Multi-view graph clustering (MVGC) for remote sensing data has gained increasing attention due to its ability to integrate complementary information across modalities while capturing spatial dependencies in heterogeneous data. Although current methods based on graph contrastive learning achieve strong performance, they often misidentify intra-cluster samples as negatives, leading to class conflicts and reduced clustering accuracy. Graph masked autoencoders have recently shown promising potential in learning robust representations through masked reconstruction, but their application to remote sensing data remains underexplored. This challenge is especially notable in the multi-view remote sensing setting, where high heterogeneity and complex spatial structures increase the difficulty of effective representation learning. To address these issues, we propose Clustering-Guided graph Mask AutoEncoder (CG-MAE), the first framework to extend graph masked autoencoders to multi-view remote sensing clustering. We introduce a clustering-guided masking strategy that selectively masks nodes near cluster centers and intra-cluster edges, which are crucial for capturing key structural information. By reconstructing these masked components, the model is encouraged to focus on learning features that are highly relevant to clustering. To further improve training stability and efficiency, we design an easy-to-hard node masking strategy that enables the model to gradually learn from increasingly challenging patterns. Additionally, we propose a dual self-adaptive learning mechanism that encourages the model to align more closely with the underlying semantic distributions. Extensive experiments on four widely used multi-view remote sensing datasets demonstrate that CG-MAE consistently outperforms state-of-the-art methods in both clustering accuracy and representation quality.

Brain network analysis technology reveals the organizational mechanism and information processing mode by constructing the structural connection network between brain regions. It has achieved satisfactory results in brain disease prediction tasks, promoting the progress of neuroscience. In recent years, graph transformer has become the most mainstream method for brain analysis with its powerful feature extraction ability and attention mechanism. However, these methods face two challenges, i.e., lack of interpretability, and neglect of semantic associations among brain regions. To solve these problems, we proposed a large language model (LLM)-driven causal knowledge brain network transformer framework, termed BrainCKT, which is plug-and-play, and can adapt to most of the existing mainstream graph transformer-based methods. Specifically, we constructed a brain region causal graph and used its adjacency matrix to guide the learning process of the self-attention mechanism. In addition, we constructed a brain science knowledge graph and encoded it through a pre-trained model to enhance the original brain region features. Finally, we integrated BrainCKT into four mainstream graph transformer baselines for verification. Experimental results on two brain imaging datasets proved the effectiveness of BrainCKT.

Fair clustering is crucial for mitigating bias in unsupervised learning, yet existing algorithms often suffer from quadratic or super-quadratic computational complexity, rendering them impractical for large-scale datasets. To bridge this gap, we introduce the Anchor-based Fair Clustering Framework (AFCF), a novel, general, and plug-and-play framework that empowers arbitrary fair clustering algorithms with linear-time scalability. Our approach first selects a small but representative set of anchors using a novel fair sampling strategy. Then, any off-the-shelf fair clustering algorithm can be applied to this small anchor set. The core of our framework lies in a novel anchor graph construction module, where we formulate an optimization problem to propagate labels while preserving fairness. This is achieved through a carefully designed group-label joint constraint, which we prove theoretically ensures that the fairness of the final clustering on the entire dataset matches that of the anchor clustering. We solve this optimization efficiently using an ADMM-based algorithm. Extensive experiments on multiple large-scale benchmarks demonstrate that AFCF drastically accelerates state-of-the-art methods, which reduces computational time by orders of magnitude while maintaining strong clustering performance and fairness guarantees.

Clustering is a fundamental task in unsupervised learning, but most existing methods heavily rely on hyperparameters such as the number of clusters or other sensitive settings, limiting their applicability in real-world scenarios. To address this long-standing challenge, we propose a novel and fully parameter-free clustering framework via Self-supervised Consensus Maximization, named SCMax. Our framework performs hierarchical agglomerative clustering and cluster evaluation in a single, integrated process. At each step of agglomeration, it creates a new, structure-aware data representation through a self-supervised learning task guided by the current clustering structure. We then introduce a nearest neighbor consensus score, which measures the agreement between the nearest neighbor-based merge decisions suggested by the original representation and the self-supervised one. The moment at which consensus maximization occurs can serve as a criterion for determining the optimal number of clusters. Extensive experiments on multiple datasets demonstrate that the proposed framework outperforms existing clustering approaches designed for scenarios with an unknown number of clusters.

Multi-view clustering aims to uncover shared semantics and complementary information across different views. However, the inherent heterogeneity among views poses significant challenges to effective collaborative modeling and information integration. While recent studies have introduced distillation-based mechanisms to enhance cross-view consistency and alleviate heterogeneity, these approaches often rely on manually defined knowledge transfer paths or fixed fusion weights, which are inflexible in handling complex and dynamic view relationships in practice. To address this issue, we propose HOARD: a novel framework for Hierarchical crOss-view Alignment for multi-view clusteRing via Decoupled information distillation. HOARD structurally decouples multi-view representations into shared and specific components, and performs hierarchical alignment. Specifically, we introduce a granular-ball contrastive alignment to enhance the semantic consistency of shared features, and a prototype collaborative transmission alignment strategy to align specific features while preserving view-specific structural characteristics. Moreover, we design an information distillation unit to adaptively model cross-view knowledge transfer in both feature spaces. An attention mechanism is further employed to integrate shared and specific information. Extensive experiments on benchmark datasets demonstrate that HOARD significantly improves alignment quality and clustering performance, achieving state-of-the-art results.

Temporal graph learning focuses on graph deep learning in real-world dynamic scenarios, which uses interaction sequence instead of adjacency matrix to observe the graph dynamic changes more microscopically from the perspective of time evolution. However, current temporal graph methods only focus on extra dynamic information, ignoring the large amount of multi-modal information contained in the real world. These information can reflect the rich changes in the real world from different perspectives. Ignoring them means that temporal graph learning still lacks the ability to restore and mine more complex real-world data. We argue that the main challenges causing the above phenomenon in temporal graph learning are the lack of multi-modal architecture and public multi-modal datasets. To solve the above challenges, we propose ModalTGL, which enhances the computational efficiency of the model in complex dynamic scenarios by introducing the dictionary graph network, and achieves multi-modal fusion by embedding tuning. In addition, we also discuss the effects of different time encoding functions on dynamic information preservation. At the data level, we build several multi-modal temporal graph datasets from different areas, and compare with multiple SOTA methods on these datasets. The experimental results verify the effectiveness of the ModalTGL method, achieving the performance improvement of up to 18.48%.

The anchor-based multi-view clustering method has recently attracted considerable attention due to its superior efficiency. However, most existing methods construct a consensus anchor graph based solely on view-level contributions, overlooking the varying importance of individual samples across different views. Moreover, these methods fail to ensure that anchors are evenly distributed across clusters. Thus, we propose a novel and scalable multi-view clustering method, called Sample-Level Weighted and Structure-Enhanced Anchor Graph Learning for Scalable Multi-View Clustering (SLWSE-AGL). Specifically, we introduce a sample-level weighting mechanism based on anchor self-representation learning, enabling the constructed consensus anchor graph to capture the varying importance of samples in different views. Additionally, we incorporate a structure-enhancement constraint to encourage the learned anchors to be more evenly distributed among clusters, leading to more balanced and meaningful cluster partitions. Furthermore, we employ an anchor-to-sample label propagation mechanism that directly yields the final clustering results, thereby avoiding the information loss associated with the two-stage clustering processes. Extensive experiments demonstrate the superior performance of our method compared to state-of-the-art multi-view clustering approaches. The code of SLWSE-AGL is publicly available at https://github.com/tangchuan2000/SLWSE-AGL.

Tensor-based multi-view clustering has been widely studied to capture high-order correlations among multiple views. Nevertheless, existing tensorial methods still exhibit several limitations. First, many approaches rely on full similarity graphs, leading to quadratic or cubic complexity in the number of samples and poor scalability. Second, view-specific anchor graphs are often tensorized without cross-view anchor alignment, yielding structurally inconsistent tensor representations and reduced cross-view comparability. Third, low-rank regularization is typically imposed via the tensor nuclear norm (TNN), which uniformly shrinks singular values and may bias the estimation of the intrinsic tensor rank. To this end, we propose a novel framework, named Align then Tensorize: Multi-level Consistent Anchor Graph Learning for Scalable Multi-View Clustering (ATTMVC). It adopts an anchor-based graph learning framework in which each view is reconstructed from a small set of anchors with sample-wise sparse noise, substantially reducing computational complexity. Unlike existing tensor-based methods that directly tensorize unaligned view-wise anchor graphs, ATTMVC first aligns view-specific anchor graphs into a shared latent space, thereby enforcing structural consistency across views and enabling more reliable modeling of cross-view higher-order correlations. Furthermore, we introduce a Threshold Tensor Rank (TTR) surrogate on the aligned anchor graph tensor, which effectively promotes low-rank structure while mitigating the over-shrinking effect commonly caused by TNN-based regularization. Finally, extensive experiments demonstrate that ATTMVC outperforms state-of-the-art multi-view clustering methods. The code is publicly available at https://github.com/tangchuan2000/ATTMVC.

Early detection of colorectal polyps is crucial for clinical screening and cancer prevention, where accurate and efficient automatic segmentation plays a pivotal role. However, colonoscopy images often suffer from low contrast, blurred boundaries, and scale variations, making segmentation challenging. Existing encoder-decoder networks (e.g., U-Net) suffer from asymmetric supervision and feature redundancy, which in turn lead to semantic inconsistency and loss of fine details. While deeper or hybrid designs alleviate these issues, their high complexity and computational burden limit feasibility in real-time clinical practice. To address these challenges, we propose a lightweight segmentation framework, Hierarchical Contextual Attention Network (HCA-Net), consisting of the Redundancy-Suppressed Dual-Path Downsampling (RS-DPD) module and the Boundary-Aware Semantic Alignment Upsampling (BA-SAU) module, applied to the encoder and decoder, respectively. RS-DPD suppresses redundancy while preserving fine-grained details through a dual-path design, whereas BA-SAU leverages cross-layer contextual attention to enforce semantic consistency and enhance boundary sensitivity. Both modules are built upon our proposed Hierarchical Contextual Attention (HCA) mechanism, which combines convolutional projection with pooling-based compression to achieve efficient global modeling and accurate local boundary restoration. In addition, a composite boundary-aware loss function is designed to improve pixel-level accuracy, structural consistency, and robustness in low-contrast and boundary-ambiguous regions. Extensive experiments on public colorectal polyp datasets demonstrate that HCA-Net achieves state-of-the-art (SOTA) segmentation accuracy with significantly improved efficiency, while maintaining robustness under low-contrast and blurred-boundary conditions.

Multi-view clustering aims to leverage complementary information from multiple data sources to improve clustering quality. Traditional graph-based Non-k multi-view clustering methods enable automatic cluster number determination but suffer from severe scalability issues due to their reliance on constructing large sample-level affinity graphs with quadratic complexity. To address this limitation, we propose a novel scalable Non-k Multi-View Clustering framework via Inter-Anchor Graph learning (MVC-IAG). Our method first extracts a small set of representative anchors via k-means on concatenated multi-view features, then learns a unified inter-anchor graph by integrating multi-view structural information and feature similarity priors. Our framework performs Non-k cluster discovery directly on this compact, learned inter-anchor graph, thereby enabling automatic cluster number determination, and subsequently propagates the results to all samples. Extensive experiments on multiple large scale datasets demonstrate that MVC-IAG significantly reduces computational cost while achieving competitive or superior clustering performance compared to state-of-the-art Non-k multi view clustering approaches.

Anchor graph learning has become a widely used technique for significantly reducing the computational complexity in existing multi-view clustering methods. However, most existing approaches select anchors independently for each view and then generate the consensus graph by directly fusing all anchor graphs. This process overlooks the correspondence between anchor sets across different views, i.e., the column order correspondence of the anchor graphs. To address this limitation, we propose a novel anchor-based tensor multi-rank constraint multi-view clustering method (TMC). Specifically, TMC captures the high-order structural information of the original data by constructing an anchor graph tensor and enforcing a multi-rank constraint to induce a block-diagonal structure. Additionally, to enhance anchor consistency across all view, we construct the anchor graph of each view into an anchor tensor and impose a low-rank constraint on it. In this way, the block-diagonal structure of each anchor graph maintains an approximate alignment between anchors. Furthermore, we provide theoretical proof that the generated anchor graphs inherently exhibit a block-diagonal structure. Extensive experimental results on six multi-view datasets demonstrate that TMC outperforms existing state-of-the-art methods, highlighting its effectiveness in multi-view clustering task.

Knowledge graph reasoning (KGR) is an important task in data mining. It aims to mine the logical rules based on the existing facts and further infer new facts, which makes the graph complete and accurate. Currently, with the development of large language models (LLMs), they are widely integrated with different baseline models for better performance. A few works are proposed on LLM-enhanced KGR models, which leaves many issues to be addressed. Inspired by the efficiency and accuracy of LLM in generating text semantic information, this article proposes a KGR method based on LLM information enhancement and subgraph alignment (LSA). LSA first utilizes LLM to generate textual descriptions corresponding to graph entities, relationships, and subgraphs. Then, it utilizes the generated textual attribute in both explicit and implicit ways: 1) explicit utilization, treating LLM-generated text features as the initialized features for the previous KGR model; and 2) implicit utilization, aligning the structural and textual information of key subgraphs via a learning mechanism. Finally, LSA is evaluated on three typical datasets. The promising performances demonstrate that our LSA leverages LLM to make the KG for richer information, and the representation learning model is empowered with better expressive ability.

Multi-view clustering (MVC) for remote sensing data has attracted increasing attention due to its ability to exploit complementary information from multiple modalities without requiring labels. Recent graph-based deep clustering methods have shown strong potential in modeling spatial structures inherent in remote sensing data. However, existing approaches often emphasize capturing rich node relations while overlooking the optimization of these relations, leading to noisy connections and weak inter-cluster discrimination. To address this issue, we propose a novel Multi-view Graph Clustering with dual Relation Optimization (MDRO) framework tailored for remote sensing data. Specifically, we first segment the remote sensing image into irregular superpixels to reduce computational complexity and use superpixels as graph nodes. Then, MDRO constructs high-order similarity matrices guided by clustering distribution matrices and performs dual relation optimization to suppress noise relations and strengthen similarity relations. Furthermore, an optimal transportation-based constraint is introduced to guide the formation of robust and balanced cluster assignments, mitigating over-smoothing and trivial solutions in graph learning. Comprehensive experiments on four benchmark remote sensing datasets demonstrate that MDRO consistently outperforms existing single-view and multi-view clustering methods, achieving superior accuracy and robustness.

Deep graph clustering (DGC) for attribute-missing graphs is an unsupervised task aimed at partitioning nodes with incomplete attributes into distinct clusters. Existing imputation methods for attribute-missing graphs often fail to account for the varying amounts of information available across node neighborhoods, leading to unreliable results. To address this issue, we propose a novel method named Divide-Then-Rule Graph Completion (DTRGC). This method first addresses nodes with sufficient known neighborhood information and treats the imputed results as new knowledge to iteratively impute more challenging nodes, while leveraging clustering information to correct imputation errors. Specifically, Dynamic Cluster-Aware Feature Propagation initializes missing node attributes by adjusting propagation weights based on the clustering structure. Subsequently, Hierarchical Neighborhood-Aware Imputation categorizes attribute-missing nodes into three groups based on the completeness of their neighborhood attributes. The imputation is performed hierarchically, prioritizing the groups with nodes that have the most available neighborhood information. The cluster structure is then used to refine the imputation and correct potential errors. Finally, Hop-wise Representation Enhancement integrates information across multiple hops, thereby enriching the expressiveness of node representations. Experimental results on 6 widely used graph datasets show that DTRGC significantly improves the clustering performance of various DGC methods under attribute-missing graphs.

In multi-view clustering (MVC), anchor technique is generally hailed as an effective means for filtering noise and improving computation efficiency. However, existing methods usually construct anchors via heuristic strategy, random sampling, or orthogonal learning, which overlook the distribution differences between anchors and original data, leading to anchors lacking structural characteristics. To generate the anchors that are with similar distributions to original data, in the paper we carefully devise a LASD algorithm from the perspective of optimal transport (OT). Concretely, we firstly design a Multi-View OT (MVOT) framework through complementary and consensus representation learning. Then, we theoretically demonstrate the convexity of MVOT using the positive semidefiniteness of its Hessian matrix, and accordingly the global optimal solution of each transport plan can be reached. Further, we establish the strong dual condition for MVOT by the relative interior. Based on dual programming, consequently, we successfully obtain the transport plan between anchors and original data for each view within linear computational complexity. Afterwards, the spectral clustering operation is employed on the consensus plan to produce the discrete cluster labels. Abundant experiments underscore that our learned anchors do well reflect the distributions of original data, and the generated clustering results outperform multiple strong MVC competitors, even under large-scale scenarios. The source code is available at https://github.com/junpuzhang/LASD.

Multi-view clustering aims to effectively integrate data from multiple views to uncover the underlying clustering structure. However, existing methods typically adopt direct fusion strategies for multiview data, neglecting the issues of view gap-induced heterogeneity and the imbalance in view quality. Particularly, when there are significant differences between views, such direct fusion often leads to the loss of critical information and a decline in clustering performance. To address these challenges, we propose a novel Dynamic Progressive Fusion Multi-View Clustering (DPFMVC). DPFMVC employs a view-adaptive fusion mechanism that dynamically selects the most similar views, reducing conflicts between views while preserving complementary information. Additionally, DPFMVC introduces a dual contrastive loss module and a progressive fusion loss, which effectively align sample features with clustering centers, promoting efficient integration of multi-view information. Specifically, the dual contrastive loss compares the similarity between sample features and cluster centers, ensuring cross-view feature consistency and thus enhancing the discriminability of clustering. Meanwhile, the progressive fusion loss progressively adjusts the fusion order of views, effectively reducing the negative impact of low-quality views on the clustering results, strengthening the synergy between views, and facilitating more effective information fusion.Comprehensive experiments on multiple public benchmarks show that DPFMVC delivers superior clustering results and exhibits overall great effectiveness compared to state-of-the-art techniques.

Most existing multi-view clustering methods aim to generate a consensus partition across all views, based on the assumption that all views share the same sample arrangement. However, in real-world scenarios, the collected data across different views is often unsynchronized, making it difficult to ensure consistent sample correspondence between views. To address this issue, we propose a scalable sample-alignment-based multi-view clustering method, referred to as SSA-MVC. Specifically, we first employ a cluster-label matching (CLM) algorithm to select the view whose clustering labels best match those of the others as the benchmark view. Then, for each of the remaining views, we construct representations of non-aligned samples by computing their similarities with aligned samples. Based on these representations, we build a similarity graph between the non-aligned samples of each view and those in the benchmark view, which serves as the alignment criterion. This alignment criterion is then integrated into a late-fusion framework to enable clustering without requiring aligned samples. Notably, the learned sample alignment matrix can be used to enhance existing multi-view clustering methods in scenarios where sample correspondence is unavailable. The effectiveness of the proposed SSA-MVC algorithm is validated through extensive experiments conducted on eight real-world multi-view datasets.

Spatial transcriptomics (ST) technologies provide gene expression measurements with spatial resolution, enabling the dissection of tissue structure and function. A fundamental challenge in ST analysis is clustering spatial spots into coherent functional regions. While existing models effectively integrate expression and spatial signals, they largely overlook sequence-level biological priors encoded in the DNA sequences of expressed genes. To bridge this gap, we propose SAINT (Sequence-Aware Integration for Nucleotide-informed Transcriptomics), a unified framework that augments spatial representation learning with nucleotide-derived features. We construct sequence-augmented datasets across 14 tissue sections from three widely used ST benchmarks (DLPFC, HBC, and MBA), retrieving reference DNA sequences for each expressed gene and encoding them using a pretrained Nucleotide Transformer. For each spot, gene-level embeddings are aggregated via expression-weighted and attention-based pooling, then fused with spatial-expression representations through a late fusion module. Extensive experiments demonstrate that SAINT consistently improves clustering performance across multiple datasets. Experiments validate the superiority, effectiveness, sensitivity, and transferability of our framework, confirming the complementary value of incorporating sequence-level priors into spatial transcriptomics clustering.

Multi-view clustering (MVC) is a fast-growing research direction. However, most existing MVC works focus on concrete objects (e.g., cats, desks) but ignore abstract objects (e.g., knowledge, thoughts), which are also important parts of our daily lives and more correlated to cognition. Relational knowledge, as a typical abstract concept, describes the relationship between entities. For example, "Cats like eating fishes," as relational knowledge, reveals the relationship "eating" between "cats" and "fishes." To fill this gap, we first point out that MVC on relational knowledge is considered an important scenario. Then, we construct 8 new datasets to lay research grounds for them. Moreover, a simple yet effective relational knowledge MVC paradigm (RK-MVC) is proposed by compensating the omitted sample-global correlations from the structural knowledge information. Concretely, the basic consensus features are first learned via adopted MVC backbones, and sample-global correlations are generated in both coarse-grained and fine-grained manners. In particular, the sample-global correlation learning module can be easily extended to various MVC backbones. Finally, both basic consensus features and sample-global correlation features are weighted fused as the target consensus feature. We adopt 9 typical MVC backbones in this paper for comparison from 7 aspects, demonstrating the promising capacity of our RK-MVC.

Multi-view clustering (MVC) has demonstrated impressive performance due to its ability to capture both consistency and diversity information among views. However, most existing techniques assume that all views are available in advance, making them inadequate for stream-view data, such as in intelligent transportation systems and medical imaging analysis, where memory constraints or privacy concerns prevent storing all previous views. Although some methods attempt to address this issue by capturing consistency information, they often fail to effectively extract diversity information and cross-view relationships. We argue that these limitations are inherent to incremental multi-view clustering (IMVC), as the inability to retain all previous views inevitably leads to insufficient information utilization, thereby compromising performance. To address these challenges, we propose a novel algorithm, termed Incremental Multi-View Clustering with Cross-View Correlation and Diversity (CDIMVC). Unlike existing methods that only retain consistency information, CDIMVC also preserves diversity information and utilizes similarity matrices to capture cross-view relationships. To implement this method, we develop three key modules: the dynamic view correlation analysis module (DVCAM), the knowledge extraction module (KEM), and the knowledge transfer module (KTM). When a new data view arrives, DVCAM first assesses its importance and correlation with historical views. Subsequently, KEM computes its consistency and diversity information by comparing it to those in the knowledge base. Finally, KTM facilitates the effective transmission of past knowledge, preventing the loss of historical information. By integrating these modules, CDIMVC can effectively capture cross-view relationships and diversity information, facilitating efficient knowledge updating and maintenance. An alternating procedure is also designed to optimize the resulting optimization problem. Experimental results show that CDIMVC exceeds state-of-the-art methods, demonstrating its effectiveness in handling stream-view data.

Graph-based multi-view clustering methods have demonstrated satisfying performance by effectively capturing relationships among data samples. However, most existing methods primarily emphasize direct pairwise relationships, neglecting the exploration of high-order correlations present within each view. To this end, a novel approach, called multiview clustering via high-order bipartite graph learning and tensor low-rank representation (HBGTLRR), is proposed. Specifically, we first construct high-order bipartite graphs to capture latent relationships and concatenate them into a tensor. By applying tensor nuclear norm (TNN) minimization, we obtain a low-rank representation that reduces noise and preserves high-order consistency. Subsequently, a consensus graph is constructed by adaptively fusing the high-order bipartite graphs with corresponding weights, and then a Laplacian low-rank constraint is imposed on it to effectively capture the intrinsic data structure. Finally, extensive experimental results show that HBGTLRR significantly outperforms existing methods, thereby validating the effectiveness of our proposed method.

Graph anomaly detection (GAD) on attributed networks aims to capture abnormal nodes whose attributes or structures differ significantly from most nodes. The existing GAD models amplify the representation differences between normal and abnormal nodes to identify anomalies via carefully designed feature extraction modules. However, these models ignore the bottlenecks encountered by abnormal nodes in message passing. In particular, when the anomalies occurs at critical crossroads, the information of multiple nodes is compressed into a fixed-length representation, and the resulting over-squashing weakens the abnormal information. To address this, we propose an unsupervisedSTructural optimization model guided by sIMilarity reconstruction (STIM). Specifically, we define redundant edges that cause over-squashing, design the Neighbor-Structure Optimization module to filter redundant edges through the edge-dropping strategy based on critical crossroads, and optimize the graph structure to alleviate over-squashing. In addition, to alleviate the over-smoothing caused by the high inter-class node similarity of the data itself and the edge-dropping strategy, we design the Neighbor-Similarity Reconstruction module based on similarity calculation, which guides the model to expand inter-class variation. Extensive experiments on benchmark datasets show that STIM can effectively optimize message passing and improve anomaly detection performance. The source code is available athttps://github.com/Junyi-Yan/STIM.

Multiview clustering has become a prominent research topic in data analysis, with wide-ranging applications across various fields. However, the existing late fusion multiview clustering (LFMVC) methods still exhibit some limitations, including variable importance and contributions and a heightened sensitivity to noise and outliers during the alignment process. To tackle these challenges, we propose a novel regularized instance weighting multiview clustering via late fusion alignment (R-IWLF-MVC), which considers the instance importance from various views, enabling information integration to be more effective. Specifically, we assign each sample an importance attribute to enable the learning process to focus more on the key sample nodes and avoid being influenced by noise or outliers, while laying the groundwork for the fusion of different views. In addition, we continue to employ late fusion alignment to integrate base clustering from various views and introduce a new regularization term with prior knowledge to ensure that the learning process does not deviate too much from the expected results. After that, we design a three-step alternating optimization strategy with proven convergence for the resultant problem. Our proposed approach has been extensively evaluated on multiple real-world datasets, demonstrating its superiority to state-of-the-art methods.

This work centers on textual adversarial attacks against large language models (LLMs) and proposes a new reproducible benchmark for future study. Unlike pre-trained language models (PLMs) which can output predicted class probabilities as feedback to instruct the generation of adversarial examples, LLMs cannot accurately provide such feedback due to their generative nature, making existing attack modes unsuitable. To address this issue, we propose Offline-Attack, an offline method tailored for LLMs that contains a novel Transformer-based Adversarial Machine Translation (AMT) framework. AMT is trained on one self-constructed large-scale adversarial dataset and used to translate original texts to adversarial examples. To mitigate training bias, we induce LLMs to generate stable prediction confidence and incorporate it into AMT training process. The evaluation, spanning four text classification datasets against LLaMA-2-13b-chat, showcases Offline-Attack’s robust performance, particularly achieving 44.3% attack success rate on average. Moreover, Offline-Attack exhibits promising attack ability to other LLMs like Vicuna-33b and ChatGPT. Our study paves the way for future study by presenting strong and reproducible baselines for textual adversarial attacks against LLMs.

Textual adversarial attacks expose the vulnerabilities of text classifiers and can be used to improve their robustness. Previous context-aware attack models suffer from several limitations. They generally rely on out-of-date substitutes, solely consider the gold label probability, and use the greedy search when generating adversarial examples, often limiting the attack efficiency. To tackle these issues, we proposeMC-PDBS, aMoreContext-aware textual adversarial attack model usingProbabilityDifference-guidedBeamSearch. MC-PDBS generates substitutes using the newest perturbed text sequences in each attack iteration, enabling the generation of more context-aware adversarial examples. The probability difference is an overall consideration of the probabilities of all class labels, which is more effective than the gold label probability in guiding the selection of attack paths. In addition, the beam search enables MC-PDBS to search attack paths from multiple search channels, thereby avoiding the limited search space problem. Extensive experiments and human evaluation demonstrate that MC-PDBS outperforms previous best models in a series of evaluation metrics, particularly bringing up to a +19.5% attack success rate. Extensive analyses further confirm the effectiveness of MC-PDBS.

Multiview clustering (MVC) sufficiently exploits the diverse and complementary information among different views to improve the clustering performance. As a representative algorithm of MVC, the newly proposed simple multiple kernel k -means (SimpleMKKM) algorithm takes a min-max formulation and applies a gradient descent algorithm to decrease the resultant objective function. It is empirically observed that its superiority is attributed to the novel min-max formulation and the new optimization. In this article, we propose to integrate the min-max learning paradigm adopted by SimpleMKKM into late fusion MVC (LF-MVC). This leads to a tri-level max-min-max optimization problem with respect to the perturbation matrices, weight coefficient, and clustering partition matrix. To solve this intractable max-min-max optimization problem, we design an efficient two-step alternative optimization strategy. Furthermore, we analyze the generalization clustering performance of the proposed algorithm from the theoretical perspective. Comprehensive experiments have been conducted to evaluate the proposed algorithm in terms of clustering accuracy (ACC), computation time, convergence, as well as the evolution of the learned consensus clustering matrix, clustering with different numbers of samples, and analysis of the learned kernel weight. The experimental results show that the proposed algorithm is able to significantly reduce the computation time and improve the clustering ACC when compared to several state-of-the-art LF-MVC algorithms. The code of this work is publicly released at: https://xinwangliu.github.io/Under-Review.

Multiview clustering (MVC) seamlessly combines homogeneous information and allocates data samples into different communities, which has shown significant effectiveness for unsupervised tasks in recent years. However, some views of samples may be incomplete due to unfinished data collection or storage failure in reality, which refers to the so-called incomplete multiview clustering (IMVC). Despite many IMVC pioneer frameworks have been introduced, the majority of their approaches are limited by the cubic time complexity and quadratic space complexity which heavily prevent them from being employed in large-scale IMVC tasks. Moreover, the massively introduced hyper-parameters in existing methods are not practical in real applications. Inspired by recent unsupervised multiview prototype progress, we propose a novel parameter-free and scalable incomplete multiview clustering framework with the prototype graph termed PSIMVC-PG to solve the aforementioned issues. Different from existing full pair-wise graph studying, we construct an incomplete prototype graph to flexibly capture the relations between existing instances and discriminate prototypes. Moreover, PSIMVC-PG can directly obtain the prototype graph without pre-process of searching hyper-parameters. We conduct massive experiments on various incomplete multiview tasks, and the performances show clear advantages over existing methods. The code of PSIMVC-PG can be publicly downloaded at https://github.com/wangsiwei2010/PSIMVC-PG.

Multiple kernel clustering (MKC) aims to learn an optimal kernel to better serve for clustering from several precomputed basic kernels. Most MKC algorithms adhere to a common assumption that an optimal kernel is linearly combined by basic kernels. Based on a min-max framework, a newly proposed MKC method termed simple multiple kernel k -means (SimpleMKKM) can acquire a high-quality unified kernel. Although SimpleMKKM has achieved promising clustering performance, we observe that it cannot benefit from any prior knowledge. This would cause the learned partition matrix may seriously deviate from the expected one, especially in clustering tasks where the ground truth is absent during the learning course. To tackle this issue, we propose a novel algorithm termed regularized simple multiple kernel k -means with kernel average alignment (R-SMKKM-KAA). According to the experimental results of existing MKC algorithms, the average partition is a strong baseline to reflect true clustering. To gain knowledge from the average partition, we add the average alignment as a regularization term to prevent the learned unified partition from being far from the average partition. After that, we have designed an efficient solving algorithm to optimize the new resulting problem. In this way, both the incorporated prior knowledge and the combination of basic kernels are helpful to learn better unified partition. Consequently, the clustering performance can be significantly improved. Extensive experiments on nine common datasets have sufficiently demonstrated the effectiveness of incorporation of prior knowledge into SimpleMKKM.

Localized incomplete multiple kernel k -means (LI-MKKM) is recently put forward to boost the clustering accuracy via optimally utilizing a quantity of prespecified incomplete base kernel matrices. Despite achieving significant achievement in a variety of applications, we find out that LI-MKKM does not sufficiently consider the diversity and the complementary of the base kernels. This could make the imputation of incomplete kernels less effective, and vice versa degrades on the subsequent clustering. To tackle these problems, an improved LI-MKKM, called LI-MKKM with matrix-induced regularization (LI-MKKM-MR), is proposed by incorporating a matrix-induced regularization term to handle the correlation among base kernels. The incorporated regularization term is beneficial to decrease the probability of simultaneously selecting two similar kernels and increase the probability of selecting two kernels with moderate differences. After that, we establish a three-step iterative algorithm to solve the corresponding optimization objective and analyze its convergence. Moreover, we theoretically show that the local kernel alignment is a special case of its global one with normalizing each base kernel matrices. Based on the above observation, the generalization error bound of the proposed algorithm is derived to theoretically justify its effectiveness. Finally, extensive experiments on several public datasets have been conducted to evaluate the clustering performance of the LI-MKKM-MR. As indicated, the experimental results have demonstrated that our algorithm consistently outperforms the state-of-the-art ones, verifying the superior performance of the proposed algorithm.

Multiple kernel clustering (MKC) optimally combines a group of predefined kernel matrices to improve clustering performance. Although demonstrating promising performance in various applications, most of existing approaches adopt the min–min formulation, which could be sensitive to perturbation with adversarial samples. Moreover, existing MKC algorithms often involve several hypermeters preventing them into further real applications. To address these issues, we propose a parameter-free effective sparse simple multiple kernel k-means algorithm with max–min optimization formulation in this paper. To be specific, we propose to optimize the widely used unsupervised kernel alignment criterion by minimizing the kernel coefficient and maximizing the clustering partition matrix. Unlike traditional min–min formulation, the max–min kernel alignment is robust to adversarial sample perturbation and free of hyper-parameters. An optimization method based on semi-infinite linear program is designed to solve the complicated optimization problem. Extensive experiments on six multiple kernel benchmark data sets demonstrate the effectiveness of the proposed method.

Adversarial attacks expose the vulnerability of deep neural networks. Compared to image adversarial attacks, textual adversarial attacks are more challenging due to the discrete nature of texts. Recent synonym-based methods achieve the current state-of-the-art results. However, these methods introduce new words against the original text, leading to that humans easily perceive the difference between the adversarial example and the original text. Motivated by the fact that humans are usually unaware of chaotic word order in some cases, we propose exchange-attack (EA), a concise and effective word-level textual adversarial attack model. Specifically, the EA model generates adversarial examples by exchanging words of the original text itself according to the contributions that these words make regarding classification results. Intuitively, the smaller the distance between the two exchanged words, the more difficult the chaotic word order to be perceived by humans. We thus take the word distance into consideration when generating the chaotic word orders. Extensive experiments on several text classification data sets show that the EA model consistently outperforms the selected baselines in terms of averaged after-attack accuracy, modification rate, query number, and semantic similarity. And human evaluation results reveal that humans difficultly perceive the adversarial examples generated by the EA model. In addition, quantitative and qualitative analyses further validate the effectiveness of the EA model, including that the generated adversarial examples are grammatically correct and semantically preserved.

Multiview clustering (MVC) collects complementary and abundant information, which draws much attention in machine learning and data mining community. Existing MVC methods usually hold the assumption that all the views are complete. However, multiple source data are often incomplete in real-world applications, and so on sensor failure or unfinished collection process, which gives rise to incomplete multiview clustering (IMVC). Although enormous efforts have been devoted in IMVC, there still are some urgent issues that need to be solved: (i) The locality among multiple views has not been utilized in the existing mechanism; (ii) Existing methods inappropriately force all the views to share consensus representation while ignoring specific structures. In this paper, we propose a novel method termed partial MVC with locality graph regularization to address these issues. First, followed the traditional IMVC approaches, we construct weighted semi-nonnegative matrix factorization models to handle incomplete multiview data. Then, upon the consensus representation matrix, the locality graph is constructed for regularizing the shared feature matrix. Moreover, we add the coefficient regression term to constraint the various base matrices among views. We incorporate the three aforementioned processes into a unified framework, whereas they can negotiate with each other serving for learning tasks. An effective iterative algorithm is proposed to solve the resultant optimization problem with theoretically guaranteed convergence. The comprehensive experiment results on several benchmarks demonstrate the effectiveness of the proposed method.

Incomplete multi-view clustering (IMVC) optimally combines multiple pre-specified incomplete views to improve clustering performance. Among various excellent solutions, the recently proposed multiple kernel k-means with incomplete kernels (MKKM-IK) forms a benchmark, which redefines IMVC as a joint optimization problem where the clustering and kernel matrix imputation tasks are alternately performed until convergence. Though demonstrating promising performance in various applications, we observe that the manner of kernel matrix imputation in MKKM-IK would incur intensive computational and storage complexities, over-complicated optimization and limitedly improved clustering performance. In this paper, we first propose an Efficient and Effective Incomplete Multi-view Clustering (EE-IMVC) algorithm to address these issues. Instead of completing the incomplete kernel matrices, EE-IMVC proposes to impute each incomplete base matrix generated by incomplete views with a learned consensus clustering matrix. Moreover, we further improve this algorithm by incorporating prior knowledge to regularize the learned consensus clustering matrix. Two three-step iterative algorithms are carefully developed to solve the resultant optimization problems with linear computational complexity, and their convergence is theoretically proven. After that, we theoretically study the generalization bound of the proposed algorithms. Furthermore, we conduct comprehensive experiments to study the proposed algorithms in terms of clustering accuracy, evolution of the learned consensus clustering matrix and the convergence. As indicated, our algorithms deliver their effectiveness by significantly and consistently outperforming some state-of-the-art ones.

Gaussian mixture model (GMM) clustering has been extensively studied due to its effectiveness and efficiency. Though demonstrating promising performance in various applications, it cannot effectively address the absent features among data, which is not uncommon in practical applications. In this article, different from existing approaches that first impute the absence and then perform GMM clustering tasks on the imputed data, we propose to integrate the imputation and GMM clustering into a unified learning procedure. Specifically, the missing data is filled by the result of GMM clustering, and the imputed data is then taken for GMM clustering. These two steps alternatively negotiate with each other to achieve optimum. By this way, the imputed data can best serve for GMM clustering. A two-step alternative algorithm with proved convergence is carefully designed to solve the resultant optimization problem. Extensive experiments have been conducted on eight UCI benchmark datasets, and the results have validated the effectiveness of the proposed algorithm.

Multiple kernel learning (MKL) has been intensively studied during the past decade. It optimally combines the multiple channels of each sample to improve classification performance. However, existing MKL algorithms cannot effectively handle the situation where some channels of the samples are missing, which is not uncommon in practical applications. This paper proposes three absent MKL (AMKL) algorithms to address this issue. Different from existing approaches where missing channels are first imputed and then a standard MKL algorithm is deployed on the imputed data, our algorithms directly classify each sample based on its observed channels, without performing imputation. Specifically, we define a margin for each sample in its own relevant space, a space corresponding to the observed channels of that sample. The proposed AMKL algorithms then maximize the minimum of all sample-based margins, and this leads to a difficult optimization problem. We first provide two two-step iterative algorithms to approximately solve this problem. After that, we show that this problem can be reformulated as a convex one by applying the representer theorem. This makes it readily be solved via existing convex optimization packages. In addition, we provide a generalization error bound to justify the proposed AMKL algorithms from a theoretical perspective. Extensive experiments are conducted on nine UCI and six MKL benchmark datasets to compare the proposed algorithms with existing imputation-based methods. As demonstrated, our algorithms achieve superior performance and the improvement is more significant with the increase of missing ratio.

Multiple kernel clustering (MKC) algorithms optimally combine a group of pre-specified base kernel matrices to improve clustering performance. However, existing MKC algorithms cannot efficiently address the situation where some rows and columns of base kernel matrices are absent. This paper proposes two simple yet effective algorithms to address this issue. Different from existing approaches where incomplete kernel matrices are first imputed and a standard MKC algorithm is applied to the imputed kernel matrices, our first algorithm integrates imputation and clustering into a unified learning procedure. Specifically, we perform multiple kernel clustering directly with the presence of incomplete kernel matrices, which are treated as auxiliary variables to be jointly optimized. Our algorithm does not require that there be at least one complete base kernel matrix over all the samples. Also, it adaptively imputes incomplete kernel matrices and combines them to best serve clustering. Moreover, we further improve this algorithm by encouraging these incomplete kernel matrices to mutually complete each other. The three-step iterative algorithm is designed to solve the resultant optimization problems. After that, we theoretically study the generalization bound of the proposed algorithms. Extensive experiments are conducted on 13 benchmark data sets to compare the proposed algorithms with existing imputation-based methods. Our algorithms consistently achieve superior performance and the improvement becomes more significant with increasing missing ratio, verifying the effectiveness and advantages of the proposed joint imputation and clustering.

Deep clustering gains superior performance than conventional clustering by jointly performing feature learning and cluster assignment. Although numerous deep clustering algorithms have emerged in various applications, most of them fail to learn robust cluster-oriented features which in turn hurts the final clustering performance. To solve this problem, we propose a two-stage deep clustering algorithm by incorporating data augmentation and self-paced learning. Specifically, in the first stage, we learn robust features by training an autoencoder with examples that are augmented by random shifting and rotating the given clean examples. Then, in the second stage, we encourage the learned features to be cluster-oriented by alternatively finetuning the encoder with the augmented examples and updating the cluster assignments of the clean examples. During finetuning the encoder, the target of each augmented example in the loss function is the center of the cluster to which the clean example is assigned. The targets may be computed incorrectly, and the examples with incorrect targets could mislead the encoder network. To stabilize the network training, we select most confident examples in each iteration by utilizing the adaptive self-paced learning. Extensive experiments validate that our algorithm outperforms the state of the arts on four image datasets.

Feature extraction and feature selection have been regarded as two independent dimensionality reduction methods in most of the existing literature. In this paper, we propose to integrate both approaches into a unified framework and design an unsupervised linear feature selective projection (FSP) for feature extraction with low-rank embedding and dual Laplacian regularization, with the aim to exploit the intrinsic relationship among data and suppress the impact of noise. Specifically, a projection matrix with an l2,1-norm regularization is introduced to project original high dimensional data points into a new subspace with lower dimension, where the l2,1-norm regularization can endow the projection with good interpretability. We deploy a coefficient matrix with low rank constraint to reconstruct the data points and the l2,1-norm is imposed to regularize the data reconstruction errors in the low-dimensional subspace and make FSP robust to noise. Furthermore, a dual graph Laplacian regularization term is imposed on the low dimensional data and data reconstruction matrix for preserving the local manifold geometrical structure of data. Finally, an alternatively iterative algorithm is carefully designed for solving the proposed optimization model. Theoretical convergence and computational complexity analysis of the algorithm are also provided. Comprehensive experiments on various benchmark datasets have been carried out to evaluate the performance of the proposed FSP. As indicated, our algorithm significantly outperforms other state-of-the-art methods for feature extraction.

Multiple kernel clustering (MKC) has been intensively studied during the last few decades. Even though they demonstrate promising clustering performance in various applications, existing MKC algorithms do not sufficiently consider the intrinsic neighborhood structure among base kernels, which could adversely affect the clustering performance. In this paper, we propose a simple yet effective neighbor-kernel-based MKC algorithm to address this issue. Specifically, we first define a neighbor kernel, which can be utilized to preserve the block diagonal structure and strengthen the robustness against noise and outliers among base kernels. After that, we linearly combine these base neighbor kernels to extract a consensus affinity matrix through an exact-rank-constrained subspace segmentation. The naturally possessed block diagonal structure of neighbor kernels better serves the subsequent subspace segmentation, and in turn, the extracted shared structure is further refined through subspace segmentation based on the combined neighbor kernels. In this manner, the above two learning processes can be seamlessly coupled and negotiate with each other to achieve better clustering. Furthermore, we carefully design an efficient iterative optimization algorithm with proven convergence to address the resultant optimization problem. As a by-product, we reveal an interesting insight into the exact-rank constraint in ridge regression by careful theoretical analysis: it back-projects the solution of the unconstrained counterpart to its principal components. Comprehensive experiments have been conducted on several benchmark data sets, and the results demonstrate the effectiveness of the proposed algorithm.

Incomplete multi-view clustering (IMVC) optimally fuses multiple pre-specified incomplete views to improve clustering performance. Among various excellent solutions, the recently proposed multiple kernel k-means with incomplete kernels (MKKM-IK) forms a benchmark, which redefines IMVC as a joint optimization problem where the clustering and kernel matrix imputation tasks are alternately performed until convergence. Though demonstrating promising performance in various applications, we observe that the manner of kernel matrix imputation in MKKM-IK would incur intensive computational and storage complexities, overcomplicated optimization and limitedly improved clustering performance. In this paper, we propose an Efficient and Effective Incomplete Multi-view Clustering (EE-IMVC) algorithm to address these issues. Instead of completing the incomplete kernel matrices, EE-IMVC proposes to impute each incomplete base matrix generated by incomplete views with a learned consensus clustering matrix. We carefully develop a three-step iterative algorithm to solve the resultant optimization problem with linear computational complexity and theoretically prove its convergence. Further, we conduct comprehensive experiments to study the proposed EE-IMVC in terms of clustering accuracy, running time, evolution of the learned consensus clustering matrix and the convergence. As indicated, our algorithm significantly and consistently outperforms some state-of-the-art algorithms with much less running time and memory.

Incomplete multi-view clustering optimally integrates a group of pre-specified incomplete views to improve clustering performance. Among various excellent solutions, multiple kernel $k$k-means with incomplete kernels forms a benchmark, which redefines the incomplete multi-view clustering as a joint optimization problem where the imputation and clustering are alternatively performed until convergence. However, the comparatively intensive computational and storage complexities preclude it from practical applications. To address these issues, we propose Late Fusion Incomplete Multi-view Clustering (LF-IMVC) which effectively and efficiently integrates the incomplete clustering matrices generated by incomplete views. Specifically, our algorithm jointly learns a consensus clustering matrix, imputes each incomplete base matrix, and optimizes the corresponding permutation matrices. We develop a three-step iterative algorithm to solve the resultant optimization problem with linear computational complexity and theoretically prove its convergence. Further, we conduct comprehensive experiments to study the proposed LF-IMVC in terms of clustering accuracy, running time, advantages of late fusion multi-view clustering, evolution of the learned consensus clustering matrix, parameter sensitivity and convergence. As indicated, our algorithm significantly and consistently outperforms some state-of-the-art algorithms with much less running time and memory.

Multilabel image annotation attracts a lot of research interest due to its practicability in multimedia and computer vision fields, while the need for a large amount of labeled training data to achieve promising performance makes it a challenging task. Fortunately, unlabeled and relevant data are widely available and these data can be used to serve the annotation task. To this end, we propose a novel adaptive hypergraph learning (AHL) method for multilabel image annotation in a semisupervised way, in which both the limited labeled data and abundant unlabeled data are utilized to facilitate the annotation performance. In detail, we seek a multilabel propagation scheme by learning a hypergraph which is used to preserve the local geometric structures of data in a high-order manner. Meanwhile, a feature projection is integrated into AHL to obtain a latent feature space where unlabeled instances can be effectively and robustly assigned with multiple labels. Experiments on six widely used image datasets are conducted to evaluate our model and the results demonstrate that the proposed AHL outperforms other state-of-the-art semisupervised methods.

With the ability to exploit the internal structure of data, graph-based models have received a lot of attention and have achieved great success in multiview subspace clustering for multimedia data. Most of the existing methods individually construct an affinity graph for each single view and fuse the result obtained from each single graph. However, the common representation shared by different views and the complementary diversity across these views are not efficiently exploited. In addition, noise and outliers are often mixed in original data, which adversely degenerate the clustering performance of many existing methods. In this paper, we propose addressing these issues by learning a joint affinity graph for multiview subspace clustering based on a low-rank representation with diversity regularization and a rank constraint. Specifically, a low-rank representation model is employed to learn a shared sample representation coefficient matrix to generate the affinity graph. At the same time, we use diversity regularization to learn the optimal weights for each view, which can suppress the redundancy and enhance the diversity among different feature views. In addition, the cluster number is used to promote affinity graph learning by using a rank constraint. The final clustering result is obtained by using normalized cuts on the learned affinity graph. An efficient algorithm based on an augmented Lagrangian multiplier with alternating direction minimization is carefully designed to solve the resulting optimization problem. Extensive experiments on various real-world datasets are conducted, and the results demonstrate well the effectiveness of the proposed algorithm.

The recently proposed multiple kernel k-means with incomplete kernels (MKKM-IK) optimally integrates a group of pre-specified incomplete kernel matrices to improve clustering performance. Though it demonstrates promising performance in various applications, we observe that it does not \emph{sufficiently consider the local structure among data and indiscriminately forces all pairwise sample similarity to equally align with their ideal similarity values}. This could make the incomplete kernels less effectively imputed, and in turn adversely affect the clustering performance. In this paper, we propose a novel localized incomplete multiple kernel k-means (LI-MKKM) algorithm to address this issue. Different from existing MKKM-IK, LI-MKKM only requires the similarity of a sample to its k-nearest neighbors to align with their ideal similarity values. This helps the clustering algorithm to focus on closer sample pairs that shall stay together and avoids involving unreliable similarity evaluation for farther sample pairs. We carefully design a three-step iterative algorithm to solve the resultant optimization problem and theoretically prove its convergence. Comprehensive experiments on eight benchmark datasets demonstrate that our algorithm significantly outperforms the state-of-the-art comparable algorithms proposed in the recent literature, verifying the advantage of considering local structure.

Multiple kernel clustering (MKC) algorithms optimally combine a group of pre-specified base kernels to improve clustering performance. However, existing MKC algorithms cannot efficiently address the situation where some rows and columns of base kernels are absent. This paper proposes a simple while effective algorithm to address this issue. Different from existing approaches where incomplete kernels are firstly imputed and a standard MKC algorithm is applied to the imputed kernels, our algorithm integrates imputation and clustering into a unified learning procedure. Specifically, we perform multiple kernel clustering directly with the presence of incomplete kernels, which are treated as auxiliary variables to be jointly optimized. Our algorithm does not require that there be at least one complete base kernel over all the samples. Also, it adaptively imputes incomplete kernels and combines them to best serve clustering. A three-step iterative algorithm with proved convergence is designed to solve the resultant optimization problem. Extensive experiments are conducted on four benchmark data sets to compare the proposed algorithm with existing imputation-based methods. Our algorithm consistently achieves superior performance and the improvement becomes more significant with increasing missing ratio, verifying the effectiveness and advantages of the proposed joint imputation and clustering.

Multiple kernel $k$-means (MKKM) aims to improve clustering performance by learning an optimal kernel, which is usually assumed to be a linear combination of a group of pre-specified base kernels. However, we observe that this assumption could: i) cause limited kernel representation capability; and ii) not sufficiently consider the negotiation between the process of learning the optimal kernel and that of clustering, leading to unsatisfying clustering performance. To address these issues, we propose an optimal neighborhood kernel clustering (ONKC) algorithm to enhance the representability of the optimal kernel and strengthen the negotiation between kernel learning and clustering. We theoretically justify this ONKC by revealing its connection with existing MKKM algorithms. Furthermore, this justification shows that existing MKKM algorithms can be viewed as a special case of our approach and indicates the extendability of the proposed ONKC for designing better clustering algorithms. An efficient algorithm with proved convergence is designed to solve the resultant optimization problem. Extensive experiments have been conducted to evaluate the clustering performance of the proposed algorithm. As demonstrated, our algorithm significantly outperforms the state-of-the-art ones in the literature, verifying the effectiveness and advantages of ONKC.