# Prototypal Analysis and Prototypal Regression

arXiv: https://arxiv.org/abs/1701.08916 · HTML: https://mlsanity.com/paper/1701.08916/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2017.

## Built on by (most cited first, 3 of 3)

- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Explainability-aided Domain Generalization for Image Classification](https://mlsanity.com/paper/2104.01742/) (2021)
- [Optimal Demixing of Nonparametric Densities](https://mlsanity.com/paper/2603.27457/) (2026)

## Abstract (arXiv)

Prototypal analysis is introduced to overcome two shortcomings of archetypal analysis: its sensitivity to outliers and its non-locality, which reduces its applicability as a learning tool. Same as archetypal analysis, prototypal analysis finds prototypes through convex combination of the data points and approximates the data through convex combination of the archetypes, but it adds a penalty for using prototypes distant from the data points for their reconstruction. Prototypal analysis can be extended---via kernel embedding---to probability distributions, since the convexity of the prototypes makes them interpretable as mixtures. Finally, prototypal regression is developed, a robust supervised procedure which allows the use of distributions as either features or labels.