The Anchors Hierarchy: Using the Triangle Inequality to Survive High Dimensional Data

This paper is about the use of metric data structures in high-dimensionalor non-Euclidean space to permit cached sufficientstatisticsaccelerationsof learning algorithms. It has recently been shown that for less than about 10 dimensions, decorating kd-trees with additional "cached sufficientstatistics"such as first and second moments and contingency tables can provide satisfying accelerationfor a very wide range of statistical learning tasks such as kernel regression, locally weighted regression, k-means clustering,mixturemodeling 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-obeyingdistance metric. We show how this, in its own right, gives a fast and effectiveclustering of data. But more importantly we show how it can produce a well-balanced structure similar to a Ball-Tree (Omohundro 1990) or a kind of metric tree (Uhlmann 1991)in a way that is n...

• Type: Conference
• Year: 2000
• Where: UAI
• Authors: Andrew W. Moore
• Keywords: Cached, Data Structure, Metric Data Structures, UAI 2000, UAI 2008