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This paper is about metric data structures in high-dimensional ornon-Euclidean space that permit cached sufficient statistics accelerations oflearning algorithms.  It has recently been shown that for less than about 10 dimensions, decoratingkd-trees with additional "cached sufficient statistics" such as first andsecond moments and contingency tables can provide satisfying acceleration for avery wide range of statistical learning tasks such as kernel regression,locally weighted regression, k-means clustering, mixture modeling and Bayes Netlearning.  In this paper, we begin by defining the anchors hierarchy - a fast datastructure and algorithm for localizing data based only on atriangle-inequality-obeying distance metric. We show how this, in its ownright, gives a fast and effective clustering of data. But more importantly weshow 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 sufficientstatistics, allows a wide variety of statistical learning algorithms to beaccelerated even in thousands of dimensions.

The Anchors Hierachy: Using the triangle inequality to survive high dimensional data