Random projection towards the Baire metric for high dimensional clustering

Fionn Murtagh; Pedro Contreras

doi:10.1007/978-3-319-17091-6_37

Random projection towards the Baire metric for high dimensional clustering

Fionn Murtagh, Pedro Contreras

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

9 Citations (Scopus)

Abstract

For high dimensional clustering and proximity finding, also referred to as high dimension and low sample size data, we use random projection with the following principle. With the greater probability of close-to-orthogonal projections, compared to orthogonal projections, we can use rank order sensitivity of projected values. Our Baire metric, divisive hierarchical clustering, is of linear computation time.

Original language	English
Title of host publication	Statistical Learning and Data Sciences
Subtitle of host publication	Third International Symposium, SLDS 2015, Egham, UK, April 20-23, 2015, Proceedings
Editors	Alexander Gammerman, Vladimir Vovk, Harris Papadopoulos
Publisher	Springer Verlag
Pages	424-431
Number of pages	8
ISBN (Electronic)	9783319170916
ISBN (Print)	9783319170909
DOIs	https://doi.org/10.1007/978-3-319-17091-6_37
Publication status	Published - 3 Apr 2015
Externally published	Yes
Event	3rd International Symposium on Statistical Learning and Data Sciences - University of London, Egham, United Kingdom Duration: 20 Apr 2015 → 23 Apr 2015 Conference number: 3 http://www.clrc.rhul.ac.uk/slds2015/ (Link to Conference Website)

Publication series

Name	Lecture Notes in Computer Science
Publisher	Springer
Volume	9047
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	3rd International Symposium on Statistical Learning and Data Sciences
Abbreviated title	SLDS 2015
Country/Territory	United Kingdom
City	Egham
Period	20/04/15 → 23/04/15
Internet address	http://www.clrc.rhul.ac.uk/slds2015/ (Link to Conference Website)

Access to Document

10.1007/978-3-319-17091-6_37Licence: Unspecified

Cite this

Murtagh, F., & Contreras, P. (2015). Random projection towards the Baire metric for high dimensional clustering. In A. Gammerman, V. Vovk, & H. Papadopoulos (Eds.), Statistical Learning and Data Sciences : Third International Symposium, SLDS 2015, Egham, UK, April 20-23, 2015, Proceedings (pp. 424-431). (Lecture Notes in Computer Science; Vol. 9047). Springer Verlag. https://doi.org/10.1007/978-3-319-17091-6_37

Murtagh, Fionn ; Contreras, Pedro. / Random projection towards the Baire metric for high dimensional clustering. Statistical Learning and Data Sciences : Third International Symposium, SLDS 2015, Egham, UK, April 20-23, 2015, Proceedings. editor / Alexander Gammerman ; Vladimir Vovk ; Harris Papadopoulos. Springer Verlag, 2015. pp. 424-431 (Lecture Notes in Computer Science).

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Murtagh, F & Contreras, P 2015, Random projection towards the Baire metric for high dimensional clustering. in A Gammerman, V Vovk & H Papadopoulos (eds), Statistical Learning and Data Sciences : Third International Symposium, SLDS 2015, Egham, UK, April 20-23, 2015, Proceedings. Lecture Notes in Computer Science, vol. 9047, Springer Verlag, pp. 424-431, 3rd International Symposium on Statistical Learning and Data Sciences, Egham, United Kingdom, 20/04/15. https://doi.org/10.1007/978-3-319-17091-6_37

Random projection towards the Baire metric for high dimensional clustering. / Murtagh, Fionn; Contreras, Pedro.

Statistical Learning and Data Sciences : Third International Symposium, SLDS 2015, Egham, UK, April 20-23, 2015, Proceedings. ed. / Alexander Gammerman; Vladimir Vovk; Harris Papadopoulos. Springer Verlag, 2015. p. 424-431 (Lecture Notes in Computer Science; Vol. 9047).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - For high dimensional clustering and proximity finding, also referred to as high dimension and low sample size data, we use random projection with the following principle. With the greater probability of close-to-orthogonal projections, compared to orthogonal projections, we can use rank order sensitivity of projected values. Our Baire metric, divisive hierarchical clustering, is of linear computation time.

KW - Big data

KW - Binary rooted tree

KW - Computational complexity

KW - Hierarchical clustering

KW - Ultrametric topology

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Murtagh F, Contreras P. Random projection towards the Baire metric for high dimensional clustering. In Gammerman A, Vovk V, Papadopoulos H, editors, Statistical Learning and Data Sciences : Third International Symposium, SLDS 2015, Egham, UK, April 20-23, 2015, Proceedings. Springer Verlag. 2015. p. 424-431. (Lecture Notes in Computer Science). doi: 10.1007/978-3-319-17091-6_37

Random projection towards the Baire metric for high dimensional clustering

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