# Feature-based morphological analysis of shape graph data

arXiv: https://arxiv.org/abs/2602.16120 · HTML: https://mlsanity.com/paper/2602.16120/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 39 references that are in the map.
- First posted on arXiv 18 Feb 2026.

## Builds on (most cited first, 13 of 13)

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [Dynamic Graph CNN for Learning on Point Clouds](https://mlsanity.com/paper/1801.07829/) (2018)
- [Geometric deep learning: going beyond Euclidean data](https://mlsanity.com/paper/1611.08097/) (2016)
- [Optimal Transport for structured data with application on graphs](https://mlsanity.com/paper/1805.09114/) (2018)
- [OSMnx: New Methods for Acquiring, Constructing, Analyzing, and Visualizing Complex Street Networks](https://mlsanity.com/paper/1611.01890/) (2016)
- [Modeling and Analyzing Urban Networks and Amenities with OSMnx](https://mlsanity.com/paper/2505.00736/) (2025)
- [Generalized Dimension Reduction Using Semi-Relaxed Gromov-Wasserstein Distance](https://mlsanity.com/paper/2405.15959/) (2024)
- [A new variational model for shape graph registration with partial matching constraints](https://mlsanity.com/paper/2105.00678/) (2021)
- [Representations, Metrics and Statistics For Shape Analysis of Elastic Graphs](https://mlsanity.com/paper/2003.00287/) (2020)
- [VariGrad: A Novel Feature Vector Architecture for Geometric Deep Learning on Unregistered Data](https://mlsanity.com/paper/2307.03553/) (2023)
- [Partial Matching in the Space of Varifolds](https://mlsanity.com/paper/2103.12441/) (2021)
- [On length measures of planar closed curves and the comparison of convex shapes](https://mlsanity.com/paper/2010.13964/) (2020)
- [SVarM: Linear Support Varifold Machines for Classification and Regression on Geometric Data](https://mlsanity.com/paper/2506.01189/) (2025)

## Abstract (arXiv)

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.