论文标题
球形聚类在检测伴随极端的群体中
Spherical clustering in detection of groups of concomitant extremes
论文作者
论文摘要
越来越多的经验证据表明，球形$ k $ - 均值聚类在识别高维度的极端群体方面的表现很好，从而导致模型稀疏。我们提供了支持这种方法的第一个理论结果之一，但也证明了一些陷阱。此外，我们表明，另一种成本函数可能更适合识别伴随的极端，并且导致了一种新型的球形$ k $ - 原始组件聚类算法。我们的主要结果建立了一个广泛满足的条件，确保了这种方法的成功，尽管它是在相当基本的环境中。最后，我们在模拟中说明了$ k $ - 原理组件的表现优于$ k $ - ameans，在组内渐近依赖性弱的情况下。
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 outperforms $k$-means in the difficult case of weak asymptotic dependence within the groups.
