Principal curves with bounded turn

Author

Sandilya, Sathyakama ; Kulkarni, Sanjeev R.

Author_Institution

Princeton Univ., NJ, USA

Volume

48

Issue

10

fYear

2002

fDate

10/1/2002 12:00:00 AM

Firstpage

2789

Lastpage

2793

Abstract

Principal curves, like principal components, are a tool used in multivariate analysis for ends like feature extraction. Defined in their original form, principal curves need not exist for general distributions. The existence of principal curves with bounded length for any distribution that satisfies some minimal regularity conditions has been shown. We define principal curves with bounded turn, show that they exist, and present a learning algorithm for them. Principal components are a special case of such curves when the turn is zero.

Keywords

feature extraction; learning systems; piecewise linear techniques; principal component analysis; set theory; bounded length; bounded turn; closed set; feature extraction; general distributions; learning algorithm; minimal regularity conditions; multivariate analysis; piecewise-linear curve; principal component analysis; principal curves; Biological system modeling; Curve fitting; Data analysis; Feature extraction; Ice; Pattern analysis; Pattern classification; Principal component analysis; Signal analysis; Speech analysis;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/TIT.2002.802614

Filename

1035131