structural homology detection

This study addresses the limitations of traditional node similarity measures, which often assume a uniform and continuous feature space and thus fail to capture the true structural equivalence among nodes in attributed networks. By integrating neighborhood attribute profiling, dimensionality reduction, and visualization techniques, the authors uncover complex nonlinear manifold structures and density biases inherent in high-dimensional feature spaces. Empirical analysis on an enterprise transaction network reveals that semantically identical industry labels can correspond to multiple disconnected regions of structural roles, and that supply chain tiers exhibit continuous transitions rather than discrete partitions. These findings motivate the proposal of a new similarity metric grounded in manifold topology to more accurately reflect structural equivalence among nodes.

Conventional node homology identification in complex networks with node class labels is constrained by connectivity assumptions, limiting discovery of functionally homologous nodes that lack direct links. Method: We propose a connectivity-agnostic approach that clusters nodes based on quantitative similarity of their neighborhood label distributions, formalizing and identifying “disconnected yet functionally homologous” node groups. Our framework jointly models network topology and semantic labels via neighborhood label distribution modeling, statistical significance–driven similarity measurement, and interpretable clustering. Results: Extensive cross-domain experiments on heterogeneous real-world networks—including biological interaction, academic citation, and social recommendation graphs—demonstrate robust identification of functionally coherent homologous node groups. The method exhibits strong generalizability, intrinsic interpretability, and practical transferability across domains.

本文探讨了模型能力与表示收敛性关系，通过构建一个2x2框架区分结构和几何在局部和全局尺度上的表现，揭示了关系结构比度量几何展现出更强的收敛性。

This work addresses the limited expressive power of unsupervised graph alignment models, particularly in discriminating matching versus non-matching node pairs and enforcing structural matching constraints (e.g., bijectivity and mutual alignment). We propose CombAlign, a theoretically grounded hybrid framework that— for the first time—formalizes model expressivity from both discriminative capability and matching constraint perspectives. CombAlign integrates Gromov–Wasserstein optimal transport with Weisfeiler–Lehman-style node embedding, incorporates non-uniform marginal priors to encode structural biases, and refines alignments via maximum-weight bipartite matching. Evaluated on standard benchmarks, CombAlign achieves a 14.5% absolute improvement in alignment accuracy over state-of-the-art methods. Empirical results consistently validate the theoretical analysis, demonstrating strong alignment between expressivity characterization and practical performance.

This paper addresses the robust joint recovery of multiple geometric structures (e.g., planes, cylinders, homography/fundamental matrices) from noisy data contaminated with outliers. We propose an online model fitting and selection-driven agglomerative clustering framework. Our method innovatively integrates dynamic linkage criteria to enable end-to-end co-optimization of model fitting and selection. It combines online RANSAC-style fitting, information-theoretic adaptive model selection, and multi-structure consistency metrics—thereby overcoming key limitations of conventional approaches, including sensitivity to inlier thresholds and severe sampling bias. Extensive evaluations on multiple public benchmarks demonstrate significant improvements over state-of-the-art methods, achieving high accuracy, strong robustness to outliers and noise, fast runtime, and insensitivity to threshold tuning. The source code is publicly available.

本文通过传播随机特征，无需复杂模型设计和训练，利用随机游走和匿名游走诱导的隐式层次结构生成图嵌入，有效捕捉节点邻近性和结构角色。

This work addresses the limitation of existing graph analysis methods that often neglect geometric structure, thereby failing to capture the joint variation of topology and shape in shape graphs. To overcome this, the authors propose an explicit feature framework that integrates topological, geometric, and directional information to construct a multidimensional representation invariant to transformations such as rotation and translation. This approach transcends the traditional reliance on connectivity alone and enables effective grouping, clustering, and classification of shape graphs. Evaluated on real-world datasets—including urban road networks, neuronal trajectories, and astrocyte images—the method significantly outperforms both feature-based and non-feature baselines, demonstrating its efficacy for statistical analysis and pattern recognition in complex shape graphs.

This work addresses the limitations of existing representation alignment methods, which predominantly rely on geometric properties and struggle to capture the global structural organization of model representations. To overcome this, the study introduces topological data analysis into the field for the first time, proposing a Mapper-based visual analytics framework. By integrating force-directed layout, Bubble Sets, motif querying, and membrane-inspired heuristics, the framework enables a unified analytical pipeline spanning global structure alignment, local region matching, and fine-grained pattern exploration. Case studies on language and multimodal models, complemented by expert evaluations, demonstrate that the approach effectively reveals and compares the topological organization of representations across different models or layers, offering deep structural insights.

This study addresses the limitation of text embeddings in capturing structural similarities and varying levels of abstraction among creative ideas. To overcome this, we propose a structured decomposition-based evaluation framework that deconstructs ideas into core components—such as purpose and mechanism—and constructs multi-layered concept graphs. By introducing shared structural representations and set-level mechanism coverage metrics, the framework enables component-wise overlap analysis to precisely quantify distinctions between core mechanisms and implementation details. Experimental results demonstrate that our approach improves alignment with expert judgments by 31%, significantly enhancing the evaluation of both similarity and diversity in large-scale ideation tasks.

This study addresses the lack of datasets and evaluation standards for recognizing topological relationships between objects in images by constructing the first large-scale topological relationship dataset comprising 11,000 annotated images. Methodologically, feature extraction techniques such as image segmentation and contour detection are integrated to systematically evaluate both traditional machine learning algorithms and deep transfer learning models, including VGG16 and InceptionResNetV2. The research establishes a new evaluation benchmark for this task and validates the effectiveness of transfer learning in spatial reasoning. Notably, the VGG16 model achieves an accuracy of 89.55%, significantly outperforming conventional methods. These contributions provide a foundational dataset and a performance benchmark for future research in visual topological reasoning.