Spherical clustering in detection of groups of concomitant extremes
研究了球面k均值聚类在高维数据中识别伴随极端值群组的理论依据，发现其有效但存在缺陷，并提出一种新的球面k主成分聚类算法，在弱渐近依赖情况下表现更优。
Summary There is growing empirical evidence that spherical $k$-means clustering performs well at identifying groups of concomitant extremes in high dimensions, thereby leading to sparse models. We provide one of the first theoretical results supporting this approach, but also demonstrate some pitfalls. Furthermore, we show that an alternative cost function may be more appropriate for identifying concomitant extremes, and it results in a novel spherical $k$-principal-components clustering algorithm. Our main result establishes a broadly satisfied sufficient condition guaranteeing the success of this method, albeit in a rather basic setting. Finally, we illustrate in simulations that $k$-principal components clustering outperforms $k$-means clustering in the difficult case of weak asymptotic dependence within the groups.