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Archetypal Analysis++: Rethinking the Initialization Strategy by Mair, Sebastian; Sjölund, Jens is a scholarly article available to read on EtoBox.

What is Archetypal Analysis++: Rethinking the Initialization Strategy about?

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.

Author

Mair, Sebastian; Sjölund, Jens

Published

2023

Language

EN