Discriminative vanishing component analysis

Hou, C; Nie, F; Tao, D

Discriminative vanishing component analysis

Hou, C Nie, F Tao, D

Permalink

Publication Type:: Conference Proceeding
Citation:: 30th AAAI Conference on Artificial Intelligence, AAAI 2016, 2016, pp. 1666 - 1672
Issue Date:: 2016-01-01

Closed Access

	Filename	Description	Size
	11968-55673-1-PB.pdf	Published version	672.59 kB	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	Hou, C	en_US
dc.contributor.author	Nie, F	en_US
dc.contributor.author	Tao, D https://orcid.org/0000-0001-7225-5449	en_US
dc.date.issued	2016-01-01	en_US
dc.identifier.citation	30th AAAI Conference on Artificial Intelligence, AAAI 2016, 2016, pp. 1666 - 1672	en_US
dc.identifier.isbn	9781577357605	en_US
dc.identifier.uri	http://hdl.handle.net/10453/106113
dc.description.abstract	© Copyright 2016, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. Vanishing Component Analysis (VCA) is a recently proposed prominent work in machine learning. It narrows the gap between tools and computational algebra: The vanishing ideal and its applications to classification problem. In this paper, we will analyze VCA in the kernel view, which is also another important research direction in machine learning. Under a very weak assumption, we provide a different point of view to VCA and make the kernel trick on VCA become possible. We demonstrate that the projection matrix derived by VCA is located in the same space as that of Kernel Principal Component Analysis (KPCA) with a polynomial kernel. Two groups of projections can express each other by linear transformation. Furthermore, we prove that KPCA and VCA have identical discriminative power, provided that the ratio trace criteria is employed as the measurement. We also show that the kernel formulated by the inner products of VCA's projections can be expressed by the KPCA's kernel linearly. Based on the analysis above, we proposed a novel Discriminative Vanishing Component Analysis (DVCA) approach. Experimental results are provided for demonstration.	en_US
dc.relation.ispartof	30th AAAI Conference on Artificial Intelligence, AAAI 2016	en_US
dc.title	Discriminative vanishing component analysis	en_US
dc.type	Conference Proceeding
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.publication-status	Published	en_US

Abstract:

© Copyright 2016, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. Vanishing Component Analysis (VCA) is a recently proposed prominent work in machine learning. It narrows the gap between tools and computational algebra: The vanishing ideal and its applications to classification problem. In this paper, we will analyze VCA in the kernel view, which is also another important research direction in machine learning. Under a very weak assumption, we provide a different point of view to VCA and make the kernel trick on VCA become possible. We demonstrate that the projection matrix derived by VCA is located in the same space as that of Kernel Principal Component Analysis (KPCA) with a polynomial kernel. Two groups of projections can express each other by linear transformation. Furthermore, we prove that KPCA and VCA have identical discriminative power, provided that the ratio trace criteria is employed as the measurement. We also show that the kernel formulated by the inner products of VCA's projections can be expressed by the KPCA's kernel linearly. Based on the analysis above, we proposed a novel Discriminative Vanishing Component Analysis (DVCA) approach. Experimental results are provided for demonstration.

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

http://hdl.handle.net/10453/106113