the numbers of selected features of different views can be determined adaptively, which avoids artificial settings. Besides, GSPL can capture the differences among multiple views adaptively, which handles the inconsistent problem among different views. 3) Succinctness: Except for the intrinsic parameters of projection-based feature selection task, GSPL does not bring extra parameters, which guarantees the applicability in practice. To solve the optimization problem involved in GSPL, a novel iterative algorithm is proposed with rigorously theoretical guarantees. Experimental results demonstrate the superb performance of GSPL on synthetic and real datasets.

Multi-view clustering is a powerful tool for improving clustering results via integrating the heterogeneous features from different views. In this work, we develop a novel invisible weighted method to this issue. Specifically, our proposed method first considers the diversities among different features of each view with kernel function, and then fuses the multiple pre-embeddings of all the views attentively. As a result, a consensus embedding can be obtained with the adaptive invisible weighted model. Besides, we provide an efficient optimization approach to solve the involved optimization problem and provide the corresponding convergence analysis. Extensive experimental results on benchmark datasets validate the superiorities of the proposed method to the state-of-the-art methods.

This paper tackles multi-view clustering via proposing a novel mixed embedding approximation (MEA) method. Formally, we aim to learn a uniform orthogonal embedding based on the orthogonal pre-embeddings of each view. At first, we hope that the uniform embedding can reconstruct the affinity graph of each view. To improve the representation of learnt embedding, we perform an embedding approximation on Grassmann manifold which is famous on subspace analysis. To perform the difference of views, a hidden weights learning module is provided. Moreover, we propose an iterative algorithm to solve the proposed MEA method and provide rigorously convergence analysis. Extensive experiments demonstrate the superiorities of the proposed method.

In user-centric network, traditional typical user analysis method based on spatial average results is no longer applicable due to the flexible spatial difference, which is the large fluctuations in user performance with spatial location. Especially because of power control leading to keen spatial competition, the spatial difference becomes much significantly, so that fine-grained analysis method is needed to evaluate its performance. This paper analyzes the spatial difference in user-centric network with power control through meta distribution from many different fine-grained perspectives to reveal that power control improves the performance not only in the sense of the spatial average, but also in the complete spatial distribution. Specifically, the complementary cumulative distribution function (CCDF) of the conditional transmitting success probability, the mean local delay and the 5%-tile users performance are given to depict power control effect on the individual links. This analysis provides the optimal values of the area and intensity for power control deployment in user-centric network. Numerical results show that after applying power control the users of high coverage probability can be improved at most by 38%, the mean local delay decreases by 2x and 4x gains can be obtained as for the 5%-tile user's performance.

This letter proposes a double-attentive principle component analysis (DA-PCA) model for image processing. Compared to the previous PCA-based works that cannot deal with normal images and outliers effectively, the proposed DA-PCA model performs a double-attentive mechanism to sever the connections with outliers and hold the effectiveness of normal images. To solve the proposed DA-PCA model, we propose an efficiently iterative algorithm and provide strict convergence analysis for it. Moreover, in the simulations, we conduct the reconstruction and classification experiments on several real datasets and the experimental results demonstrate the superb performance of our proposal.

Many modern clustering models can be divided into two separated steps, i.e., constructing a similarity graph (SG) upon samples and partitioning each sample into the corresponding cluster based on SG. Therefore, learning a reasonable SG has become a hot issue in the clustering field. Many previous works that focus on constructing better SG have been proposed. However, most of them follow an ideal assumption that the importance of different features is equal, which is not adapted in practical applications. To alleviate this problem, this article proposes a self-weighted clustering with adaptive neighbors (SWCAN) model that can assign weights for different features, learn an SG, and partition samples into clusters simultaneously. In experiments, we observe that the SWCAN can assign weights for different features reasonably and outperform than comparison clustering models on synthetic and practical data sets.