# FAST NEAREST NEIGHBOR SEARCH IN PSEUDOSEMIMETRIC SPACES

### Markus Lessmann, Rolf P. Würtz

#### Abstract

Nearest neighbor search in metric spaces is an important task in pattern recognition because it allows a query pattern to be associated with a known pattern from a learned dataset. In low-dimensional spaces a lot of good solutions exist that minimize the number of comparisons between patterns by partitioning the search space using tree structures. In high-dimensional spaces tree methods become useless because they fail to prevent scanning almost the complete dataset. Locality sensitive hashing methods solve the task approximately by grouping patterns that are nearby in search space into buckets. Therefore an appropriate hash function has to be known that is highly likely to assign a query pattern to the same bucket as its nearest neighbor. This works fine as long as all the patterns are of the same dimensionality and exist in the same vector space with a complete metric. Here, we propose a locality-sensitive hashing-scheme that is able to process patterns which are built up of several possibly missing subpatterns causing the patterns to be in vector spaces of different dimensionality. These patterns can only be compared using a pseudosemimetric.

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#### Paper Citation

#### in Harvard Style

Lessmann M. and P. Würtz R. (2012). **FAST NEAREST NEIGHBOR SEARCH IN PSEUDOSEMIMETRIC SPACES** . In *Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2012)* ISBN 978-989-8565-03-7, pages 667-674. DOI: 10.5220/0003809006670674

#### in Bibtex Style

@conference{visapp12,

author={Markus Lessmann and Rolf P. Würtz},

title={FAST NEAREST NEIGHBOR SEARCH IN PSEUDOSEMIMETRIC SPACES},

booktitle={Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2012)},

year={2012},

pages={667-674},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0003809006670674},

isbn={978-989-8565-03-7},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the International Conference on Computer Vision Theory and Applications - Volume 1: VISAPP, (VISIGRAPP 2012)

TI - FAST NEAREST NEIGHBOR SEARCH IN PSEUDOSEMIMETRIC SPACES

SN - 978-989-8565-03-7

AU - Lessmann M.

AU - P. Würtz R.

PY - 2012

SP - 667

EP - 674

DO - 10.5220/0003809006670674