论文标题
通过调整指数量度的指数级家庭聚类
Clustering above Exponential Families with Tempered Exponential Measures
论文作者
论文摘要
与指数家庭的链接允许$ k $ -Means的聚类推广到指数式家庭中的各种数据生成分布，并在Bregman Diverence之间群体扭曲。使框架以高指数家庭工作为重要，这对于举起障碍很重要，例如某些人口最小化的人的公理化量很小。当前对指数级家庭（例如$ Q $ - 指数家庭甚至指数型家庭）的概括无法实现目标。在本文中，我们提供了一种新的尝试来获得完整的框架，这基于我们引入的指数级家庭的新概括（TEM）。 TEMS保留$ Q $ - 指定家庭的最大熵公理化框架，但不准确地标准化了一个称为共同分布的双重二元。出现了许多有趣的特性，用于聚类，例如对人群最小化的改进和可控的鲁棒性，这些属性保持了简单的分析形式。
The link with exponential families has allowed $k$-means clustering to be generalized to a wide variety of data generating distributions in exponential families and clustering distortions among Bregman divergences. Getting the framework to work above exponential families is important to lift roadblocks like the lack of robustness of some population minimizers carved in their axiomatization. Current generalisations of exponential families like $q$-exponential families or even deformed exponential families fail at achieving the goal. In this paper, we provide a new attempt at getting the complete framework, grounded in a new generalisation of exponential families that we introduce, tempered exponential measures (TEM). TEMs keep the maximum entropy axiomatization framework of $q$-exponential families, but instead of normalizing the measure, normalize a dual called a co-distribution. Numerous interesting properties arise for clustering such as improved and controllable robustness for population minimizers, that keep a simple analytic form.
