Anchor graph clustering improves scalability by replacing the full sample graph with a sample-anchor bipartite graph. However, existing methods still face three limitations: relaxation-based spectral methods may lose discriminative information during post-processing discretization; hard anchor-based clustering cannot describe boundary uncertainty; and existing fuzzy anchor-based methods often require multiple regularization terms to avoid degenerate fuzzy assignments. To address these issues, we propose FAFCN, a fast anchor-based fuzzy clustering method with nuclear-norm regularization. FAFCN jointly learns sample-level and anchor-level fuzzy memberships under rowsimplex constraints, enabling direct fuzzy label inference without relaxation-discretization. The nuclear-norm term implicitly suppresses completely fuzzy and severely imbalanced assignments while promoting balanced and discriminative membership structures. Since maximizing the nuclear norm makes the objective non-convex, we design an efficient alternating optimization algorithm: the sample membership subproblem is solved by an iteratively reweighted strategy, and the anchor membership subproblem is solved by coordinate descent with closed-form row-wise updates. The algorithm achieves linear scalability with respect to the number of samples. Experiments on synthetic and real-world datasets demonstrate the effectiveness and efficiency of FAFCN.
Anchor guidance mechanism has demonstrated strong scalability for clustering large-scale datasets, driving its widespread applications in multiview clustering in recent years. Accordingly, a series of anchor-based multiview subspace clustering methods have been proposed to improve computational efficiency. However, many of these methods suffer from three major limitations. First, they generally focus on the integrated or specific local structures, while ignoring global information. Second, the typical postprocessing with singular value decomposition and k-means incurs extra time burden and yields volatile clustering performance. Third, different views may contain noise and exhibit complex relationships, making crisp partitioning unreliable and thereby requiring robust, uncertainty-aware learning. To address these issues, a scalable dual fuzzy learning and structure fusion multiview subspace clustering (DFFMSC) framework is proposed. Inspired by the effectiveness of fuzzy clustering in handling uncertain data, we incorporate fuzzy learning to enable more flexible and robust cluster partitioning. Unlike many multiview fuzzy clustering methods involving intricate cooperative learning terms, we incorporate two concise fuzzy learning terms into a dual-facilitated fuzzy learning component. One integrates the separate compact representations to learn a unified fuzzy membership matrix, while the other simultaneously enhances it through global-local structure fusion learning. With a fast alternating optimization algorithm, the labels are directly obtained from the optimal fuzzy membership matrix. Overall, the proposed DFFMSC not only adequately fuses the local and global structures, but also achieves one-step clustering without postprocessing. Extensive experiments on nine popular multiview datasets validate its effectiveness and efficiency.
This paper investigates a multi-player reach-avoid differential game incorporating a goal region and obstacles. Unlike existing works based on single-integrator dynamics, this study considers multiple pursuers and evaders with damped double-integrator dynamics. The system damping coefficient is initially assumed to be precisely known a priori. Based on this, the target point is uniquely determined via geometric methods, leading to the explicit derivation of optimal game strategies. The optimality of these strategies is then rigorously verified based on the properties of the Hamiltonian, which ensures that the designed value function satisfies the Hamilton-Jacobi-Isaacs equation. Subsequently, to bridge the gap where the damping coefficient is actually unknown, a robust adaptive fuzzy logic system is employed to approximate the unknown dynamics online. Meanwhile, to ensure safety during the game process, the obstacle avoidance problem of players is addressed based on the artificial potential field method. Finally, extensive simulations are conducted to validate the optimality and effectiveness of the proposed strategies.
Existing superpixel methods are often constrained by hand-crafted features, sensitivity to initialization, heuristic loss designs, or reliance on annotated data. To overcome these limitations, this paper proposes a novel unsupervised zero-shot per-image optimization framework driven by principled fuzzy energy-based minimization. Superpixel segmentation is cast as finding an optimal fuzzy partition by minimizing an energy function that integrates data fidelity, entropy-based fuzziness control, spatial coherence, and edge preservation. Bypassing traditional alternating minimization, a lightweight CNN is deployed as a parametric solver. Initialized randomly, it is trained from scratch on each individual image via backpropagation to directly predict fuzzy memberships that minimize the target energy. Furthermore, an adaptive convergence criterion based on energy stability automatically terminates the optimization, eliminating the accuracy-efficiency trade-off inherent to fixed iteration limits. Extensive experiments on natural (BSDS500, SBD) and medical (DRIVE) benchmarks demonstrate that the proposed framework outperforms state-of-the-art unsupervised methods and rivals supervised techniques, notably excelling in boundary adherence and exhibiting exceptional numerical stability.
Performing logical queries on incomplete knowledge graphs (KGs) represents a fundamental yet challenging problem. While embedding-based logical reasoning have been extensively studied, they exhibit two gaps: 1) incapacity to process queries that incorporate temporal, spatial, or fuzzy information, restricting their scope to entity-centric query; 2) lack of mechanisms to integrate topological logics for fuzzy spatiotemporal data. Thus, this paper introduces a logical query method designed for fuzzy spatiotemporal KGs (STKGs), which can resolve queries involving fuzzy spatiotemporal topological constraints. Our method models atomic queries using cones, where zero-aperture cones correspond to distinct elements such as entities, timestamps, spatial points, or fuzzy membership values. This cone-based expression facilitates the flexible construction of diverse query types tailored to user requirements. We further propose a computational framework to supports complex query structures composed of multiple atomic queries. By operating in vector space, our method enables efficient computation of cone axis angles and apertures across various logical operations. Experimental shows that our method surpasses state-of-the-art baselines and can answer a wide range of query structures in fuzzy STKGs.
