# SPOT: A framework for selection of prototypes using optimal transport

arXiv: https://arxiv.org/abs/2103.10159 · HTML: https://mlsanity.com/paper/2103.10159/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 61 references that are in the map.
- First posted on arXiv 18 Mar 2021.

## Builds on (most cited first, 18 of 18)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [ImageNet Large Scale Visual Recognition Challenge](https://mlsanity.com/paper/1409.0575/) (2014)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Understanding Black-box Predictions via Influence Functions](https://mlsanity.com/paper/1703.04730/) (2017)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [DeCAF: A Deep Convolutional Activation Feature for Generic Visual Recognition](https://mlsanity.com/paper/1310.1531/) (2013)
- [Joint Distribution Optimal Transportation for Domain Adaptation](https://mlsanity.com/paper/1705.08848/) (2017)
- [YFCC100M: The New Data in Multimedia Research](https://mlsanity.com/paper/1503.01817/) (2015)
- [Fast Computation of Wasserstein Barycenters](https://mlsanity.com/paper/1310.4375/) (2013)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [Representer Point Selection for Explaining Deep Neural Networks](https://mlsanity.com/paper/1811.09720/) (2018)
- [The Bayesian Case Model: A Generative Approach for Case-Based Reasoning and Prototype Classification](https://mlsanity.com/paper/1503.01161/) (2015)
- [Restricted Strong Convexity Implies Weak Submodularity](https://mlsanity.com/paper/1612.00804/) (2016)
- [Faster k-Medoids Clustering: Improving the PAM, CLARA, and CLARANS Algorithms](https://mlsanity.com/paper/1810.05691/) (2018)
- [MatConvNet - Convolutional Neural Networks for MATLAB](https://mlsanity.com/paper/1412.4564/) (2014)
- [Geometry-aware Domain Adaptation for Unsupervised Alignment of Word Embeddings](https://mlsanity.com/paper/2004.08243/) (2020)

## Built on by (most cited first, 13 of 13)

- [RoVRM: A Robust Visual Reward Model Optimized via Auxiliary Textual Preference Data](https://mlsanity.com/paper/2408.12109/) (2024)
- [Riemannian block SPD coupling manifold and its application to optimal transport](https://mlsanity.com/paper/2201.12933/) (2022)
- [Submodular Framework for Structured-Sparse Optimal Transport](https://mlsanity.com/paper/2406.04914/) (2024)
- [A Riemannian Approach to Ground Metric Learning for Optimal Transport](https://mlsanity.com/paper/2409.10085/) (2024)
- [UniPROT: Uniform Prototype Selection via Partial Optimal Transport with Submodular Guarantees](https://mlsanity.com/paper/2604.10952/) (2026)
- [Deep SIMBAD: Active Landmark-based Self-localization Using Ranking -based Scene Descriptor](https://mlsanity.com/paper/2109.02786/) (2021)
- [A Riemannian Approach to Low-Rank Optimal Transport](https://mlsanity.com/paper/2606.12120/) (2026)
- [CoverPrune: Coverage-Driven Token Pruning for 3D VLMs via Optimal Transport](https://mlsanity.com/paper/2608.13226/) (2026)
- [ProtoBandit: Efficient Prototype Selection via Multi-Armed Bandits](https://mlsanity.com/paper/2210.01860/) (2022)
- [Prototype Selection Using Topological Data Analysis](https://mlsanity.com/paper/2511.04873/) (2025)
- [Adaptive Test-Time Training for Predicting Need for Invasive Mechanical Ventilation in Multi-Center Cohorts](https://mlsanity.com/paper/2512.06652/) (2025)
- [Minibatch Selection for Language Models via Partition Matroid Constrained Gradient Matching](https://mlsanity.com/paper/2606.07954/) (2026)
- [Skeletal Prototypes on Iterative Nerve Expansions](https://mlsanity.com/paper/2609.16170/) (2026)

## Abstract (arXiv)

In this work, we develop an optimal transport (OT) based framework to select informative prototypical examples that best represent a given target dataset. Summarizing a given target dataset via representative examples is an important problem in several machine learning applications where human understanding of the learning models and underlying data distribution is essential for decision making. We model the prototype selection problem as learning a sparse (empirical) probability distribution having the minimum OT distance from the target distribution. The learned probability measure supported on the chosen prototypes directly corresponds to their importance in representing the target data. We show that our objective function enjoys a key property of submodularity and propose an efficient greedy method that is both computationally fast and possess deterministic approximation guarantees. Empirical results on several real world benchmarks illustrate the efficacy of our approach.