11,439 research outputs found
Ptolemaic Indexing
This paper discusses a new family of bounds for use in similarity search,
related to those used in metric indexing, but based on Ptolemy's inequality,
rather than the metric axioms. Ptolemy's inequality holds for the well-known
Euclidean distance, but is also shown here to hold for quadratic form metrics
in general, with Mahalanobis distance as an important special case. The
inequality is examined empirically on both synthetic and real-world data sets
and is also found to hold approximately, with a very low degree of error, for
important distances such as the angular pseudometric and several Lp norms.
Indexing experiments demonstrate a highly increased filtering power compared to
existing, triangular methods. It is also shown that combining the Ptolemaic and
triangular filtering can lead to better results than using either approach on
its own
A geometric framework for modelling similarity search
The aim of this paper is to propose a geometric framework for modelling
similarity search in large and multidimensional data spaces of general nature,
which seems to be flexible enough to address such issues as analysis of
complexity, indexability, and the `curse of dimensionality.' Such a framework
is provided by the concept of the so-called similarity workload, which is a
probability metric space (query domain) with a distinguished finite
subspace (dataset), together with an assembly of concepts, techniques, and
results from metric geometry. They include such notions as metric transform,
\e-entropy, and the phenomenon of concentration of measure on
high-dimensional structures. In particular, we discuss the relevance of the
latter to understanding the curse of dimensionality. As some of those concepts
and techniques are being currently reinvented by the database community, it
seems desirable to try and bridge the gap between database research and the
relevant work already done in geometry and analysis.Comment: 11 pages, LaTeX 2.
Multidimensional Binning Techniques for a Two Parameter Trilinear Gauge Coupling Estimation at LEP II
This paper describes two generalization schemes of the Optimal Variables
technique in estimating simultaneously two Trilinear Gauge Couplings. The first
is an iterative procedure to perform a 2-dimensional fit using the linear terms
of the expansion of the probability density function with respect to the
corresponding couplings, whilst the second is a clustering method of
probability distribution representation in five dimensions. The pair production
of W's at 183 GeV center of mass energy, where one W decays leptonically and
the other hadronically, was used to demonstrate the optimal properties of the
proposed estimation techniques.Comment: (25 pages, 11 figures
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