# Estimating matching affinity matrix under low-rank constraints

arXiv: https://arxiv.org/abs/1612.09585 · HTML: https://mlsanity.com/paper/1612.09585/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Dec 2016.

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## Abstract (arXiv)

In this paper, we address the problem of estimating transport surplus (a.k.a. matching affinity) in high dimensional optimal transport problems. Classical optimal transport theory specifies the matching affinity and determines the optimal joint distribution. In contrast, we study the inverse problem of estimating matching affinity based on the observation of the joint distribution, using an entropic regularization of the problem. To accommodate high dimensionality of the data, we propose a novel method that incorporates a nuclear norm regularization which effectively enforces a rank constraint on the affinity matrix. The low-rank matrix estimated in this way reveals the main factors which are relevant for matching.