Archetypal Analysis++: Rethinking the Initialization Strategy
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Archetypal analysis is a matrix factorization method with convexity constraints. Due to local minima, a good initialization is essential. 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, 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 13 real-world data sets of varying sizes and dimensionalities and considering two pre-processing strategies, we show that AA++ almost consistently outperforms all baselines, including the most frequently used ones.
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