Construction Algorithm of Principal Curves in the Sense of Limit

Zhao, L; Zhao, Y; Luo, S; Shao, C

Construction Algorithm of Principal Curves in the Sense of Limit

Zhao, L Zhao, Y Luo, S Shao, C

Permalink

Publisher:: Springer
Publication Type:: Conference Proceeding
Citation:: AI 2005: Advances in Artificial Intelligence, 18th Australian Joint Conference on Artificial Intelligence Proceedings, 2005, pp. 264 - 273
Issue Date:: 2005-01

Open Access

Copyright Clearance Process

Recently Added
In Progress
Open Access

This item is open access.

Adobe PDF

Download full textAdobe PDF (260.86 kB)

View on publisher's site

View statistics

Full metadata record

Field	Value	Language
dc.contributor.author	Zhao, L	en_US
dc.contributor.author	Zhao, Y	en_US
dc.contributor.author	Luo, S	en_US
dc.contributor.author	Shao, C	en_US
dc.contributor.editor	Zhang, S	en_US
dc.contributor.editor	Jarvis, R	en_US
dc.date	2005-12-05	en_US
dc.date.issued	2005-01	en_US
dc.identifier.citation	AI 2005: Advances in Artificial Intelligence, 18th Australian Joint Conference on Artificial Intelligence Proceedings, 2005, pp. 264 - 273	en_US
dc.identifier.isbn	3-540-30462-2	en_US
dc.identifier.uri	http://hdl.handle.net/10453/2748
dc.description.abstract	Principal curves have been defined as self-consistent, smooth, one-dimensional curves which pass through the middle of a multidimensional data set. They are nonlinear generalization of the first Principal Component. In this paper, we take a new approach by defining principal curves as continuous curves based on the local tangent space in the sense of limit. It is proved that this new principal curves not only satisfy the self-consistent property, but also are the unique existence for any given open covering. Based on the new definition, a new practical algorithm for constructing principal curves is given. And the convergence properties of this algorithm are analyzed. The new construction algorithm of principal curves is illustrated on some simulated data sets.	en_US
dc.publisher	Springer	en_US
dc.relation.ispartof	AI 2005: Advances in Artificial Intelligence, 18th Australian Joint Conference on Artificial Intelligence Proceedings	en_US
dc.relation.ispartof	Australasian Joint Conference on Artificial Intelligence	en_US
dc.relation.isbasedon	10.1007/11589990_29	en_US
dc.rights	This is a post-peer-review, pre-copyedit version of an article published in AI 2005: Advances in Artificial Intelligence, 18th Australian Joint Conference on Artificial Intelligence Proceedings. The final authenticated version is available online at: https://dx.doi.org/10.1007/11589990_29.	en_US
dc.rights	This is a post-peer-review, pre-copyedit version of an article published in Australasian Joint Conference on Artificial Intelligence. The final authenticated version is available online at: https://dx.doi.org/10.1007/11589990_29.	en_US
dc.subject.classification	Artificial Intelligence & Image Processing	en_US
dc.title	Construction Algorithm of Principal Curves in the Sense of Limit	en_US
dc.type	Conference Proceeding
utslib.location	Berlin, Germany	en_US
utslib.location.activity	Sydney, Australia	en_US
utslib.for	080109 Pattern Recognition and Data Mining	en_US
dc.location.activity	Sydney, Australia	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
utslib.copyright.status	open_access
pubs.consider-herdc	true	en_US
pubs.place-of-publication	Berlin, Germany	en_US
pubs.start-date	2005-12-05	en_US

Abstract:

Principal curves have been defined as self-consistent, smooth, one-dimensional curves which pass through the middle of a multidimensional data set. They are nonlinear generalization of the first Principal Component. In this paper, we take a new approach by defining principal curves as continuous curves based on the local tangent space in the sense of limit. It is proved that this new principal curves not only satisfy the self-consistent property, but also are the unique existence for any given open covering. Based on the new definition, a new practical algorithm for constructing principal curves is given. And the convergence properties of this algorithm are analyzed. The new construction algorithm of principal curves is illustrated on some simulated data sets.

Please use this identifier to cite or link to this item:

http://hdl.handle.net/10453/2748