Presentation	2001/1/12 Fundamental studies of normal distributions on manifold Yukihiko Yamashita,
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Abstract(in English)	The category which a pattern vector belongs to does not depend on its norm. Then, in many cases, by the normalization of the norm, after it is mapped on the sphere, its category is decided. Although a few researches on pattern recognition use normal distributions on the sphere, their definition is not clear theoretically. Therefore, we study on normal distributions on manifolds. First, we provide the characterizations of normal distributions on the vector space. We provide the concept of local uniform independence and define the uniform normal distribution on manifolds. We also study normal distributions and the Mahalanobis metric which is an extension of Mahalanobis distance.
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Keyword(in English)	normal distribution / manifold / local uniform independence / sphere / Mahalanobis metric
Paper #	PRMU2000-174
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Conference Information
Committee	PRMU
Conference Date	2001/1/12(1days)
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Paper Information
Registration To	Pattern Recognition and Media Understanding (PRMU)
Language	JPN
Title (in Japanese)	(See Japanese page)
Sub Title (in Japanese)	(See Japanese page)
Title (in English)	Fundamental studies of normal distributions on manifold
Sub Title (in English)
Keyword(1)	normal distribution
Keyword(2)	manifold
Keyword(3)	local uniform independence
Keyword(4)	sphere
Keyword(5)	Mahalanobis metric
1st Author's Name	Yukihiko Yamashita
1st Author's Affiliation	Department of International Development Engineering Faculty of Engineering Tokyo Institute of Technology()
Date	2001/1/12
Paper #	PRMU2000-174
Volume (vol)	vol.100
Number (no)	566
Page	pp.pp.-
#Pages	8
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