In multi-view classification tasks (MVC), each view provides an unique perspective on the data, offering complementary information that can improve classification performance when properly integrated. However, traditional methods typically adopt a uniform processing strategy for all views before fusion, overlooking the fact that different views may require different treatments due to variations in their quality and informativeness. To address this limitation, we propose a novel framework called Uncertainty-Guided View-Strength-Aware Feature Utilization (UVF) for multi-view classification. Our approach introduces a view uncertainty estimation module to quantify the discriminative strength of each view. Based on this estimation, a Differentiated Feature Selector (DFS) adaptively selects features, retaining informative dimensions in weak views while preserving original features in strong views. Furthermore, we employ an uncertainty-guided fusion strategy that assigns dynamic weights to each view's contribution based on its uncertainty score, enhancing the robustness and reliability of the final decision. Experimental results on benchmark datasets demonstrate that our method significantly outperforms conventional approaches, achieving better classification accuracy and interpretability through strength-aware feature processing and fusion.

With the growing demand for decentralized collaborative analysis of privacy-sensitive data, federated multi-view clustering (FMVC) has attracted widespread attention due to its ability to balance privacy protection and collaborative modeling. However, current methods still face the following challenges: (1) Clients need to frequently upload high-dimensional data such as model parameters or graph structures, resulting in high communication costs; (2) The structured data uploaded often contains semantic features and has a high risk of being inverted; (3) The server usually merges the data from all clients with the fixed fusion rule, which may result in a suboptimized clustering result when there exist low-quality clients. To address the issues, we propose a new trusted federated multi-view clustering framework (EvoFMVC) that introduces three key innovations: First, lightweight trusted evidence serves as a compact communication medium, significantly reducing overhead compared to conventional model parameters or graph structures. Second, trusted evidences express clustering results in the form of probability distribution, which avoids the risk of structured information being easily inverted. Lastly, we formalize the server-side aggregation process as a neural architecture search (NAS) task where the server flexibly uses different fusion operators to filter and fuse necessary views through evolutionary algorithms, which significantly improves the fusion effect and model performance. Experimental results on multiple datasets show that our method is superior to existing FMVC methods in terms of clustering accuracy and communication efficiency.

Balanced clustering aims to partition data into cohesive groups while satisfying size constraints. It is important in applications such as load balancing, resource allocation, and capacity-aware data analysis. In practice, structural quality and size balance often compete, which makes balanced clustering difficult for methods that commit to a single operating point. To address this issue, we propose Pairwise Multi-Objective Evolutionary Balanced Clustering (P-MOEBC), a permutation-invariant evolutionary framework that searches for a diverse set of structure-balance trade-offs. We formulate the task with a pairwise graph-cut objective and a flexible balance-violation objective, and then design two label-free operators tailored to this formulation: (1) a Consensus Block Crossover that recombines reliable co-membership structures without label alignment, and (2) a Balance-Aware Mutation with exact local updates that evaluates candidate moves in O(knn) time. Experiments on synthetic data show that scalarized baselines can be sensitive to penalty selection, while real-world benchmarks show that P-MOEBC is competitive across strict and relaxed feasibility regimes and remains scalable. Code is available at https://github.com/zjh308/P-MOEBC.

Multi-view data is widely present in the real world. Multi-view clustering is an unsupervised method for capturing the grouping structure of such data. However, multi-view clustering struggles to meet the requirements of real-world scenarios, such as distributed storage of different views and data protection needs. These requirements align with the setting of vertical federated clustering. However, vertical federated clustering still faces two challenges: (1) Under the constraints of privacy protection mechanisms, how to theoretically analyze the clustering consistency between the data uploaded by clients to the server and the original client data is challenging. (2) The feature space differences among different clients make cross-view information sharing and fusion difficult. To address the first challenge, we provide a theoretical analysis of the upper bound of the loss of k-means for transformation matrix mapping, revealing the relationship between the k-means loss of the transformed data and the original data. We then propose a vertical federated clustering method (V-HDKM). In this method, clients handle the second challenge by transposing the feature matrix. Guided by the projected k-means loss bound, we expand the feature space and perform k-means clustering to obtain feature cluster centers, which are then uploaded to the server. The server aggregates the global centers and feeds back the optimized results, achieving cross-view knowledge fusion through iterative interactions. Experimental results show that V-HDKM significantly improves local clustering performance and performances better than other seven vertical federated mthods on 20 multi-view datasets. Furthermore, sensitivity analysis on 8 UCI datasets with respect to the number of clients demonstrates the stability of the method. The code is available at https://github.com/jiangjh/V-HDKM.

Clustering is widely used to organize large-scale multimedia collections, but standard clustering methods can inherit and amplify demographic imbalance in the underlying data. Existing fair clustering methods still face two practical limitations: many scale poorly to high-dimensional visual datasets, and many rely on a fairness-weight coefficient that must be tuned for each dataset. We propose FairFBC, a scalable fair fuzzy clustering framework for large-scale data. FairFBC first constructs a group-balanced anchor graph to obtain a sparse and scalable representation. It then learns a shared fuzzy partition by maximizing the sum of group-specific trace-sqrt quality terms, which encourages balanced structure across sensitive groups without introducing an explicit fairness-accuracy trade-off coefficient. Finally, a confidence-aware quota-constrained assignment step converts fuzzy memberships into a discrete partition while preserving consistency with the learned structure. Experiments on ten datasets from vision, vision-language, and tabular domains, including FairFace, CelebA, and ChestX-ray, show that FairFBC achieves a strong accuracy-fairness trade-off while remaining stable on large datasets where several competitive baselines fail to run. The code for our method is publicly available at https://github.com/Whale-Waves/FairFBC.

Subspace clustering is one of the most popular clustering methods due to its effectiveness. Although subspace clustering methods have been demonstrated to achieve promising performance, they still lack interpretability, especially when handling high-dimensional complicated data. To bridge this gap, this paper focuses on the interpretability of subspace clustering and proposes a novel interpretable subspace clustering method. Our goal is to answer two key questions about the interpretability in subspace clustering: 1) when handling an individual sample, which features should work for this sample? 2) Which cluster or subspace will the features that work put this sample into? To answer these two questions, we design two new interpretability regularized terms and plug them into the subspace clustering. In this way, we show that interpretability can be used to improve the clustering performance in turn. Extensive experiments on benchmark data sets demonstrate the effectiveness of our method in terms of clustering performance and interpretability.

Subgraph Federated Learning (FL) has emerged as a promising paradigm for node classification tasks wherein subgraphs derived from a global graph are distributed across multiple devices to mitigate data leakage risks. Similar to other FL systems, subgraph FL faces significant security challenges, particularly from backdoor attacks, an area that remains extensively underexplored. Existing attacks typically follow a two-phase strategy to implant backdoors. However, in subgraph FL, such attacks often lead toDivergence Amplification, a phenomenon characterized by significant parameter discrepancies between normal and backdoored models, thereby compromising attack stealthiness. To tackle this challenge, we propose BEEF, a Backdoor attack with an End-to-End Framework designed for effectiveness, stealth, and durability. Unlike conventional methods, BEEF incorporates a dedicated trigger generator, which is jointly trained with a backdoored model. To increase its stealthiness, BEEF crafts adversarial perturbations as triggers that provoke misclassification while leaving the model’s parameters entirely untouched. Furthermore, by calibrating a subset of low-salience parameters associated with backdoor activation, BEEF ensures stable performance and sustained effectiveness across FL rounds. Comprehensive evaluations across eight datasets, four models, five state-of-the-art attacks, and six aggregation methods demonstrate BEEF’s effectiveness in deceiving GNNs while maintaining minimal impact on normal data performance. Additionally, we adapt BEEF to federated graph classification tasks, broadening its applicability and practicality.

Multi-view clustering (MVC) aims to integrate complementary information from multiple views to enhance clustering performance. Late Fusion Multi-View Clustering (LFMVC) has shown promise by synthesizing diverse clustering results into a unified consensus. However, current LFMVC methods struggle with noisy and redundant partitions and often fail to capture high-order correlations across views. To address these limitations, we present a novel theoretical framework for analyzing the generalization error bounds of multiple kernel k-means, leveraging local Rademacher complexity and principal eigenvalue proportions. Our analysis establishes a convergence rate of O(1/n), significantly improving upon the existing rate in the order of O(sqrt(k/n)). Building on this insight, we propose a low-pass graph filtering strategy within a multiple linear K-means framework to mitigate noise and redundancy, further refining the principal eigenvalue proportion and enhancing clustering accuracy. Experimental results on benchmark datasets confirm that our approach outperforms state-of-the-art methods in clustering performance and robustness.

Clustering ensemble has been a popular research topic in data science due to its ability to improve the robustness of the single clustering method. Many clustering ensemble methods have been proposed, most of which can be categorized into clustering-view and sample-view methods. The clustering-view method is generally efficient, but it could be affected by the unreliability that existed in base clustering results. The sample-view method shows good performance, while the construction of the pairwise sample relation is time-consuming. In this paper, the clustering ensemble is formulated as a k-HyperEdge Medoids discovery problem and a clustering ensemble method based on k-HyperEdge Medoids that considers the characteristics of the above two types of clustering ensemble methods is proposed. In the method, a set of hyperedges is selected from the clustering view efficiently, then the hyperedges are diffused and adjusted from the sample view guided by a hyperedge loss function to construct an effective k-HyperEdge Medoid set. The loss function is mainly reduced by assigning samples to the hyperedge with the highest degree of belonging. Theoretical analyses show that the solution can approximate the optimal, the assignment method can gradually reduce the loss function, and the estimation of the belonging degree is statistically reasonable. Experiments on artificial data show the working mechanism of the proposed method. The convergence of the method is verified by experimental analysis of twenty data sets. The effectiveness and efficiency of the proposed method are also verified on these data, with nine representative clustering ensemble algorithms as reference.

Unsupervised multi-view outlier detection has garnered increasing attention in recent years, yet existing methods face persistent challenges. Many approaches rely predominantly on first-order neighborhood information, overlooking the richer insights offered by higher-order structures, which can degrade detection accuracy. Additionally, some methods suffer from outlier domination in their objective functions, leading to suboptimal performance. Integrating information effectively across multiple views also remains a significant hurdle. To address these challenges, we propose a novel Multi-View Outlier Detection method based on Optimal Graph Filtering (MODGF). Our approach detects outliers using a high-order graph filtering mechanism, ensuring consistency between feature and neighborhood spaces by sharing filtering parameters. Furthermore, we incorporate the Corr-entropy Induced Metric (CIM) to refine the objective function and introduce an efficient scoring strategy for enhanced detection reliability. Extensive experimental results demonstrate that our method is both stable and efficient across scenarios. The code is available at https://github.com/criticcc/MODGF.

Multi-view Clustering (MVC) has gained significant attention for its ability to utilize consistent and complementary information from multiple views. Graph filter-based MVC methods have recently demonstrated promising performance, attracting growing interest. However, existing graph filter-based methods typically rely on a single filter for each view. These filters are usually derived from either a specific view or a consensus graph across all views, which limits their effectiveness in fully integrating multi-view information. To address this limitation, we propose a novel method, Consensus Graph Filter Learning for Multiple Graph Clustering (CGFMVC). Unlike existing methods that rely on a single filter per view, we construct multiple graph filters by integrating information from all views. For each view, we generate intra-view graph filters to intermediate high-order information and bridge local-global structures. This approach facilitates neighborhood smoothing and preserves local consistency within each view. By learning a consensus graph filter from these multiple filters, we effectively capture global complementary information across views while preserving local consistency. CGFMVC demonstrates excellent efficiency and effectiveness on various benchmark datasets, outperforming state-of-the-art methods. The code is publicly available at https://github.com/Sean-zjl/CGFMVC.

As data sources and modalities become more diverse, existing multi-view graph clustering methods face high computational complexity, hindering scalability. Bipartite graph clustering overcomes this by using anchors to build association graphs, reducing complexity to linear time. However, the quality of bipartite graphs and the neglect of higher-order correlations remain significant limitations. To tackle these challenges, we propose MCBGF, a scalable bipartite graph-based multi-view clustering method enhanced by consensus graph filtering. By integrating the original bipartite structure to counteract degradation from over-smoothing in high-order filters, MCBGF achieves robust and consistent performance. With linear time complexity, MCBGF efficiently processes large-scale datasets and consistently outperforms state-of-the-art methods in experimental evaluations. The code has been released at https://github.com/sxuHui/MCBGF.

Multi-Kernel Clustering (MKC) uses several kernels or graphs to boost clustering performance. Traditional early fusion methods try to combine these into one consensus structure, but this often ends up with an averaging effect that weakens the final clustering result and depends on heavy matrix operations. In contrast, late fusion methods create separate clustering results for each kernel and then merge them, yet they suffer from high computational costs and do not make full use of the complementary information among kernels. Many researchers have assumed that generating separate partitions for every kernel at each iteration is too expensive because of the intensive matrix computations required. To overcome these issues, we introduce a new framework called Scalable MKC with Dynamic Procrustes (SMKCDP), which learns both the individual base partitions and the final consensus clustering at the same time. SMKCDP not only avoids the dilution seen in early fusion but also improves the quality of the base partitions in late fusion. An interesting finding in our approach is that the optimization only needs the more efficient Singular Value Decomposition (SVD) of rectangular matrices, which greatly reduces the overall computational burden. Experiments on benchmark datasets show that SMKCDP significantly improves both clustering accuracy and efficiency, opening up new directions for scalable MKC methods. The code has been released at https://github.com/WuLizhu-SXU/SMKCDP.

Automatic Modulation Classification (AMC) serves as a foundational pillar for cognitive radio systems, enabling critical functionalities including dynamic spectrum allocation, non-cooperative signal surveillance, and adaptive waveform optimization. However, practical deployment of AMC faces a fundamental challenge: prediction ambiguity arising from intrinsic similarity among modulation schemes and exacerbated under low signal-to-noise ratio (SNR) conditions. This phenomenon manifests as near-identical probability distributions across confusable modulation types, significantly degrading classification reliability. To address this, we propose Fuzzy Regularization-enhanced AMC (FR-AMC), a novel framework that integrates uncertainty quantification into the classification pipeline. The proposed FR has three features: (1) Explicitly model prediction ambiguity during backpropagation, (2) dynamic sample reweighting through adaptive loss scaling, (3) encourage margin maximization between confusable modulation clusters. Experimental results on benchmark datasets demonstrate that the FR achieves superior classification accuracy and robustness compared to compared methods, making it a promising solution for real-world spectrum management and communication applications.

Multi-view classification (MVC) based on the Dempster-Shafer theory has gained significant recognition for its reliability in safety-critical applications. However, existing methods predominantly focus on providing confidence levels for decision outcomes without explaining the reasoning behind these decisions. Moreover, the reliance on first-order statistical magnitudes of belief masses often inadequately capture the intrinsic uncertainty within the evidence. To address these limitations, we propose a novel framework termed Trusted Multi-view Classification Constrained with Expert Knowledge (TMCEK). TMCEK integrates expert knowledge to enhance feature-level interpretability and introduces a distribution-aware subjective opinion mechanism to derive more reliable and realistic confidence estimates. The theoretical superiority of the proposed uncertainty measure over conventional approaches is rigorously established. Extensive experiments conducted on three multi-view datasets for sleep stage classification demonstrate that TMCEK achieves state-of-the-art performance while offering interpretability at both the feature and decision levels. These results position TMCEK as a robust and interpretable solution for MVC in safety-critical domains. The code is available at https://github.com/jie019/TMCEK_ICML2025.

In multi-view classification tasks, integrating information from multiple views effectively is crucial for improving model performance. However, most existing methods fail to fully leverage the complex relationships between views, often treating them independently or using static fusion strategies. In this paper, we propose a View-Association-Guided Dynamic Multi-View Classification method (AssoDMVC) to address these limitations. Our approach dynamically models and incorporates the relationships between different views during the classification process. Specifically, we introduce a view-relation-guided mechanism that captures the dependencies and interactions between views, allowing for more flexible and adaptive feature fusion. This dynamic fusion strategy ensures that each view contributes optimally based on its contextual relevance and the inter-view relationships. Extensive experiments on multiple benchmark datasets demonstrate that our method outperforms traditional multi-view classification techniques, offering a more robust and efficient solution for tasks involving complex multi-view data.

Medical image segmentation is an important task in medical artificial intelligence. Traditional segmentation methods often suffer from the information loss problem, especially in medical image data which contain many different-scale organs or tissues. To address this problem, we propose a novel medical image segmentation method called Wavelet Multi-scale Region-Enhanced Network (WMREN), which has a UNet structure. In the encoder, we design a bi-branch feature extraction architecture, which simultaneously learns the representations with Haar wavelet transform and the residual blocks. The bi-branch architecture can effectively tackle the information loss problem when extracting features. In the decoder we design an innovative Spatial Adaptive Fusion Module to enhance the regions of interest. As we know, the boundaries of objects play an important role in segmentation. To this end, we also carefully design a Contrast Refinement Enhancement Module to highlight the boundaries of the medical objects. Extensive experiments on several benchmark datasets show that our method outperforms state-of-the-art medical image segmentation methods, demonstrating its effectiveness and superiority. The source code is publicly available at https://github.com/C101812/WMREN/tree/master.

Deep learning-based speech enhancement (SE) methods predominantly draw upon two architectural frameworks: generative adversarial networks and diffusion models. In the realm of SE, capturing the local and global relations between signal frames is crucial for the success of these methods. These frameworks typically employ a UNet architecture as their foundational backbone, integrating Long Short-Term Memory (LSTM) networks or attention mechanisms within the UNet to effectively model both local and global signal relations. However, the coupled relation modeling way may not fully harness the potential of these relations. In this paper, we propose an innovative Association-based Fusion Speech Enhancement method (AFSE), a decoupled method. AFSE first constructs a graph that encapsulates the association between each time window of the speech signal, and then models the global relations between frames by fusing the features of these time windows in a manner akin to graph neural networks. Furthermore, AFSE leverages a UNet with dilated convolutions to model the local relations, enabling the network to maintain a high-resolution representation while benefiting from a wider receptive field. Experimental results demonstrate that the AFSE method significantly improves performance in speech enhancement tasks, validating the effectiveness and superiority of our approach. The code is available at https://github.com/jie019/AFSE_IJCAI2025.

Ensemble clustering learns a consensus result by integrating a set of base clustering results. Recently, anchor-based methods construct an anchor similarity matrix to represent the affinity relationships among samples, significantly improving computational efficiency. However, these methods struggle with fixed anchors generated by static anchor learning strategies, which lead to low-quality anchor similarity matrix and poor clustering accuracy. To address this issue, we propose a novel method named dynamic anchor-based ensemble clustering via hypergraph reconstruction (YACHT). Specifically, YACHT first transforms the base clustering results into a hypergraph and designs a novel hypergraph enhancement strategy to improve the reliability of the initial hypergraph. YACHT reconstructs the hypergraph through matrix factorization and introduces a mapping matrix to filter out redundant information, capturing a high-quality anchor similarity matrix. Then, YACHT attempts to incorporate the hypergraph into the optimization objective to achieve hypergraph updates. To ensure the accuracy of hypergraph updates, we impose a hypergraph regularizer and a local consensus information alignment term. The alignment term is implemented by minimizing the discrepancy between the label partition derived from the hypergraph regularizer and the local consensus information indicator matrix extracted from the base clustering results. Extensive experimental results demonstrate the outstanding performance of the proposed YACHT. The code is available at https://github.com/scu-kdde/YACHT.

Clustering, a fundamental task in machine learning and data mining, is essential for uncovering patterns by grouping data points with similar characteristics. Traditional methods struggle with nonlinear data structures, but kernel-based approaches alleviate this issue by mapping data to high dimensional spaces. Multiple Kernel Clustering (MKC) further improves clustering by automating kernel selection and integration. However, MKC faces challenges related to kernel graph quality, information loss during relax-and-discretization, neglect of balanced clustering constraints, and the trade-off between high clustering quality and balance. To address these challenges, we introduce Balanced Multiple Kernel Clustering (BMKC). BMKC utilizes local kernel reconstruction and advanced high-order diffusion techniques for comprehensive kernel graph learning. It directly learns a discrete partition matrix using a robust L1-induced local reconstruction criterion, eliminating the two step process. BMKC incorporates an automatic mechanism for trade-off control between clustering and balance, supported by a versatile optimization algorithm accommodating various balance regularization choices. Experimental validation demonstrates the superior performance of MKC on benchmarks data sets, showcasing its effectiveness. The code for our method is publicly available at https://github.com/ChenYan01TYUT/BMKC-ACM-MM-2025.

The rapid proliferation of multi-view data has necessitated robust and scalable clustering techniques capable of capturing complex, high-dimensional patterns. While Multi-view Bipartite Graph Clustering (MVBGC) has shown promising results, existing approaches often overlook that the generated bipartite graph is susceptible to disturbances from complex structures and noise. To address these challenges, we propose RTGD-MVC, a novel framework for Robust Tensor Learning with Graph Diffusion tailored for efficient and scalable multi-view graph clustering. RTGD-MVC integrates a graph diffusion mechanism to suppress noise propagation and employs cross-view diffusion to enhance global consistency while capturing complementary information across views. Additionally, a non-convex Tensor Exponential Norm (TEN) is introduced as a tighter surrogate for the tensor rank, enabling the learning of more discriminative and noise-robust representations. By embedding these components into a unified optimization model with linear computational complexity, RTGD-MVC achieves both theoretical efficiency and practical scalability. Extensive experiments on diverse benchmark datasets demonstrate that RTGD-MVC significantly outperforms state-of-the-art methods, highlighting its superior ability to capture intricate multi-view correlations and structural patterns.

Ensemble clustering has emerged as a powerful paradigm to improve clustering robustness by aggregating multiple base results. However, traditional methods treat ensemble features statically, failing to account for the inconsistencies and variations that arise from differing base clustering outputs. To tackle this, we propose a novel iterative ensemble clustering framework that adaptively refines consensus representations via high-order graph diffusion and feedback-driven refinement. Unlike static consensus methods, our approach uniquely embeds evolving cluster structures within the feature space, enabling progressive self-correction through global inconsistency suppression and reliability-aware weighting. Our approach uniquely integrates: (1) Adaptive affinity weighting to prioritize reliable base clusterings, (2) Higher-order graph diffusion to capture topological dependencies and suppress high-frequency noise, and (3) Feedback-driven consensus evolution that iteratively replaces unreliable base clusterings with improved consensus outputs. Our method consistently outperforms 9 state-of-the-art ensemble techniques across 10 multimedia datasets, achieving \(\mathbf {+2.2-17.8\%}\) accuracy and \(\mathbf {+3-11.6\%}\) consensus quality, alongside cluster balance improvement up to \(\mathbf {+10.5\%}\). The proposed framework is scalable, model-agnostic, and ideal for real-world multimedia tasks with heterogeneous data sources.

Evolutionary multi-view classification (EMVC) methods have gained wide recognition due to their adaptive mechanisms. Fitness evaluation (FE), which aims to calculate the classification performance of each individual in the population and provide reliable performance ranking for subsequent operations, is a core step in such methods. Its accuracy directly determines the correctness of the evolutionary direction. That is, when FE fails to correctly reflect the superiority-inferiority relationship among individuals, it will lead to confusion in individual performance ranking, which in turn misleads the evolutionary direction and results in trapping into local optima. This paper is the first to identify the aforementioned issue in the field of EMVC and call it as fitness evaluation bias (FEB). FEB may be caused by a variety of factors, and this paper approaches the issue from the perspective of view information content: existing methods generally adopt joint training strategies, which restrict the exploration of key information in views with low information content. This makes it difficult for multi-view model (MVM) to achieve optimal performance during convergence, which in turn leads to FE failing to accurately reflect individual performance rankings and ultimately triggering FEB. To address this issue, we propose an evolutionary multi-view classification via eliminating individual fitness bias (EFB-EMVC) method, which alleviates the FEB issue by introducing evolutionary navigators for each MVM, thereby providing more accurate individual ranking. Experimental results fully verify the effectiveness of the proposed method in alleviating the FEB problem, and the EMVC method equipped with this strategy exhibits more superior performance compared with the original EMVC method. (The code is available at https://github.com/LiShuailzn/Neurips-2025-EFB-EMVC)

Clustering ensemble has been widely studied in data mining and machine learning. However, the existing clustering ensemble methods do not pay attention to fairness, which is important in real-world applications, especially in applications involving humans. To address this issue, this paper proposes a novel fair clustering ensemble method, which takes multiple base clustering results as inputs and learns a fair consensus clustering result. When designing the algorithm, we observe that one of the widely used definitions of fairness may cause a cluster imbalance problem. To tackle this problem, we give a new definition of fairness that can simultaneously characterize fairness and cluster capacity equality. Based on this new definition, we design an extremely simple yet effective regularized term to achieve fairness and cluster capacity equality. We plug this regularized term into our clustering ensemble framework, finally leading to our new fair clustering ensemble method. The extensive experiments show that, compared with the state-of-the-art clustering ensemble methods, our method can not only achieve a comparable or even better clustering performance, but also obtain a much fairer and better capacity equality result, which well demonstrates the effectiveness and superiority of our method.

To partition samples into distinct clusters, Fuzzy C-Means (FCM) calculates the membership degrees of samples to cluster centers and provides soft labels, gaining significant attention in recent years. However, existing FCM methods encounter the following challenges. First, traditional FCM focuses on learning membership degrees, neglecting the data similarity structures. Second, graph-based FCM typically separates graph construction from clustering, overlooking the knowledge interaction between graphs and clustering, obtaining suboptimal performance. Third, exploring the similarity structures among all samples is computationally expensive for large-scale tasks. To solve these dilemmas, we propose a scalable fuzzy clustering with collaborative structure learning and preservation (CSLP), which simultaneously leverages both cluster information and similarity structures to learn an optimal membership degree representation. Specifically, a self-weighted manner is devised to measure the sample importance, thereby reducing the adverse impacts of outliers. Moreover, the graph is updated according to the data similarities in the membership degree representation, such that CSLP collaboratively learns the graph and membership degrees in a mutually reinforcing manner. Thus, the similarity structures are fully explored during clustering processes and preserved in the learned membership degrees, enhancing the discrimination of clustering labels. To further improve efficiency, an acceleration solution is developed to reduce the computational cost of CSLP by propagating membership degrees from potential centers to samples, making CSLP scalable for large-scale tasks. An iterative strategy is designed to solve the formulated objective function. Extensive experiments demonstrate that CSLP outperforms other fuzzy clustering methods in terms of both effectiveness and scalability.

Clustering, a key unsupervised learning method, is widely used in various fields. While the classic K-means algorithm is popular, it often neglects valuable high-order information in data. To address this, we have proposed an improved K-means algorithm incorporating a Chebyshev polynomial approximated graph filter. This approach offers two main advantages. First, the adaptive graph filter, approximated by Chebyshev polynomial, provides a smoother representation that aids subsequent clustering. Second, the clustering results guide the search for optimal adaptive coefficients. This work underscores the potential of combining filter design with machine learning tasks, thereby improving data representation capabilities and demonstrating superior performance in experiments across multiple datasets. Code is available at https://github.com/lxh8684/CGFKM.

In the field of machine learning, multi-view clustering aims to reveal hidden clustering patterns across different data perspectives. However, traditional methods often struggle due to their reliance on low-order similarity data. To overcome this, we propose a new approach that integrates the learning of multiple graph filters, approximated through Chebyshev polynomials, with consensus structural graph learning into a unified framework. This method fully utilizes high-order statistical information from multiple data sources, thereby enhancing multi-view clustering. Comprehensive experiments conducted on multiple datasets consistently demonstrate significant performance improvements over traditional methods. Code is available at https://github.com/lxd1204/HMGC.

Incomplete Multi-View Clustering (IMVC) is crucial for multi-media data analysis. While graph learning-based IMVC methods have shown promise, they still have limitations. The prevalent first-order affinity graph often misclassifies out-neighborhood intra-cluster and in-neighbor inter-cluster samples, worsened by data incompleteness. These inaccuracies, combined with high computational demands, restrict their suitability for large-scale IMVC tasks. To address these issues, we propose a novel Fast and Scalable IMVC with duality Optimal graph Filtering (FSIMVC-OF). Specifically, we refine the clustering-friendly structure of the bipartite graph by learning an optimal filter within a consensus clustering framework. Instead of learning a sample-side filter, we optimize an anchor-side graph filter and apply it to the anchor side, ensuring computational efficiency with linear complexity, supported by the provable equivalence between these two types of graph filters. We present an alternative optimization algorithm with linear complexity. Extensive experimental analysis demonstrates the superior performance of FSIMVC-OF over current IMVC methods. The codes of this article are released in https://github.com/sroytik/FSIMVC-OF.

Multi-view clustering is an important task in multimedia and machine learning. In multi-view clustering, multi-view spectral clustering is one kind of the most popular and effective methods. However, existing multi-view spectral clustering ignores the fairness in the clustering result, which may cause discrimination. To tackle this problem, in this paper, we propose an innovative Fair Multi-view Spectral Clustering (FMSC) method. Firstly, we provide a new perspective of fairness from the graph theory viewpoint, which constructs a relation between fairness and the average degree in graph theory. Secondly, based on this relation, we design a novel fairness-aware regularized term, which has the same form as the ratio cut in spectral clustering. Thirdly, we seamlessly plug this fairness-aware regularized term into the multi-view spectral clustering, leading to our one-stage FMSC, which can directly obtain the final clustering result without any post-processing. We also conduct extensive experiments compared with state-of-the-art fair clustering and multi-view clustering methods, which shows that our method can achieve better fairness.

Kernel k-means has been widely studied in machine learning. However, existing kernel k-means methods often ignore the \textit{fairness} issue, which may cause discrimination. To address this issue, in this paper, we propose a novel Fair Kernel K-Means (FKKM) framework. In this framework, we first propose a new fairness regularization term that can lead to a fair partition of data. The carefully designed fairness regularization term has a similar form to the kernel k-means which can be seamlessly integrated into the kernel k-means framework. Then, we extend this method to the multiple kernel setting, leading to a Fair Multiple Kernel K-Means (FMKKM) method. We also provide some theoretical analysis of the generalization error bound, and based on this bound we give a strategy to set the hyper-parameter, which makes the proposed methods easy to use. At last, we conduct extensive experiments on both the single kernel and multiple kernel settings to compare the proposed methods with state-of-the-art methods to demonstrate their effectiveness.

Recent advancements in Multi-view Clustering (MVC) have highlighted the benefits of late fusion techniques. However, existing late fusion-based MVC (LFMVC) approaches often struggle with intrinsic noise and redundancy within base clustering embeddings generated by traditional method, and fail to capture higher-order correlations among samples and across views. We propose a novel method that incorporates an optimal consensus heat kernel-induced graph filter to address these issues. Our approach leverages diffusion processes to construct filters that capture high-order information, achieving neighborhood smoothing while maintaining local consistency within each view. By integrating a consensus graph filter with downstream clustering tasks within a unified learning framework, our method enhances performance through mutual reinforcement. In particular, our method does not require additional hyperparameter tuning, simplifying the optimization process. Experimental results on various benchmark datasets demonstrate the superior effectiveness of our approach, outperforming state-of-the-art methods in terms of clustering performance.

Fair feature selection for classification decision tasks has recently garnered significant attention from researchers. However, existing fair feature selection algorithms fall short of providing a full explanation of the causal relationship between features and sensitive attributes, potentially impacting the accuracy of fair feature identification. To address this issue, we propose a fair causal feature selection algorithm, called FairCFS . Specifically, FairCFS constructs a localized causal graph that identifies the Markov blankets of class and sensitive variables, to block the transmission of sensitive information for selecting fair causal features. Extensive experiments on seven public real-world datasets validate that FairCFS has accuracy comparable to eight state-of-the-art feature selection algorithms while presenting more superior fairness.

Clustering ensemble often provides robust and stable results without accessing original features of data, and thus has been widely studied. The conventional clustering ensemble methods often take the full multiple base partitions as inputs and provide a consensus clustering result. However, in many real-world applications, full base partitions are hard to obtain because some data may be missing in some base partitions. To tackle this problem, in this paper, we propose a novel partial clustering ensemble method, which takes the partial multiple base partitions as inputs. In this method, we simultaneously fill the missing values in the base partitions and ensemble them by fully considering the consensus and diversity. Moreover, to address the unreliability issue in the partial data scenario, we seamlessly plug it into a self-paced learning framework. The extensive experiments on benchmark data sets demonstrate the effectiveness and efficiency of the proposed method when handling incomplete data.

Existing clustering ensemble methods often directly integrate multiple weak base results to obtain a consensus one which can improve the clustering performance. However, since the base results are weak and the clustering ensemble can improve the performance, why not refine the weak base results via the clustering ensemble, and then boost the clustering ensemble with the refined base results? To fulfill this idea, in this article, we propose a novel clustering ensemble method with an adaptive multiplex. We first use the multiplex to represent the multiple weak base results. Then, we learn an updated representation by diffusing the representation on the multiplex with a manifold ranking model. Since the multiplex characterizes the structure information of all base results, the learned representation can ensemble such structure information during diffusion. Next, the multiplex is refined by such representation, which is a process of refining base results via ensemble. We iteratively learn the representation (i.e., do ensemble) and update the multiplex (i.e., do refinement), which can make the ensemble and refinement be boosted by each other. At last, the final consensus result is obtained from the refined multiplex. The extensive experiments demonstrate the effectiveness and superiority of the proposed framework.

A clustering ensemble provides an elegant framework to learn a consensus result from multiple prespecified clustering partitions. Though conventional clustering ensemble methods achieve promising performance in various applications, we observe that they may usually be misled by some unreliable instances due to the absence of labels. To tackle this issue, we propose a novel active clustering ensemble method, which selects the uncertain or unreliable data for querying the annotations in the process of the ensemble. To fulfill this idea, we seamlessly integrate the active clustering ensemble method into a self-paced learning framework, leading to a novel self-paced active clustering ensemble (SPACE) method. The proposed SPACE can jointly select unreliable data to label via automatically evaluating their difficulty and applying easy data to ensemble the clusterings. In this way, these two tasks can be boosted by each other, with the aim to achieve better clustering performance. The experimental results on benchmark datasets demonstrate the significant effectiveness of our method. The codes of this article are released in https://Doctor-Nobody.github.io/codes/space.zip.

Multi-view clustering is an important machine learning task for multi-media data. Recently, graph filter based multi-view clustering achieves promising performance and attracts much attention. However, the conventional graph filter based methods only use a pre-defined graph filter for each view and the used graph filters ignore the rich information among all views. Different from the conventional methods, in this paper, we aim to tackle a new problem, i.e., instead of using the pre-defined graph filters, how to construct an appropriate consensus graph filter by considering the information in all views. To achieve this, we propose a novel multi-view clustering method with graph filter learning. In our method, we learn an appropriate consensus graph filter from all views of data with multiple graph learning rather than directly pre-defining it. Then, we provide an iterative algorithm to obtain the consensus graph filter and analyze why it can lead to better clustering results. The extensive experiments on benchmark data sets demonstrate the effectiveness and superiority of the proposed method. The codes of this article are released in http://Doctor-Nobody.github.io/codes/MCLGF.zip.

In many real-world unsupervised learning applications, given data with balanced distribution, that is, there are an approximately equal number of instances in each class, we often need to construct a model to reveal such balance. However, in many data, especially the high-dimensional ones, the data in the original feature space often do not present such balance due to the redundant and noisy features. To tackle this problem, we apply an unsupervised spectral feature selection method to select some informative features, which can better reveal the balanced structure of data. Although spectral feature selection is one of the most popular unsupervised feature selection methods and has been widely studied, none of the existing spectral feature selection methods consider the balance property of data. To address this issue, in this article, we propose a novel balanced spectral feature selection (BSFS) method, which not only selects the discriminative features but also picks those to reveal the balanced structure of data. To the best of our knowledge, this is the first spectral feature selection method considering balance structure of data. By introducing a balanced regularization term, we integrate the balanced spectral clustering and feature selection into a unified framework seamlessly. At last, the experiments on benchmark datasets show that the proposed one outperforms the conventional feature selection methods in both clustering performance and balance, which demonstrates the effectiveness and efficiency of the proposed method.

Consensus clustering provides an elegant framework to aggregate multiple weak clustering results to learn a consensus one that is more robust and stable than a single result. However, most of the existing methods usually use all data for consensus learning, whereas ignoring the side effects caused by some unreliable or difficult data. To address this issue, in this article, we propose a novel self-paced consensus clustering method with adaptive bipartite graph learning to gradually involve data from more reliable to less reliable ones in consensus learning. At first, we construct an initial bipartite graph from the base results, where the nodes represent the clusters and instances, and the edges indicate that an instance belongs to a cluster. Then, we adaptively learn a structured bipartite graph from this initial one by self-paced learning, i.e., we automatically determine the reliability of each edge with adaptive cluster similarity measuring and involve the edges in bipartite graph learning in order of their reliability. At last, we obtain the final consensus result from the learned structured bipartite graph. We conduct extensive experiments on both toy and benchmark datasets, and the results show the effectiveness and superiority of our method. The codes of this article are released in http://Doctor-Nobody.github.io/codes/code_SCCABG.zip.

Consensus clustering, which learns a consensus clustering result from multiple weak base results, has been widely studied. However, conventional consensus clustering methods only focus on the ensemble process while ignoring the quality improvement of the base results, and thus they just use the fixed base results for consensus learning. In this paper, we provide an alternative idea to improve the final consensus clustering performance by considering the base results refining. In our framework, we adaptively refine the base results in the process of the ensemble. In more detail, on one hand, we ensemble multiple K-means results to learn the consensus one by considering the consensus and diversity; on the other hand, we apply the consensus result to design a graph filter to learn a more cluster-friendly embedding for refining the base K-means results. In our framework, the consensus learning and base results refining are integrated into one unified objective function so that these two tasks can be boosted by each other. Then we design an effective iterative algorithm to optimize the carefully designed objective function. The extensive experiments on benchmark data sets demonstrate that the proposed method can outperform both the single clustering and the state-of-the-art consensus clustering methods. The codes of this paper are released inhttp://Doctor-Nobody.github.io/codes/ACMK.zip.

Clustering ensemble generates a consensus clustering result by integrating multiple weak base clustering results. Although it often provides more robust results compared with single clustering methods, it still suffers from the robustness problem if it does not treat the unreliability of base results carefully. Conventional clustering ensemble methods often use all data for ensemble, while ignoring the noises or outliers on the data. Although some robust clustering ensemble methods are proposed, which extract the noises on the data, they still characterize the robustness in a single level, and thus they cannot comprehensively handle the complicated robustness problem. In this paper, to address this problem, we propose a novel Tri-level Robust Clustering Ensemble (TRCE) method by transforming the clustering ensemble problem to a multiple graph learning problem. Just as its name implies, the proposed method tackles robustness problem in three levels: base clustering level, graph level and instance level. By considering the robustness problem in a more comprehensive way, the proposed TRCE can achieve a more robust consensus clustering result. Experimental results on benchmark datasets also demonstrate it. Our method often outperforms other state-of-the-art clustering ensemble methods. Even compared with the robust ensemble methods, ours also performs better.

The clustering ensemble has emerged as an important extension of the classical clustering problem. It provides an elegant framework to integrate multiple weak base clusterings to generate a strong consensus result. Most existing clustering ensemble methods usually exploit all data to learn a consensus clustering result, which does not sufficiently consider the adverse effects caused by some difficult instances. To handle this problem, we propose a novel self-paced clustering ensemble (SPCE) method, which gradually involves instances from easy to difficult ones into the ensemble learning. In our method, we integrate the evaluation of the difficulty of instances and ensemble learning into a unified framework, which can automatically estimate the difficulty of instances and ensemble the base clusterings. To optimize the corresponding objective function, we propose a joint learning algorithm to obtain the final consensus clustering result. Experimental results on benchmark data sets demonstrate the effectiveness of our method.

Consensus clustering provides a framework to ensemble multiple clustering results to obtain a consensus and robust result. Most existing consensus clustering methods usually apply all data to ensemble learning, whereas ignoring the side effects caused by some difficult or unreliable instances. To tackle this problem, we propose a novel self-paced consensus clustering method to gradually involve instances from more reliable to less reliable ones into the ensemble learning. We first construct an initial bipartite graph from the multiple base clustering results, where the nodes represent the instances and clusters and the edges indicate that an instance belongs to a cluster. Then, we learn a structured bipartite graph from the initial one by self-paced learning, i.e., we automatically decide the reliability of each edge and involves the edges into graph learning in order of their reliability. At last, we obtain the final consensus clustering result from the learned bipartite graph. The extensive experimental results demonstrate the effectiveness and superiority of the proposed method.

Multi-view classification has received considerable attention in recent years. We observed that the existing multi-view classification methods learn a consensus result by collecting all views and thus have two critical limitations. First, it is not scalable. Second, in many applications views of data are available over time; it is in-feasible to apply the existing multi-view learning methods to such streaming views. To address the two limitations, in this paper we propose a novel incremental multi-view SVM method, i.e., instead of processing all views simultaneously, we integrate them one by one in an incremental way. We first learn an initial model from the first view; next when a new view is available, we update the model and then apply it to learn a new consensus result. This incremental method is scalable and applicable to streaming views. We present a block coordinate descent algorithm whose convergence is theoretically guaranteed to optimize the induced objective function. Experimental results on several benchmark data sets further demonstrate the effectiveness of our method.

Graph-based semi-supervised learning (SSL) has attracted great attention over the past decade. However, there are still several open problems in this paper, including: 1) how to construct an effective graph over data with complex distribution and 2) how to define and effectively use pair-wise similarity for robust label propagation. In this paper, we utilize a simple and effective graph construction method to construct the graph over data lying on multiple data manifolds. The method can guarantee the connectiveness between pair-wise data points. Then, the global pair-wise data similarity is naturally characterized by geodesic distance-based joint probability, where the geodesic distance is approximated by the graph distance. The new data similarity is much more effective than previous Euclidean distance-based similarities. To apply data structure for robust label propagation, Kullback-Leibler divergence is utilized to measure the inconsistency between the input pair-wise similarity and the output similarity. In order to further consider intraclass and interclass variances, a novel regularization term on sample-wise margins is introduced to the objective function. This enables the proposed method fully utilizes the input data structure and the label information for classification. An efficient optimization method and the convergence analysis have been proposed for our problem. Besides, out-of-sample extension is discussed and addressed. Comparisons with the state-of-the-art SSL methods on image classification tasks have been presented to show the effectiveness of the proposed method.

Recently, structured sparsity inducing based feature selection has become a hot topic in machine learning and pattern recognition. Most of the sparsity inducing feature selection methods are designed to rank all features by certain criterion and then select the k top ranked features, where k is an integer. However, the k top features are usually not the top k features and therefore maybe a suboptimal result. In this paper, we propose a novel supervised feature selection method to directly identify the top k features. The new method is formulated as a classic regularized least squares regression model with two groups of variables. The problem with respect to one group of the variables turn out to be a 0-1 integer programming, which had been considered very hard to solve. To address this, we utilize an efficient optimization method to solve the integer programming, which first replaces the discrete 0-1 constraints with two continuous constraints and then utilizes the alternating direction method of multipliers to optimize the equivalent problem. The obtained result is the top subset with k features under the proposed criterion rather than the subset of k top features. Experiments have been conducted on benchmark data sets to show the effectiveness of proposed method.

Active learning is a machine learning technique that trains a classifier after selecting a subset from an unlabeled dataset for labeling and using the selected data for training. Recently, batch mode active learning, which selects a batch of samples to label in parallel, has attracted a lot of attention. Its challenge lies in the choice of criteria used for guiding the search of the optimal batch. In this paper, we propose a novel approach to selecting the optimal batch of queries by minimizing the α-relative Pearson divergence (RPE) between the labeled and the original datasets. This particular divergence is chosen since it can distinguish the optimal batch more easily than other measures especially when available candidates are similar. The proposed objective is a min-max optimization problem, and it is difficult to solve due to the involvement of both minimization and maximization. We find that the objective has an equivalent convex form, and thus a global optimal solution can be obtained. Then the subgradient method can be applied to solve the simplified convex problem. Our empirical studies on UCI datasets demonstrate the effectiveness of the proposed approach compared with the state-of-the-art batch mode active learning methods.

In classification tasks, labeled data is a necessity but sometimes difficult or expensive to obtain. On the contrary, unlabeled data is usually abundant. Recently, different active learning algorithms are proposed to alleviate this issue by selecting the most informative data points to label. One family of active learning methods comes from Optimum Experimental Design (OED) in statistics. Instead of selecting data points one by one iteratively, OED-based approaches select data in a one-shot manner, that is, a fixed-sized subset is selected from the unlabeled dataset for manually labeling. These methods usually use kernels to represent pair-wise similarities between different data points. It is well known that choosing optimal kernel types (e.g. Gaussian kernel) and kernel parameters (e.g. kernel width) is tricky, and a common way to resolve it is by Multiple Kernel Learning (MKL), i.e., to construct a few candidate kernels and merge them to form a consensus kernel. There would be different ways to combine multiple kernels, one of which, called the the globalised approach is to assign a weight to each candidate kernel. In practice different data points in the same candidate kernel may not have the same contribution in the consensus kernel, this requires assigning different weights to different data points in the same candidate kernel, leading to the localized approach. In this paper, we introduce MKL to OED-based active learning, specifically we propose globalised and localized multiple kernel active learning methods, respectively. Our experiments on six benchmark datasets demonstrate that the proposed methods have better performance than existing OED-based active learning methods.

The problem of feature selection has raised considerable interests in the past decade. Traditional unsupervised methods select the features which can faithfully preserve the intrinsic structures of data, where the intrinsic structures are estimated using all the input features of data. However, the estimated intrinsic structures are unreliable/inaccurate when the redundant and noisy features are not removed. Therefore, we face a dilemma here: one need the true structures of data to identify the informative features, and one need the informative features to accurately estimate the true structures of data. To address this, we propose a unified learning framework which performs structure learning and feature selection simultaneously. The structures are adaptively learned from the results of feature selection, and the informative features are reselected to preserve the refined structures of data. By leveraging the interactions between these two essential tasks, we are able to capture accurate structures and select more informative features. Experimental results on many benchmark data sets demonstrate that the proposed method outperforms many state of the art unsupervised feature selection methods.

With unstructured heterogeneous multimedia data such as texts, images being more and more widely used on the web, cross-media retrieval has become an increasingly important task. One of the key techniques in cross-media retrieval is how to compute distances or similarities among different types of media data. In this paper, we propose a novel heterogeneous metric learning method to compute distances between images and texts. We extend Locally Linear Embedding (LLE) to deal with heterogeneous data, so that we can not only preserve homogeneous local information but also capture heterogeneous constraints. In order to handle the out-of-sample problem, we learn two map functions from the embedding, and use them to transform heterogeneous data into a homogeneous space and do the retrieval in the new space. The experimental results on two real-world datasets show the effectiveness of our approach.

In this paper, we consider the problem of unsupervised feature selection. Recently, spectral feature selection algorithms, which leverage both graph Laplacian and spectral regression, have received increasing attention. However, existing spectral feature selection algorithms suffer from two major problems: 1) since the graph Laplacian is constructed from the original feature space, noisy and irrelevant features may have adverse effect on the estimated graph Laplacian and hence degenerate the quality of the induced graph embedding, 2) since the cluster labels are discrete in natural, relaxing and approximating these labels into a continuous embedding can inevitably introduce noise into the estimated cluster labels. Without considering the noise in the cluster labels, the feature selection process may be misguided. In this paper, we propose a Robust Spectral learning framework for unsupervised Feature Selection (RSFS), which jointly improves the robustness of graph embedding and sparse spectral regression. Compared with existing methods which are sensitive to noisy features, our proposed method utilizes a robust local learning method to construct the graph Laplacian and a robust spectral regression method to handle the noise on the learned cluster labels. In order to solve the proposed optimization problem, an efficient iterative algorithm is proposed. We also show the close connection between the proposed robust spectral regression and robust Huber M-estimator. Experimental results on different datasets show the superiority of RSFS.

The problem of software artifact retrieval has the goal to effectively locate software artifacts, such as a piece of source code, in a large code repository. This problem has been traditionally addressed through the textual query. In other words, information retrieval techniques will be exploited based on the textual similarity between queries and textual representation of software artifacts, which is generated by collecting words from comments, identifiers, and descriptions of programs. However, in addition to these semantic information, there are rich information embedded in source codes themselves. These source codes, if analyzed properly, can be a rich source for enhancing the efforts of software artifact retrieval. To this end, in this paper, we develop a feature extraction method on source codes. Specifically, this method can capture both the inherent information in the source codes and the semantic information hidden in the comments, descriptions, and identifiers of the source codes. Moreover, we design a heterogeneous metric learning approach, which allows to integrate code features and text features into the same latent semantic space. This, in turn, can help to measure the artifact similarity by exploiting the joint power of both code and text features. Finally, extensive experiments on real-world data show that the proposed method can help to improve the performances of software artifact retrieval with a significant margin.

In this paper, we consider the problem of feature selection in unsupervised learning scenario. Recently, spectral feature selection methods, which leverage both the graph Laplacian and the learning mechanism, have received considerable attention. However, when there are lots of irrelevant or noisy features, such graphs may not be reliable and then mislead the selection of features. In this paper, we propose the Local and Global Discriminative learning for unsupervised Feature Selection (LGDFS), which integrates a global and a set of locally linear regression model with weighted l2-norm regularization into a unified learning framework. By exploring the discriminative and geometrical information in the weighted feature space, which alleviates the effects of the irrelevant features, our approach can find the most representative features to well respect the cluster structure of the data. Experimental results on several benchmark data sets are provided to validate the effectiveness of the proposed approach.

Due to the fast evolution of the information on the Internet, update summarization has received much attention in recent years. It is to summarize an evolutionary document collection at current time supposing the users have read some related previous documents. In this paper, we propose a graph-ranking-based method. It performs constrained reinforcements on a sentence graph, which unifies previous and current documents, to determine the salience of the sentences. The constraints ensure that the most salient sentences in current documents are updates to previous documents. Since this method is NP-hard, we then propose its approximate method, which is polynomial time solvable. Experiments on the TAC 2008 and 2009 benchmark data sets show the effectiveness and efficiency of our method.

Nonnegative matrix factorization (NMF) is a popular technique for learning parts-based representation and data clustering. It usually uses the squared residuals to quantify the quality of factorization, which is optimal specifically to zero-mean, Gaussian noise and sensitive to outliers in general cases. In this paper, we propose a robust NMF method based on the correntropy induced metric, which is much more insensitive to outliers. A half-quadratic optimization algorithm is developed to solve the proposed problem efficiently. The proposed method is further extended to handle outlier rows by incorporating structural knowledge about the outliers. Experimental results on data sets with and without apparent outliers demonstrate the effectiveness of the proposed algorithms.

Update summarization is to summarize a document collection B given that the users have already read another document collection A, which has time stamp prior to that of B. An important and challenging issue in update summarization is that contents in B already covered by A should be excluded from the update summary. In this paper, we propose a graph-based regularization framework MarginRank for update summarization. MarginRank extends the cost function of Zhou's Manifold Ranking with suppression terms, suppression of A on B, to fulfil the assumption that users have read A. MarginRank ranks sentences in B in a way that the top ranked sentences are most important and at the same time cover different contents from A. Experiments on the benchmark data sets TAC 2008 and 2009 show the effectiveness of the proposed method.

Novelty, coverage and balance are important requirements in topic-focused summarization, which to a large extent determine the quality of a summary. In this paper, we propose a novel method that incorporates these requirements into a sentence ranking probability model. It differs from the existing methods in that the novelty, coverage and balance requirements are all modeled w.r.t. a given topic, so that summaries are highly relevant to the topic and at the same time comply with topic-aware novelty, coverage and balance. Experimental results on the DUC 2005, 2006 and 2007 benchmark data sets demonstrate the effectiveness of our method.

In this paper, we propose the Interval-valued Matrix Factorization (IMF) framework. Matrix Factorization (MF) is a fundamental building block of data mining. MF techniques, such as Nonnegative Matrix Factorization (NMF) and Probabilistic Matrix Factorization (PMF), are widely used in applications of data mining. For example, NMF has shown its advantage in Face Analysis (FA) while PMF has been successfully applied to Collaborative Filtering (CF). In this paper, we analyze the data approximation in FA as well as CF applications and construct interval-valued matrices to capture these approximation phenomenons. We adapt basic NMF and PMF models to the interval-valued matrices and propose Interval-valued NMF (I-NMF) as well as Interval-valued PMF (I-PMF). We conduct extensive experiments to show that proposed I-NMF and I-PMF significantly outperform their single-valued counterparts in FA and CF applications.