Geometric mean for subspace selection

Tao, D; Li, X; Wu, X; Maybank, SJ

Geometric mean for subspace selection

Tao, D

Li, X Wu, X Maybank, SJ

Permalink

Publication Type:: Journal Article
Citation:: IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009, 31 (2), pp. 260 - 274
Issue Date:: 2009-05-28

Closed Access

	Filename	Description	Size
	2011000201OK.pdf		3.93 MB	Adobe PDF	View/Open

Copyright Clearance Process

Recently Added
In Progress
Closed Access

This item is closed access and not available.

Full metadata record

Field	Value	Language
dc.contributor.author	Tao, D https://orcid.org/0000-0001-7225-5449	en_US
dc.contributor.author	Li, X	en_US
dc.contributor.author	Wu, X	en_US
dc.contributor.author	Maybank, SJ	en_US
dc.date.issued	2009-05-28	en_US
dc.identifier.citation	IEEE Transactions on Pattern Analysis and Machine Intelligence, 2009, 31 (2), pp. 260 - 274	en_US
dc.identifier.issn	0162-8828	en_US
dc.identifier.uri	http://hdl.handle.net/10453/15225
dc.description.abstract	Subspace selection approaches are powerful tools in pattern classification and data visualization. One of the most important subspace approaches is the linear dimensionality reduction step in the Fisher's linear discriminant analysis (FLDA), which has been successfully employed in many fields such as biometrics, bioinformatics, and multimedia information management. However, the linear dimensionality reduction step in FLDA has a critical drawback: for a classification task with c classes, if the dimension of the projected subspace is strictly lower than c - 1, the projection to a subspace tends to merge those classes, which are close together in the original feature space. If separate classes are sampled from Gaussian distributions, all with identical covariance matrices, then the linear dimensionality reduction step in FLDA maximizes the mean value of the Kullback-Leibler (KL) divergences between different classes. Based on this viewpoint, the geometric mean for subspace selection is studied in this paper. Three criteria are analyzed: 1) maximization of the geometric mean of the KL divergences, 2) maximization of the geometric mean of the normalized KL divergences, and 3) the combination of 1 and 2. Preliminary experimental results based on synthetic data, UCI Machine Learning Repository, and handwriting digits show that the third criterion is a potential discriminative subspace selection method, which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in FLDA and its several representative extensions. © 2009 IEEE.	en_US
dc.relation.ispartof	IEEE Transactions on Pattern Analysis and Machine Intelligence	en_US
dc.relation.isbasedon	10.1109/TPAMI.2008.70	en_US
dc.subject.classification	Artificial Intelligence & Image Processing	en_US
dc.subject.mesh	Data Interpretation, Statistical	en_US
dc.subject.mesh	Discriminant Analysis	en_US
dc.subject.mesh	Algorithms	en_US
dc.subject.mesh	Models, Theoretical	en_US
dc.subject.mesh	Artificial Intelligence	en_US
dc.subject.mesh	Computer Simulation	en_US
dc.subject.mesh	Pattern Recognition, Automated	en_US
dc.title	Geometric mean for subspace selection	en_US
dc.type	Journal Article
utslib.citation.volume	2	en_US
utslib.citation.volume	31	en_US
utslib.for	0806 Information Systems	en_US
utslib.for	0906 Electrical and Electronic Engineering	en_US
utslib.for	0801 Artificial Intelligence and Image Processing	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	closed_access
pubs.issue	2	en_US
pubs.publication-status	Published	en_US
pubs.volume	31	en_US

Abstract:

Subspace selection approaches are powerful tools in pattern classification and data visualization. One of the most important subspace approaches is the linear dimensionality reduction step in the Fisher's linear discriminant analysis (FLDA), which has been successfully employed in many fields such as biometrics, bioinformatics, and multimedia information management. However, the linear dimensionality reduction step in FLDA has a critical drawback: for a classification task with c classes, if the dimension of the projected subspace is strictly lower than c - 1, the projection to a subspace tends to merge those classes, which are close together in the original feature space. If separate classes are sampled from Gaussian distributions, all with identical covariance matrices, then the linear dimensionality reduction step in FLDA maximizes the mean value of the Kullback-Leibler (KL) divergences between different classes. Based on this viewpoint, the geometric mean for subspace selection is studied in this paper. Three criteria are analyzed: 1) maximization of the geometric mean of the KL divergences, 2) maximization of the geometric mean of the normalized KL divergences, and 3) the combination of 1 and 2. Preliminary experimental results based on synthetic data, UCI Machine Learning Repository, and handwriting digits show that the third criterion is a potential discriminative subspace selection method, which significantly reduces the class separation problem in comparing with the linear dimensionality reduction step in FLDA and its several representative extensions. © 2009 IEEE.

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

http://hdl.handle.net/10453/15225