The graph-based clustering aims to utilize structural information from graphs to provide clustering solutions. However, many existing graph clustering methods separate graph construction from the learning of clustering results, and rely on the assumption of consistent feature importance, which often leads to suboptimal clustering outcomes. Anchor-based graph clustering offers an efficient and scalable solution for clustering tasks. Nevertheless, the need to manually specify the number of anchors limits its practicality. Motivated by these issues, this paper proposes a method called Multi-granularity Granular-ball Anchor Graph Clustering with self-weighting (MGAGC). The MGAGC utilizes granular-ball computing to adaptively generate granular-ball anchors based on the data distribution, where the number of granular-ball anchors is much smaller than the number of data samples. Then, by enabling interaction between fine-granularity sample points and coarse-granularity granular-ball anchors in a self-weighting feature space, the MGAGC integrates graph construction with the learning of clustering results. Extensive experiments are conducted on fourteen public datasets to compare the proposed MGAGC with nine classic or state-of-the-art baseline clustering methods. Experimental results show that MGAGC achieves an average ACC of 75.50% and an average NMI of 51.22%, outperforming other clustering methods by an average of 13.60% and 12.21%, respectively. Moreover, statistical test results indicate that its performance differences are statistically significant compared to most of the competing methods. Code is available at https://github.com/awaw-Liyely/2026-IPM-MGAGC.

Continual learning is plagued by catastrophic forgetting. While storing representative exemplars is an effective mitigation strategy, such exemplars often lack cross-task representativeness and their knowledge may interfere with new task learning. This issue is particularly prominent in tabular settings under high-heterogeneity feature spaces. Inspired by the neurobiological framework of memory and forgetting, we propose a Tabular Continual Learning method from high-heterogeneity feature spaces via Memory and Forgetting dual-driven (MFTCL). Specifically, MFTCL combines two complementary strategies. First, a memory storage strategy based on evidence theory is designed to select exemplars that preserve both intra-task and cross-task representativeness. Second, an adaptive active forgetting strategy based on task similarity is developed to integrate network parameters, reducing interference from old knowledge during new task learning. Extensive comparisons on three benchmark tabular datasets (Isolet, Helena, and Nslkdd) validate the effectiveness of MFTCL in high-heterogeneity feature spaces. Further, a case study on five tabular datasets for disease diagnosis confirms its practical applicability. On the Helena dataset (heterogeneity rate: [0.61, 1.00]), MFTCL consistently outperforms all baseline methods across all evaluation metrics. Notably, it reduces the Forgetting Rate of Average Area Under the Curve (AAUCF) by at least 34.51%.

To overcome the computational bottlenecks of traditional density-based clustering, we propose Granular-Ball SKeleton clustering (GBSK), a scalable algorithm that achieves near-linear time complexity while preserving topological accuracy. GBSK introduces a strategic shift from full density estimation to the sketching of geometric density skeleton-recover a graph connecting high-density modes that captures essential cluster connectivity. Theoretically, we find that granular-ball density statistics can serve as a computationally efficient, asymptotically approximate local proxy for kernel density estimation (KDE), providing a statistical support for discrete mode extraction within the well-established KDE framework. Methodologically, GBSK integrates three key components: adaptive granular-ball construction for efficient local data approximation, multi-stage sampling for rapid density estimation, and a secondary refinement process that aggregates candidate modes from all sample sets to produce a robust final density skeleton. To enhance usability, we introduce an adaptive variant, AGBSK, which reduces hyperparameters to just the cluster count. Extensive experiments on datasets scaling up to 100 million instances and 3072 dimensions demonstrate that GBSK and AGBSK maintain competitive accuracy while achieving orders-of-magnitude speedup over state-of-the-art methods.

The k-Nearest Neighbor (KNN) algorithm is widely used across various tasks. The selection of the k value is a key issue because it significantly impacts performance. In this paper, an adaptive and efficient KNN approach via granular-ball computing is proposed. The method consists of two stages. In the training stage, the dataset is first coarsely partitioned to reduce the complexity of data distributions within a granular ball, and then the Fisher criterion is introduced to control ball splitting and stopping, yielding a multi-granularity granular ball representation. In the prediction stage, the nearest granular ball is first located through a weighted distance mechanism, and an adaptive neighborhood is then constructed around the test sample. The effective k value is dynamically determined by the actual number of samples contained in this neighborhood. The neighborhood induced by the nearest granular ball provides more stable local group information, thereby improving robustness against noise and local perturbations. Experimental results demonstrate that the proposed method outperforms existing KNN variants across multiple datasets in terms of both accuracy and efficiency. The code has been open-sourced for reproducibility: https://github.com/lianxiaoyu724/Adaptive-GBKNN.

Pathological image diagnosis faces challenges such as complex tissue textures, high heterogeneity, and difficulty in capturing global contextual features. Traditional CNNs, such as ResNet, rely on fixed-size integer-order kernels, which limit their ability to model long-range dependencies and subtle morphological variations. To address these issues, inspired by the brain’s non-local connectivity and memory mechanisms, we propose FracResNet34—an enhanced ResNet34 architecture incorporating Grünwald-Letnikov fractional-order convolutions. This design improves sensitivity to both local details and non-local patterns without increasing parameter complexity. Experiments on PathMNIST, Colorectal Cancer Histology Textures, and LC-L datasets demonstrate that FracResNet34 consistently outperforms conventional ResNet34 and state-of-the-art models such as MedViT and SwinV2 in classification accuracy, robustness, and stability. It achieves lower variance, more negative skewness, and higher kurtosis, indicating more reliable and consistent predictions. These results highlight the promise of fractional-order convolution as a powerful tool for medical image analysis.

Incremental learning has emerged as a vital paradigm in machine learning, enabling models to adaptively learn from streaming or continuously arriving data without retraining from scratch. However, incremental learning faces two fundamental challenges: the uncertainty in datasets and the efficiency to handle massive data volumes. Granular-ball computing (GBC), as a recent development in granular computing, excels in rapidly generating robust and scalable information granules, called granular-balls (GBs), that naturally support coarse-to-fine data approximation. By integrating GBC with incremental learning, we propose an adaptive model incremental learning with granular-ball shadowed sets (ILGBSS). ILGBSS constructs and updates GBs incrementally, minimizing the need for frequent structural adjustments such as granular-ball (GB) splitting. To further improve the model’s robustness in uncertain environments, we extend ILGBSS with three-way decision theory, resulting in ILGBSS with three-way classification (ILGBSS-3WC). We conduct experiments on sixteen benchmark datasets, comparing our methods with three state-of-the-art GB-based algorithms and three widely used incremental learning models. The results consistently demonstrate that ILGBSS-3WC classifiers achieve superior classification accuracy and computational efficiency, validating the effectiveness of our approach in both static and evolving data environments.

Current studies on explaining graph neural networks (GNNs) are proposed separately at the model or instance levels, each offering unique insights into GNNs’ prediction behaviors. Few studies have explored the potential of bridging multiple-level explainers to enhance explanation quality. To fill this gap, we propose IMOE, a simple yet effective framework that Incorporates Model-level explanations into the Optimization of instance-level Explainers. IMOE learns model-level explanations using GFlowNet. It further extracts representative prototype graph patterns with appropriate diversity via graph clustering, mitigating noise and computational overhead associated with large amounts of graph patterns. Moreover, IMOE leverages the prototype graph patterns to guide the optimization of the instance-level explainer, offering global information for learning faithful explanations. Experiments conducted on four datasets demonstrate the effectiveness and generalization of IMOE. Qualitative studies emphasize IMOE’s ability to generate explanations that align with human intuition and domain knowledge. Data and code are available at https://anonymous.4open.science/r/IMOE-0FFC

Graph Neural Networks (GNNs) have demonstrated superior performance in text classification by modeling textual data as graphs, where nodes represent words or documents, and edges denote semantic or syntactic relationships. However, existing studies either fail to construct expressive yet noise-free text graphs or lack sufficient representational power for learning text graph representations. To mitigate these limitations, we propose a novel Gated Fusion Network, called GFork, for heterogeneous text graph construction and representation learning to enhance the accuracy of GNN-based text classification. Specifically, we construct chunk-level graphs with multi-granularity, semantically meaningful phrases as nodes, and incorporate cross-sentence connections derived from coreference resolution to model long-range dependencies. To mitigate interference from noisy information, we employ attribute-enhanced personalized PageRank (aPPR) to prune irrelevant information, highlighting the weights of critical information based on global contextual relevance. Furthermore, during the graph learning phase, we design a BERT-enhanced fusion GNN that incorporates a gradient gating mechanism (G2). This network leverages BERT for rich contextual features and a GNN to model global dependencies. The mechanism generates gating values based on local graph gradients, adaptively controlling node updates during GNN propagation. This effectively integrates information from different sources while mitigating noise from irrelevant or heterophilic edges. Experiments conducted on five benchmark datasets show that GFork consistently achieves the best performance on 4 out of 5 popular datasets, compared with 13 state-of-the-art methods. In particular, GFork significantly outperforms others on the long-text dataset Ohsumed, with an absolute accuracy improvement of approximately 11% over the second-best method. The code is available at https://github.com/sss-Cris/GFork.

GNN-to-MLP (G2M) distillation has been proven effective in alleviating the inference latency of Graph Neural Networks (GNNs) by distilling graph representations and knowledge from GNNs to MLPs. However, the existing methods face two notable issues: (1) the graph representation module of the methods neglects the importance of nodes, resulting in student MLPs lacking the ability to focus on significant nodes; (2) they ignore that G2M distillation is a cross-architecture knowledge distillation involving a model gap between teacher and student models, leading to low knowledge transferability. To address the above issues, this paper proposes a novel method called Hybrid Graph Representation and Latent Space Translation (GRLT). The proposed GRLT captures richer graph information and enhances knowledge transferability, thereby improving the performance of the student model. Specifically, we incorporate graph prior knowledge into the hybrid graph representation module to obtain structural embeddings of the graphs and the aggregated features of nodes. In addition, we introduce a latent space translation feature distillation module, which transforms conventional feature map distillation into a two-stage process by first aligning the consensus representations between the teacher and the student via the Generalized Procrustes Analysis (GPA) and then performing feature distillation through cosine similarity. This design reduces the model gap and enhances knowledge transferability. GRLT has been experimentally verified on seven datasets and achieves superior overall performance. When SAGE is used as the teacher model, the distilled student MLP obtains average performance improvements of 1.72%, 3.72%, and 22.41% over the state-of-the-art method NOSMOG, the teacher GNN, and the vanilla MLP, respectively.

Graph Neural Network (GNN) explainers aim to identify explanatory subgraphs that provide rationales for GNNs' predictions. Nevertheless, the distribution shift of subgraphs introduces out-of-distribution (OOD) issues into GNNs' predictions. The OOD issues compromise explainers' optimization, as the optimization relies on the prediction differences between the original graph and the subgraph. To this end, we propose a plug-and-play framework to adjust the distribution shift of subgraphs during the explainers' optimization. By introducing a distribution shift consistency objective, we constrain explanatory subgraphs of similar graphs to be consistent, modeling the learning of explanation as a consistency-guided “denoising” process. Additionally, we propose a parameter-sharing generator to act as a “noise-adding” process in each epoch. This generator learns proxy graphs of explanatory subgraphs to adjust the distribution shift, enhancing the explainers' optimization. We apply the proposed framework to three state-of-the-art explainers and evaluate its performance on four real-world datasets. The results demonstrate that the learned graphs align with the original graphs' distribution and enhance the performance of explainers in terms of AUC-ROC, Robust Fidelity, and Stability. Furthermore, it significantly outperforms three state-of-the-art distribution shift adjusting algorithms. Datasets and codes are available at https://github.com/hegy1024/EnDist.

Recommender systems enhance user experience by delivering personalized suggestions derived from users' historical behavior. However, conventional approaches face challenges in processing large-scale data while simultaneously preserving user privacy and maintaining stable training. To address these issues, we propose Fed-MWAE, a novel federated variational autoencoder (VAE) framework for recommendation tasks. The framework incorporates a sparsely activated Mixture-of-Experts (MoE) module to model diverse user behavior patterns across expert subnetworks. A top-$k$ gating mechanism selectively aggregates expert outputs, thereby improving computational efficiency without compromising accuracy. Furthermore, Fed-MWAE employs VAEs to capture complex latent structures and replaces the conventional Kullback-Leibler (KL) divergence with the Wasserstein distance, enabling smoother optimization and more stable convergence. Training is conducted in a federated learning setting, where local clients perform on-device updates to safeguard data privacy, and the updates are aggregated using the Federated Averaging (FedAvg) algorithm to enhance scalability and communication efficiency. Extensive experiments on four public datasets demonstrate that Fed-MWAE consistently outperforms strong baselines, achieving improvements of 5.46% in NDCG, 0.66% in Recall@20, 4.85% in Recall@50, and a 2.99% reduction in loss. These results validate the effectiveness of Fed-MWAE in balancing accuracy, efficiency, stability, and privacy in federated recommender systems.

Federated learning, as a new technology to protect data privacy, effectively solves the problem of data silos. To solve the problem of data heterogeneity in distributed architecture, this paper proposes a personalized federated learning method called FedPL. It is based on iterative partitioning and parameter hierarchy. Firstly, to address the slow model convergence caused by non-independent and identically distributed (Non-IID) data, and considering the advantages of clustering in resolving weight divergence, this paper proposes an iterative partitioning method based on a ternary cosine similarity measure. In the process of model training, the proposed method dynamically adjusts the division results according to the similarity of parameter updates. It realizes the rapid convergence of the local model and thus guides the rapid convergence of the global model. Secondly, aiming at the high complexity of federated computing, considering the advantage of SVD in reducing the computational complexity of massive data, a method of computing similarity based on SVD is proposed. This method performs dimensionality reduction on the base level parameters of the clients, achieving improved efficiency in similarity computation. Finally, to address the problem of local distributional differences, this paper proposes a personalized federated learning method based on parameter layering, taking into account that different preferences can be captured from clients' raw data. This method trains the base layer on the global data and the personalized layer on the local data respectively. It helps mitigate the issues arising from local heterogeneity, thereby achieving personalized customization for client models. The experiments demonstrate that this method can accelerate the federated training process while providing personalization for individual clients, thereby enhancing the adaptability of local models.

In the realm of machine learning, the challenge of extracting meaningful low-dimensional structures from high-dimensional data is paramount. Deep learning techniques, particularly Variational Autoencoders (VAE), have proven adept at this task yet often lack semantic interpretability in their representations. To address this issue, disentangled representation learning has been proposed and utilized to learn interpretable representations from data. However, existing methods often rely on heuristic constraints that are manually set and fixed, hindering adaptability and optimization. In this paper, the Adaptive Weighted Disentangling Variational Autoencoder (AwingVAE) is proposed, which introduces a feedback mechanism into the VAE framework, allowing for dynamic parameter optimization and adaptive dimension weighting based on Kullback-Leibler divergence. This feedback mechanism effectively enhances the model's disentanglement, generation, and robustness, with maximum gains of 17.4%, 7.565, and 15.8%, respectively. The proposed method thus offers a new perspective on VAE utilization for representation learning, with extensive evaluations on benchmark datasets supporting its effectiveness. Implementation available at https://github.com/YuSanTu/AwingVAE.

Dynamic influence maximization (IM) is challenging because network evolution can invalidate previous seed sets and make repeated diffusion evaluations expensive. Existing methods often optimize snapshots independently, search over individual nodes, and make limited use of temporal continuity. We propose GBKT-ADE, an adaptive differential evolution framework driven by granular-ball guidance and knowledge transfer. For each snapshot, GBKT-ADE constructs topology-induced granular-balls and extracts representative nodes to guide initialization, repair, and mutation. It transfers repaired elite solutions, structural information, and successful evolutionary parameters from the preceding snapshot, while relative edge overlap regulates structural and parameter reuse. GBKT-ADE redesigns differential evolution for discrete seed sets and controls its search parameters adaptively. A lightweight surrogate score screens trial seed sets before full Monte Carlo evaluations under the independent cascade model, reducing costly evaluations while retaining the original IM objective for final selection. Experiments against eight baselines on six dynamic social networks show larger estimated influence spread, faster convergence, and shorter running time across different seed budgets and propagation probabilities. Compared with the strongest baseline, GBKT-ADE improves influence spread by up to 20.11%. It also reduces running time by up to 66.30% compared with the fastest metaheuristic baseline and by 99.66% compared with greedy search.

Graph Neural Networks (GNNs) have made significant strides in the analysis and modeling of complex network data, particularly excelling in graph and node classification tasks. However, the "closed box" nature of GNNs impedes user understanding and trust, thereby restricting their broader application. This challenge has spurred a growing focus on demystifying GNNs to make their decision-making processes more transparent. Traditional methods for explaining GNNs often rely on selecting subgraphs and employing combinatorial optimization to generate understandable outputs. However, these methods are closely linked to the inherent complexity of GNNs, leading to higher explanation costs. To address this issue, we introduce a lower-complexity proxy model to explain GNNs. Our approach leverages knowledge distillation with inter-layer alignment, specifically targeting the challenge of over-smoothing and its detrimental impact on model explanation. Initially, we distill critical insights from complex GNN models into a more manageable proxy model. We then apply an inter-layer alignment-based distillation technique to ensure alignment between the proxy and the original model, facilitating the extraction of node or edge-level explanations within the proxy framework. We theoretically prove that the explanations derived from the proxy model are faithful to both the proxy and the original model. Additionally, we show that the upper bound of unfaithfulness between the proxy and the original model remains consistent when the distillation error is infinitesimal. This inter-layer alignment knowledge distillation technique enables the proxy model to retain the knowledge learning and topological representation capabilities of the original model to the greatest extent. Experimental evaluations on numerous real-world datasets confirm the effectiveness of our method, demonstrating robust performance.

Clustering is a significant technique in data mining, which can uncover the hidden correlation information and obtain deeper understanding of the inherent structure of data. However, when dealing with the data with extremely uneven density and increasingly complex structure, most current clustering algorithms only obtain results at a single granular level, resulting in a unilateral understanding of the data. Therefore, a novel multigranularity clustering algorithm based on grid partition and fuzzy quotient space (MGCGF) is proposed in this article. First, by introducing the Gaussian kernel density function to characterize the distribution characteristics of data, a grid partition method is designed to select representative points for clustering. Second, based on the results of grid partition, the representative points composed of the maximum density values in each dimension of the grids are used for multigranularity clustering to improve the clustering efficiency. Finally, a multigranularity clustering algorithm is proposed by introducing fuzzy quotient space theory with representative points as input. MGCGF can be used to uncover the hierarchical structure of the data itself and form a multigranularity space. And the clustering results with multigranularity can be directly provided from multigranularity spaces without reclustering. By comparing with the other six clustering algorithms, the feasibility is verified in terms of both efficiency and accuracy.

Histopathological image diagnosis is an important component of intelligent medical systems. Although deep learning has significantly advanced this field, existing methods often rely on models pre-trained on natural image datasets, leading to domain shift and suboptimal generalization to histopathological images. Furthermore, current approaches are constrained by insufficient multi-granularity feature extraction and complex model architectures, which hinder deployment in clinical environments. To address these challenges, we propose a novel method that incorporates Gr & uuml;nwald-Letnikov (GL) fractionalorder derivatives into a deep neural network named MGFD. The integration of fractional-order derivatives enables MGFD to effectively extract morphological features across multiple granularities. By efficiently capturing multi-scale representations, our model eliminates the need for pre-trained models. Experimental results on three histopathological datasets demonstrate that the proposed method achieves competitive classification performance under different conditions. Furthermore, by adjusting the fractional order alpha, the model can flexibly control the granularity of feature representation, reducing dependence on large training samples and improving adaptability across diverse tasks. Such a property allows MGFD to support deployment on resource-constrained

Granger causality based on multivariate autoregressive (MVAR) models provides a principled way to estimate directed brain networks, represent hidden neural dynamics, and analyze information flow in EEG. However, MVAR parameter estimation is easily affected by intrinsic artifacts, such as muscle and eye-movement contamination, especially when only short EEG windows are available. To construct sparse causal brain networks under these conditions, we propose GG-Lap, a Bayesian MVAR estimation method that combines a generalized Gaussian prior for MVAR coefficients with a Laplace distribution for fitting errors. A scaled-Gaussian variational approximation is introduced to solve the resulting non-Gaussian posterior, allowing the model to jointly suppress outlier effects and induce controllable sparsity. Compared with Lap-SBL, which may over-prune causal coefficients through ARD-type sparsity, and DLap, which may retain relatively dense noisy connections, GG-Lap provides a more balanced sparse and robust estimate. Simulation experiments show that GG-Lap accurately recovers sparse directed connections under severe artifact contamination and short noisy sequences. Applications to motor imagery (MI) and epilepsy EEG further indicate that GG-Lap captures task-related and lesion-related connectivity patterns more clearly than comparison methods. GG-Lap can therefore serve as an effective method for robust causal connectivity inference, with potential applications in brain-computer interfaces (BCI), brain-machine interaction, and neurological or psychiatric network analysis. The source code of GG-Lap is available at https://github.com/yyzcqupt/GG-Lap.

Granular-Ball Computing (GBC) is an efficient, robust, and highly interpretable multi-granularity representation and computation method. Nonetheless, most feature selection methods based on GBC require considerable time to calculate the significance measures of features or repeatedly generate granular balls, which limits their applicability to high-dimensional data. The graph-based feature selection effectively reduces dimensionality by exploiting feature correlations and redundancies. However, most graph-based feature selection methods are limited to a fine and single granularity knowledge space. Driven by these issues, this paper first proposes the granular-ball divergence-based fuzzy rough set to characterize the uncertain information from a multi-granularity perspective. Then, the minimum discriminative criterion for constructing a hypergraph is evaluated by the approximation operators, and the correlations between theories are established. On this basis, the importance of features is defined as the weights of hypernodes, and the strategies of Important Retaining (IR) and Redundant Pruning (RP) are designed to select the most important feature and improve execution efficiency, respectively, which is equivalent to an iterative weighted maximum coverage problem with dynamic weight updates. Finally, a feature selection algorithm is designed to select the best feature subset. The experimental results show that our algorithm achieves better classification performance and higher execution efficiency.