13,224 research outputs found
Space Exploration via Proximity Search
We investigate what computational tasks can be performed on a point set in
, if we are only given black-box access to it via nearest-neighbor
search. This is a reasonable assumption if the underlying point set is either
provided implicitly, or it is stored in a data structure that can answer such
queries. In particular, we show the following: (A) One can compute an
approximate bi-criteria -center clustering of the point set, and more
generally compute a greedy permutation of the point set. (B) One can decide if
a query point is (approximately) inside the convex-hull of the point set.
We also investigate the problem of clustering the given point set, such that
meaningful proximity queries can be carried out on the centers of the clusters,
instead of the whole point set
Indexing Metric Spaces for Exact Similarity Search
With the continued digitalization of societal processes, we are seeing an
explosion in available data. This is referred to as big data. In a research
setting, three aspects of the data are often viewed as the main sources of
challenges when attempting to enable value creation from big data: volume,
velocity and variety. Many studies address volume or velocity, while much fewer
studies concern the variety. Metric space is ideal for addressing variety
because it can accommodate any type of data as long as its associated distance
notion satisfies the triangle inequality. To accelerate search in metric space,
a collection of indexing techniques for metric data have been proposed.
However, existing surveys each offers only a narrow coverage, and no
comprehensive empirical study of those techniques exists. We offer a survey of
all the existing metric indexes that can support exact similarity search, by i)
summarizing all the existing partitioning, pruning and validation techniques
used for metric indexes, ii) providing the time and storage complexity analysis
on the index construction, and iii) report on a comprehensive empirical
comparison of their similarity query processing performance. Here, empirical
comparisons are used to evaluate the index performance during search as it is
hard to see the complexity analysis differences on the similarity query
processing and the query performance depends on the pruning and validation
abilities related to the data distribution. This article aims at revealing
different strengths and weaknesses of different indexing techniques in order to
offer guidance on selecting an appropriate indexing technique for a given
setting, and directing the future research for metric indexes
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