TY - JOUR
T1 - Principal curves with bounded turn
AU - Sandilya, Sathyakama
AU - Kulkarni, Sanjeev R.
N1 - Funding Information:
Manuscript received March 6, 2001; revised February 21, 2002. This work was supported in part by the National Science Foundation under NYI Grant IRI-9457645 and Grant ECS-9873451, and the MURI through the Army Research Office under Grant DAAD19-00-1-0466. S. Sandilya was with Princeton University, Princeton, NJ 08544 USA. He is now with Siemens Corporate Research, Princeton, NJ 08540 USA (e-mail: [email protected]). S. R. Kulkarni is with the Department of Electrical Engineering, Princeton University, Princeton, NJ 08544 USA (e-mail: [email protected]). Communicated by G. Lugosi, Associate Editor for Nonparametric Estimation, Classification, and Neural Networks. Publisher Item Identifier 10.1109/TIT.2002.802614.
PY - 2002/10
Y1 - 2002/10
N2 - 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.
AB - 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.
KW - Bounded turn
KW - Curve fitting
KW - Feature extraction
KW - Learning
KW - Multivariate analysis
KW - Principal components
KW - Principal curves
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U2 - 10.1109/TIT.2002.802614
DO - 10.1109/TIT.2002.802614
M3 - Article
AN - SCOPUS:0036794475
SN - 0018-9448
VL - 48
SP - 2789
EP - 2793
JO - IEEE Transactions on Information Theory
JF - IEEE Transactions on Information Theory
IS - 10
ER -