Feature-based morphological analysis of shape graph data

2026-02-17

AI Summary

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.

Technology Category

• Machine Learning: Graph-based Machine Learning
• Data Mining & Knowledge Management: Graph Mining, Social Network Analysis & Community
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

This paper introduces and demonstrates a computational pipeline for the statistical analysis of shape graph datasets, namely geometric networks embedded in 2D or 3D spaces. Unlike traditional abstract graphs, our purpose is not only to retrieve and distinguish variations in the connectivity structure of the data but also geometric differences of the network branches. Our proposed approach relies on the extraction of a specifically curated and explicit set of topological, geometric and directional features, designed to satisfy key invariance properties. We leverage the resulting feature representation for tasks such as group comparison, clustering and classification on cohorts of shape graphs. The effectiveness of this representation is evaluated on several real-world datasets including urban road/street networks, neuronal traces and astrocyte imaging. These results are benchmarked against several alternative methods, both feature-based and not.

Problem

• shape graph
• morphological analysis
• geometric network
• feature-based analysis
• statistical shape analysis

Innovation

• shape graph
• geometric network
• feature-based analysis
• topological features
• geometric invariance