On the Surprising Behavior of Distance Metric in High-Dimensional Space

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AGGARWAL, Charu C., Alexander HINNEBURG, Daniel A. KEIM, 2001. On the Surprising Behavior of Distance Metric in High-Dimensional Space. In: VAN DEN BUSSCHE, Jan, ed., Victor VIANU, ed.. Database Theory — ICDT 2001. Berlin, Heidelberg:Springer Berlin Heidelberg, pp. 420-434. ISBN 978-3-540-41456-8

@inproceedings{Aggarwal2001-10-12Surpr-5715, title={On the Surprising Behavior of Distance Metric in High-Dimensional Space}, year={2001}, doi={10.1007/3-540-44503-X_27}, number={1973}, isbn={978-3-540-41456-8}, address={Berlin, Heidelberg}, publisher={Springer Berlin Heidelberg}, series={Lecture Notes in Computer Science}, booktitle={Database Theory — ICDT 2001}, pages={420--434}, editor={Van den Bussche, Jan and Vianu, Victor}, author={Aggarwal, Charu C. and Hinneburg, Alexander and Keim, Daniel A.} }

<rdf:RDF xmlns:rdf="http://www.w3.org/1999/02/22-rdf-syntax-ns#" xmlns:bibo="http://purl.org/ontology/bibo/" xmlns:dc="http://purl.org/dc/elements/1.1/" xmlns:dcterms="http://purl.org/dc/terms/" xmlns:xsd="http://www.w3.org/2001/XMLSchema#" > <rdf:Description rdf:about="https://kops.uni-konstanz.de/rdf/resource/123456789/5715"> <dcterms:title>On the Surprising Behavior of Distance Metric in High-Dimensional Space</dcterms:title> <bibo:uri rdf:resource="http://kops.uni-konstanz.de/handle/123456789/5715"/> <dc:creator>Aggarwal, Charu C.</dc:creator> <dc:contributor>Hinneburg, Alexander</dc:contributor> <dc:format>application/pdf</dc:format> <dcterms:rights rdf:resource="https://creativecommons.org/licenses/by-nc-nd/2.0/legalcode"/> <dcterms:issued>2001-10-12</dcterms:issued> <dc:contributor>Aggarwal, Charu C.</dc:contributor> <dcterms:abstract xml:lang="eng">In recent years, the effect of the curse of high dimensionality has been studied in great detail on several problems such as clustering, nearest neighbor search, and indexing. In high dimensional space the data becomes sparse, and traditional indexing and algorithmic techniques fail from a efficiency and/or effectiveness perspective. Recent research results show that in high dimensional space, the concept of proximity, distance or nearest neighbor may not even be qualitatively meaningful. In this paper, we view the dimensionality curse from the point of view of the distance metrics which are used to measure the similarity between objects. We specially examine the behavior of the commonly used Lk norm and show that the problem of meaningfulness in high dimensionality is sensitive to the value of k. For example, this means that the Manhattan distance metric (L1 norm) is consistently more preferable than the Euclidean distance metric (L2 norm) for high dimensional data mining applications. Using the intuition derived from our analysis, we introduce and examine a natural extension of the Lk norm to fractional distance metrics. We show that the fractional distance metric provides more meaningful results both from the theoretical and empirical perspective. The results show that fractional distance metrics can significantly improve the effectiveness of standard clustering algorithms such as the k-means algorithm.</dcterms:abstract> <dc:language>eng</dc:language> <dc:creator>Keim, Daniel A.</dc:creator> <dc:rights>deposit-license</dc:rights> <dc:date rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-24T15:59:33Z</dc:date> <dcterms:bibliographicCitation>First publ. in: Database theory, ICDT 200, 8th International Conference, London, UK, January 4 - 6, 2001 / Jan Van den Bussche ... (eds.). Berlin: Springer, 2001, pp. 420-434 (=Lecture notes in computer science ; 1973)</dcterms:bibliographicCitation> <dc:creator>Hinneburg, Alexander</dc:creator> <dc:contributor>Keim, Daniel A.</dc:contributor> <dcterms:available rdf:datatype="http://www.w3.org/2001/XMLSchema#dateTime">2011-03-24T15:59:33Z</dcterms:available> </rdf:Description> </rdf:RDF>

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