Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Anchors Hierachy: Using the triangle inequality to survive high
  dimensional data   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.

31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
2
The categories of this paper are: math
28
The categories of this paper are: alg-geom
7
The categories of this paper are: hep-th