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• W2950595896 abstract "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 $omegainOmega$, 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 ${omegacolon f(omega)geq a}$, $ainR$ 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 $d$." @default.
• W2950595896 created "2019-06-27" @default.
• W2950595896 creator A5086565358 @default.
• W2950595896 date "2008-11-30" @default.
• W2950595896 modified "2023-09-27" @default.
• W2950595896 title "Lower Bounds on Performance of Metric Tree Indexing Schemes for Exact Similarity Search in High Dimensions" @default.
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• W2950595896 hasPublicationYear "2008" @default.
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