Structure of indicator function classes with finite vapnik-chervonenkis dimensions

Zhang, C; Tao, D

Structure of indicator function classes with finite vapnik-chervonenkis dimensions

Zhang, C Tao, D

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Publication Type:: Journal Article
Citation:: IEEE Transactions on Neural Networks and Learning Systems, 2013, 24 (7), pp. 1156 - 1160
Issue Date:: 2013-04-01

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Field	Value	Language
dc.contributor.author	Zhang, C	en_US
dc.contributor.author	Tao, D https://orcid.org/0000-0001-7225-5449	en_US
dc.date.issued	2013-04-01	en_US
dc.identifier.citation	IEEE Transactions on Neural Networks and Learning Systems, 2013, 24 (7), pp. 1156 - 1160	en_US
dc.identifier.issn	2162-237X	en_US
dc.identifier.uri	http://hdl.handle.net/10453/30893
dc.description.abstract	The Vapnik-Chervonenkis (VC) dimension is used to measure the complexity of a function class and plays an important role in a variety of fields, including artificial neural networks and machine learning. One major concern is the relationship between the VC dimension and inherent characteristics of the corresponding function class. According to Sauer's lemma, if the VC dimension of an indicator function class {cal F} is equal to D, the cardinality of the set {cal F}{S{1}{N}} will not be larger than sum{d=0}{D}C{N}d. Therefore, there naturally arises a question about the VC dimension of an indicator function class: what kinds of elements will be contained in the function class {cal F} if {cal F} has a finite VC dimension? In this brief, we answer the above question. First, we investigate the structure of the function class {cal F} when the cardinality of the set {cal F}{S{1}{N}} reaches the maximum value sum{d=0}{D}C{N}d. Based on the derived result, we then figure out what kinds of elements will be contained in {cal F} if {cal F} has a finite VC dimension. © 2012 IEEE.	en_US
dc.relation.ispartof	IEEE Transactions on Neural Networks and Learning Systems	en_US
dc.relation.isbasedon	10.1109/TNNLS.2013.2251746	en_US
dc.subject.classification	Artificial Intelligence & Image Processing	en_US
dc.title	Structure of indicator function classes with finite vapnik-chervonenkis dimensions	en_US
dc.type	Journal Article
utslib.citation.volume	7	en_US
utslib.citation.volume	24	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	7	en_US
pubs.publication-status	Published	en_US
pubs.volume	24	en_US

Abstract:

The Vapnik-Chervonenkis (VC) dimension is used to measure the complexity of a function class and plays an important role in a variety of fields, including artificial neural networks and machine learning. One major concern is the relationship between the VC dimension and inherent characteristics of the corresponding function class. According to Sauer's lemma, if the VC dimension of an indicator function class {cal F} is equal to D, the cardinality of the set {cal F}{S{1}{N}} will not be larger than sum{d=0}{D}C{N}d. Therefore, there naturally arises a question about the VC dimension of an indicator function class: what kinds of elements will be contained in the function class {cal F} if {cal F} has a finite VC dimension? In this brief, we answer the above question. First, we investigate the structure of the function class {cal F} when the cardinality of the set {cal F}{S{1}{N}} reaches the maximum value sum{d=0}{D}C{N}d. Based on the derived result, we then figure out what kinds of elements will be contained in {cal F} if {cal F} has a finite VC dimension. © 2012 IEEE.

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