Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lower Bounds on Performance of Metric Tree Indexing Schemes for Exact
  Similarity Search in High Dimensions   Within a mathematically rigorous model, we analyse the curse of
dimensionality for deterministic exact similarity search in the context of
popular indexing schemes: metric trees. The datasets $X$ are sampled randomly
from a domain $\Omega$, equipped with a distance, $\rho$, and an underlying
probability distribution, $\mu$. While performing an asymptotic analysis, we
send the intrinsic dimension $d$ of $\Omega$ to infinity, and assume that the
size of a dataset, $n$, grows superpolynomially yet subexponentially in $d$.
Exact similarity search refers to finding the nearest neighbour in the dataset
$X$ to a query point $\omega\in\Omega$, where the query points are subject to
the same probability distribution $\mu$ as datapoints. Let $\mathscr F$ denote
a class of all 1-Lipschitz functions on $\Omega$ that can be used as decision
functions in constructing a hierarchical metric tree indexing scheme. Suppose
the VC dimension of the class of all sets $\{\omega\colon f(\omega)\geq a\}$,
$a\in\R$ is $o(n^{1/4}/\log^2n)$. (In view of a 1995 result of Goldberg and
Jerrum, even a stronger complexity assumption $d^{O(1)}$ is reasonable.) We
deduce the $\Omega(n^{1/4})$ lower bound on the expected average case
performance of hierarchical metric-tree based indexing schemes for exact
similarity search in $(\Omega,X)$. In paricular, this bound is superpolynomial
in $d$.

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The categories of this paper are: math
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: astro-ph