下一篇：使用三角不等式生存高维数据
The Anchors Hierachy: Using the triangle inequality to survive high dimensional data
摘要：
本文研究了高维或非欧空间中的度量数据结构，它允许缓存足够的学习算法的统计加速。最近已经表明，对于小于约10个维度，用额外的“缓存足够的统计数据”（如一阶和二阶矩和列联表）装饰kd树可以为非常广泛的统计学习任务（如核回归，局部加权回归，k均值聚类，混合建模和贝叶斯网络学习）提供令人满意的加速。在本文中，我们首先定义了锚层次结构-一个快速的数据结构和算法，用于定位数据的基础上，只有一个三角形不等式服从距离度量。我们展示了如何，在其本身的权利，提供了一个快速和有效的数据聚类。但更重要的是，我们展示了它如何以一种既不是“自上而下”也不是“自下而上”而是“中间向外”的方式产生一种类似于球树（Omohundro，1991）或一种度量树（Uhlmann，1991; Ciaccia，Patella，& Zezula，1997）的平衡结构。然后，我们展示了这种结构，装饰与缓存足够的统计数据，允许各种各样的统计学习算法被加速，甚至在数千个维度。
英文摘要：
This paper is about metric data structures in high-dimensional or non-Euclidean space that permit cached sufficient statistics accelerations of learning algorithms. It has recently been shown that for less than about 10 dimensions, decorating kd-trees with additional "cached sufficient statistics" such as first and second moments and contingency tables can provide satisfying acceleration for a very wide range of statistical learning tasks such as kernel regression, locally weighted regression, k-means clustering, mixture modeling and Bayes Net learning. In this paper, we begin by defining the anchors hierarchy - a fast data structure and algorithm for localizing data based only on a triangle-inequality-obeying distance metric. We show how this, in its own right, gives a fast and effective clustering of data. But more importantly we show how it can produce a well-balanced structure similar to a Ball-Tree (Omohundro, 1991) or a kind of metric tree (Uhlmann, 1991; Ciaccia, Patella, & Zezula, 1997) in a way that is neither "top-down" nor "bottom-up" but instead "middle-out". We then show how this structure, decorated with cached sufficient statistics, allows a wide variety of statistical learning algorithms to be accelerated even in thousands of dimensions.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
