Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Random Projection Trees Revisited   The Random Projection Tree structures proposed in [Freund-Dasgupta STOC08]
are space partitioning data structures that automatically adapt to various
notions of intrinsic dimensionality of data. We prove new results for both the
RPTreeMax and the RPTreeMean data structures. Our result for RPTreeMax gives a
near-optimal bound on the number of levels required by this data structure to
reduce the size of its cells by a factor $s \geq 2$. We also prove a packing
lemma for this data structure. Our final result shows that low-dimensional
manifolds have bounded Local Covariance Dimension. As a consequence we show
that RPTreeMean adapts to manifold dimension as well.

9
The categories of this paper are: nlin
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
4
The categories of this paper are: cond-mat