With the rapid development of social media, predicting derived topic propagation faces three core challenges: data sparsity, high-dimensional noise, and complex group interactions. To address these in a coherent manner, this paper proposes an integrated framework that sequentially tackles each challenge. First, to combat data sparsity, a multi-task learning (MTL) mechanism is introduced. It enables knowledge transfer from data-rich original topics to sparse derived topics by learning shared feature representations, effectively augmenting the training signal for derived topics. Building on this, to handle the resultant high-dimensional and noisy feature space, a sparse representation module is applied. It performs low-rank and sparse coding to distill essential propagation features and eliminate redundancy, producing a purified and robust input for the final stage. Finally, to model the strategic group interactions that drive propagation, we quantify intra-group identity and inter-group confrontation using evolutionary game theory. These dynamics are embedded into a novel Identification–Confrontation Graph Convolutional Network (IC-GCN), which explicitly captures strategy-aware social influences for precise behavior prediction. Extensive experiments on four real-world derived topics from Weibo and Twitter demonstrate the framework’s effectiveness. The complete IC-GCN model consistently and significantly outperforms state-of-the-art baselines, validating that the logical integration of MTL (for sparsity), sparse coding (for purification), and game-theoretic GCN (for interaction modeling) substantially enhances prediction accuracy.
In this paper we study a shape optimization problem for a variational-hemivariational inequality describing the steady-state Navier-Stokes model of an incompressible fluid of the Bingham type in a bounded domain with a nonmonotone slip boundary condition. First, we provide results on the stability of solutions to the variational-hemivariational inequality on variations of the domain. Then, an existence result is proved for an optimal shape design problem for the variational-hemivariational inequality. Finally, we discuss the convergence of shape optimization problems for the regularized variational-hemivariational inequality when the regularization parameter tends to zero.
Multimodal optimization problem (MMOP) seeks multiple solutions for a single objective under varying preferences. Differential Evolution (DE), known for its strong search capability, is widely applied, with niching as a key divide-and-conquer assistance technique. However, existing niching methods often fail to capitalize on population distribution knowledge accumulated through historical iterations, and are often hindered by parameter sensitivity and complex designs. To this end, we propose AMDE-GN, an adaptive multimodal DE framework with granular ball niching. It leverages a granular ball structure to adaptively partition the population from coarse-to-fine based on distance and distribution driven criteria. This regionalizes learning and search within subpopulations, effectively preserving diversity and enabling simultaneous tracking of different global optima. We further introduce an elite-led mutation strategy that maintains stochastic exploration while biasing search toward promising regions, improving convergence efficiency. In addition, AMDE-GN incorporates adaptive DE parameter control and heterogeneity-aware local search, applying differentiated refinement according to individual quality to enhance solution accuracy and achieve a better exploration-exploitation balance. Experiments on 20 multimodal benchmark problems confirm that AMDE-GN generally achieves competitive performance against state-of-the-art methods.
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%.
Multi-view data with complementary information and consensus provides powerful modeling capabilities for unsupervised clustering. Existing methods typically model each view independently, overlooking the semantic alignment and structural differences between views. Meanwhile, in the process of ensuring multi-view consistency, they fail to adequately consider the quality of the views, resulting in representation degradation. To that end, this paper proposes the PA-LRG framework, which combines feature-aware aggregation with Low-rank adaptive fusion to enhance cluster consistency. Specifically, we design a hierarchical feature aggregation module (HFAB), which introduces dynamic learnable prototypes to serve as cross-view semantic anchors. This enables each view feature to actively perceive its semantic attribution during the modeling process and to carry out structural enhancement and semantic aggregation under the guidance of the prototypes. Furthermore, we propose a Low-rank Adaptive Fusion (LRAF) module. This module enhances clustering structure by imposing low-rank constraints on the view correlation matrix and combining Laplacian low-rank optimization with adaptive fusion, which achieves dynamic fusion under structure-aware guidance. Finally, feature space alignment and clustering structure consistency are jointly optimized under a multi-contrastive learning mechanism to improve the discriminative ability of the model and the robustness of the clustering. Experimental results show that PA-LRG outperforms existing 14 competitive methods on several multi-view datasets.
