# Archetypal Analysis++: Rethinking the Initialization Strategy

arXiv: https://arxiv.org/abs/2301.13748 · HTML: https://mlsanity.com/paper/2301.13748/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 65 references that are in the map.
- First posted on arXiv 31 Jan 2023.

## Builds on (most cited first, 10 of 10)

- [FMA: A Dataset For Music Analysis](https://mlsanity.com/paper/1612.01840/) (2016)
- [Generalized Low Rank Models](https://mlsanity.com/paper/1410.0342/) (2014)
- [Fast and Robust Archetypal Analysis for Representation Learning](https://mlsanity.com/paper/1405.6472/) (2014)
- [Probabilistic Archetypal Analysis](https://mlsanity.com/paper/1312.7604/) (2013)
- [Learning Extremal Representations with Deep Archetypal Analysis](https://mlsanity.com/paper/2002.00815/) (2020)
- [Graph-based Neural Acceleration for Nonnegative Matrix Factorization](https://mlsanity.com/paper/2202.00264/) (2022)
- [Finding Archetypal Spaces Using Neural Networks](https://mlsanity.com/paper/1901.09078/) (2019)
- [Deep Archetypal Analysis](https://mlsanity.com/paper/1901.10799/) (2019)
- [Near-Convex Archetypal Analysis](https://mlsanity.com/paper/1910.00821/) (2019)
- [Probabilistic methods for approximate archetypal analysis](https://mlsanity.com/paper/2108.05767/) (2021)

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

- [A Survey on Archetypal Analysis](https://mlsanity.com/paper/2504.12392/) (2025)
- [Simplex Demixing: Disentangling Multiple Light-Flavor Jets at Colliders](https://mlsanity.com/paper/2607.24921/) (2026)

## Abstract (arXiv)

Archetypal analysis is a matrix factorization method with convexity constraints. Due to local minima, a good initialization is essential, but frequently used initialization methods yield either sub-optimal starting points or are prone to get stuck in poor local minima. In this paper, we propose archetypal analysis++ (AA++), a probabilistic initialization strategy for archetypal analysis that sequentially samples points based on their influence on the objective function, similar to k-means++. In fact, we argue that k-means++ already approximates the proposed initialization method. Furthermore, we suggest to adapt an efficient Monte Carlo approximation of k-means++ to AA++. In an extensive empirical evaluation of 15 real-world data sets of varying sizes and dimensionalities and considering two pre-processing strategies, we show that AA++ almost always outperforms all baselines, including the most frequently used ones.