# MIXER: Multiattribute, Multiway Fusion of Uncertain Pairwise Affinities

arXiv: https://arxiv.org/abs/2210.08360 · HTML: https://mlsanity.com/paper/2210.08360/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 53 references that are in the map.
- First posted on arXiv 15 Oct 2022.

## Builds on (most cited first, 22 of 22)

- [YOLOv3: An Incremental Improvement](https://mlsanity.com/paper/1804.02767/) (2018)
- [Simple Online and Realtime Tracking](https://mlsanity.com/paper/1602.00763/) (2016)
- [GNN3DMOT: Graph Neural Network for 3D Multi-Object Tracking with Multi-Feature Learning](https://mlsanity.com/paper/2006.07327/) (2020)
- [Probabilistic 3D Multi-Modal, Multi-Object Tracking for Autonomous Driving](https://mlsanity.com/paper/2012.13755/) (2020)
- [Multimodal Object Detection via Probabilistic Ensembling](https://mlsanity.com/paper/2104.02904/) (2021)
- [Projection onto the probability simplex: An efficient algorithm with a simple proof, and an application](https://mlsanity.com/paper/1309.1541/) (2013)
- [Robust Multi-Modality Multi-Object Tracking](https://mlsanity.com/paper/1909.03850/) (2019)
- [Kimera-Multi: Robust, Distributed, Dense Metric-Semantic SLAM for Multi-Robot Systems](https://mlsanity.com/paper/2106.14386/) (2021)
- [Multi-Image Matching via Fast Alternating Minimization](https://mlsanity.com/paper/1505.04845/) (2015)
- [CLIPPER: A Graph-Theoretic Framework for Robust Data Association](https://mlsanity.com/paper/2011.10202/) (2020)
- [Near-Optimal Joint Object Matching via Convex Relaxation](https://mlsanity.com/paper/1402.1473/) (2014)
- [Synchronisation of Partial Multi-Matchings via Non-negative Factorisations](https://mlsanity.com/paper/1803.06320/) (2018)
- [Escaping Saddle Points in Constrained Optimization](https://mlsanity.com/paper/1809.02162/) (2018)
- [A General Multi-Graph Matching Approach via Graduated Consistency-regularized Boosting](https://mlsanity.com/paper/1502.05840/) (2015)
- [Robust Multi-object Matching via Iterative Reweighting of the Graph Connection Laplacian](https://mlsanity.com/paper/2006.06658/) (2020)
- [Fast, Accurate and Memory-Efficient Partial Permutation Synchronization](https://mlsanity.com/paper/2203.16505/) (2022)
- [Distributed Consistent Data Association](https://mlsanity.com/paper/1609.07015/) (2016)
- [Scalable Cluster-Consistency Statistics for Robust Multi-Object Matching](https://mlsanity.com/paper/2201.04797/) (2022)
- [CLEAR: A Consistent Lifting, Embedding, and Alignment Rectification Algorithm for Multi-View Data Association](https://mlsanity.com/paper/1902.02256/) (2019)
- [Kernelized multi-graph matching](https://mlsanity.com/paper/2210.05206/) (2022)
- [Distributed and Consistent Multi-Image Feature Matching via QuickMatch](https://mlsanity.com/paper/1910.13317/) (2019)
- [Efficient Joint Object Matching via Linear Programming](https://mlsanity.com/paper/2108.11911/) (2021)

## Built on by (most cited first, 1 of 1)

- [CLIPPER+: A Fast Maximal Clique Algorithm for Robust Global Registration](https://mlsanity.com/paper/2402.15464/) (2024)

## Abstract (arXiv)

We present a multiway fusion algorithm capable of directly processing uncertain pairwise affinities. In contrast to existing works that require initial pairwise associations, our MIXER algorithm improves accuracy by leveraging the additional information provided by pairwise affinities. Our main contribution is a multiway fusion formulation that is particularly suited to processing non-binary affinities and a novel continuous relaxation whose solutions are guaranteed to be binary, thus avoiding the typical, but potentially problematic, solution binarization steps that may cause infeasibility. A crucial insight of our formulation is that it allows for three modes of association, ranging from non-match, undecided, and match. Exploiting this insight allows fusion to be delayed for some data pairs until more information is available, which is an effective feature for fusion of data with multiple attributes/information sources. We evaluate MIXER on typical synthetic data and benchmark datasets and show increased accuracy against the state of the art in multiway matching, especially in noisy regimes with low observation redundancy. Additionally, we collect RGB data of cars in a parking lot to demonstrate MIXER's ability to fuse data having multiple attributes (color, visual appearance, and bounding box). On this challenging dataset, MIXER achieves 74% F1 accuracy and is 49x faster than the next best algorithm, which has 42% accuracy. Open source code is available at https://github.com/mit-acl/mixer.