# Learning Universe Model for Partial Matching Networks over Multiple Graphs

arXiv: https://arxiv.org/abs/2210.10374 · HTML: https://mlsanity.com/paper/2210.10374/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 23 of its 63 references that are in the map.
- First posted on arXiv 19 Oct 2022.

## Builds on (most cited first, 23 of 23)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Realtime Multi-Person 2D Pose Estimation using Part Affinity Fields](https://mlsanity.com/paper/1611.08050/) (2016)
- [PWC-Net: CNNs for Optical Flow Using Pyramid, Warping, and Cost Volume](https://mlsanity.com/paper/1709.02371/) (2017)
- [Pyramid Stereo Matching Network](https://mlsanity.com/paper/1803.08669/) (2018)
- [Exact Combinatorial Optimization with Graph Convolutional Neural Networks](https://mlsanity.com/paper/1906.01629/) (2019)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [Learning Multi-Domain Convolutional Neural Networks for Visual Tracking](https://mlsanity.com/paper/1510.07945/) (2015)
- [SplineCNN: Fast Geometric Deep Learning with Continuous B-Spline Kernels](https://mlsanity.com/paper/1711.08920/) (2017)
- [Learning Combinatorial Embedding Networks for Deep Graph Matching](https://mlsanity.com/paper/1904.00597/) (2019)
- [SfM-Net: Learning of Structure and Motion from Video](https://mlsanity.com/paper/1704.07804/) (2017)
- [Neural Graph Matching Network: Learning Lawler's Quadratic Assignment Problem with Extension to Hypergraph and Multiple-graph Matching](https://mlsanity.com/paper/1911.11308/) (2019)
- [Deep Graph Matching via Blackbox Differentiation of Combinatorial Solvers](https://mlsanity.com/paper/2003.11657/) (2020)
- [Neural Subgraph Matching](https://mlsanity.com/paper/2007.03092/) (2020)
- [PoseTrack: Joint Multi-Person Pose Estimation and Tracking](https://mlsanity.com/paper/1611.07727/) (2016)
- [Multi-Image Matching via Fast Alternating Minimization](https://mlsanity.com/paper/1505.04845/) (2015)
- [A Study of Lagrangean Decompositions and Dual Ascent Solvers for Graph Matching](https://mlsanity.com/paper/1612.05476/) (2016)
- [DS*: Tighter Lifting-Free Convex Relaxations for Quadratic Matching Problems](https://mlsanity.com/paper/1711.10733/) (2017)
- [GLSearch: Maximum Common Subgraph Detection via Learning to Search](https://mlsanity.com/paper/2002.03129/) (2020)
- [Near-Optimal Joint Object Matching via Convex Relaxation](https://mlsanity.com/paper/1402.1473/) (2014)
- [Multi-Image Semantic Matching by Mining Consistent Features](https://mlsanity.com/paper/1711.07641/) (2017)
- [A General Multi-Graph Matching Approach via Graduated Consistency-regularized Boosting](https://mlsanity.com/paper/1502.05840/) (2015)
- [Zero-Assignment Constraint for Graph Matching with Outliers](https://mlsanity.com/paper/2003.11928/) (2020)

## Built on by (most cited first, 2 of 2)

- [Jigsaw: Learning to Assemble Multiple Fractured Objects](https://mlsanity.com/paper/2305.17975/) (2023)
- [Learning Partial Graph Matching via Optimal Partial Transport](https://mlsanity.com/paper/2410.16718/) (2024)

## Abstract (arXiv)

We consider the general setting for partial matching of two or multiple graphs, in the sense that not necessarily all the nodes in one graph can find their correspondences in another graph and vice versa. We take a universe matching perspective to this ubiquitous problem, whereby each node is either matched into an anchor in a virtual universe graph or regarded as an outlier. Such a universe matching scheme enjoys a few important merits, which have not been adopted in existing learning-based graph matching (GM) literature. First, the subtle logic for inlier matching and outlier detection can be clearly modeled, which is otherwise less convenient to handle in the pairwise matching scheme. Second, it enables end-to-end learning especially for universe level affinity metric learning for inliers matching, and loss design for gathering outliers together. Third, the resulting matching model can easily handle new arriving graphs under online matching, or even the graphs coming from different categories of the training set. To our best knowledge, this is the first deep learning network that can cope with two-graph matching, multiple-graph matching, online matching, and mixture graph matching simultaneously. Extensive experimental results show the state-of-the-art performance of our method in these settings.