Results 1  10
of
38
Principal Curves Revisited
 Statistics and Computing
, 1992
"... A principal curve (Hastie and Stuetzle, 1989) is a smooth curve passing through the "middle" of a distribution or data cloud, and is a generalization of linear principal components. We give an alternative definition of a principal curve, based on a mixture model. Estimation is carried out ..."
Abstract

Cited by 67 (0 self)
 Add to MetaCart
A principal curve (Hastie and Stuetzle, 1989) is a smooth curve passing through the "middle" of a distribution or data cloud, and is a generalization of linear principal components. We give an alternative definition of a principal curve, based on a mixture model. Estimation is carried out
Ice floe identification in satellite images using mathematical morphology and clustering about principal curves
 JASA
, 1992
"... Identification of ice floes and their outlines in satellite images is important for understanding physical processes in the polar regions, for transportation in icecovered seas and for the design of offshore structures intended to survive in the presence of ice. At present this is done manually, ..."
Abstract

Cited by 61 (5 self)
 Add to MetaCart
, a long and tedious process which precludes full use of the great volume of relevant images now available. We describe an automatic and accurate method for identifying ice floes and their outlines. Floe outlines are modeled as closed principal curves (Hastie and Stuetzle, 1989), a flexible class
Principal Curves: Learning, Design, And Applications
, 1999
"... The subjects of this thesis are unsupervised learning in general, and principal curves in particular. Principal curves were originally defined by Hastie \cite{Has84} and Hastie and Stuetzle \cite{HaSt89} (hereafter HS) to formally capture the notion of a smooth curve passing through the ``middle&apo ..."
Abstract

Cited by 18 (3 self)
 Add to MetaCart
'' of a $d$dimensional probability distribution or data cloud. Based on the definition, HS also developed an algorithm for constructing principal curves of distributions and data sets. The field has been very active since Hastie and Stuetzle's groundbreaking work. Numerous alternative definitions
Joint Statistical Meetings Section on Nonparametric Statistics Smoothings, Ridges
"... In this paper, we seek to formulate a geometrically based alternative to nonlinear, nonparametric regression. Hastie and Stuetzle (1989) introduced the ideas of principal curves and surfaces. These were 1 and 2dimensional nonlinear regressiontype estimators, which were consistent with respect to ..."
Abstract
 Add to MetaCart
In this paper, we seek to formulate a geometrically based alternative to nonlinear, nonparametric regression. Hastie and Stuetzle (1989) introduced the ideas of principal curves and surfaces. These were 1 and 2dimensional nonlinear regressiontype estimators, which were consistent with respect
Parametric Subspace Modeling Of Speech Transitions
 Speech Communication
, 1998
"... This report describes an attempt at capturing segmental transition information for speech recognition tasks. The slowly varying dynamics of spectral trajectories carries much discriminant information that is very crudely modelled by traditional approaches such as HMMs. In approaches such as recurren ..."
Abstract

Cited by 13 (2 self)
 Add to MetaCart
the principal curves method of Hastie and Stuetzle and the Generative Topographic map (GTM...
On Adaptation to Sparse Design in Bivariate Local Linear Regression
, 1996
"... INTRODUCTION Problems of nonparametric regression with multivariate design points arise with increasing frequency in a range of applications, including dimensionreduction methods such as projection pursuit and ACE (e.g. Friedman and Stuetzle 1981, Breiman and Friedman 1985, Huber 1985), flexible m ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
INTRODUCTION Problems of nonparametric regression with multivariate design points arise with increasing frequency in a range of applications, including dimensionreduction methods such as projection pursuit and ACE (e.g. Friedman and Stuetzle 1981, Breiman and Friedman 1985, Huber 1985), flexible
Hierarchical Computation Of Pl Harmonic Embeddings
, 1997
"... this paper, we present a method for computing PL harmonic maps that appears to have complexity O(n), thereby speeding up the remeshing algorithm. Our approach is to replace the CG algorithm by the preconditioned conjugate gradients (PCG) algorithm [5]. Our preconditioner is a hierarchical preconditi ..."
Abstract

Cited by 37 (0 self)
 Add to MetaCart
the computation of harmonic maps was developed independently by Aaron Lee [9]. Date: July 11, 1997. This work was partially supported through NSF grants DMS9402734 and 9661288. 1 2 DUCHAMP, CERTAIN, DEROSE AND STUETZLE The paper is organized as follows. In Section 2 we discuss the definition of harmonic maps
Automatic Smoothing Spline Projection Pursuit
 Journal of Computational and Graphical Statistics
, 1994
"... A highly flexible nonparametric regression model for predicting a response y given covariates fx k g d k=1 is the projection pursuit regression (PPR) model y = h(x) = fi 0 + P j fi j f j (ff T j x), where the f j are general smooth functions with mean zero and norm one, and P d k=1 ff 2 k ..."
Abstract

Cited by 18 (1 self)
 Add to MetaCart
kj = 1. The standard PPR algorithm of Friedman and Stuetzle (1981) estimates the smooth functions f j using the supersmoother nonparametric scatterplot smoother. Friedman's algorithm constructs a model with M max linear combinations, then prunes back to a simpler model of size M M max , where
n p T
"... e 8 d b This paper studies the ksegments algorithm proposed by Verbeek et al. [Verbeek, J.J., Vlassis, N., Krose, B., 2002. A ksegments algorithm for finding principal curves, Pattern Recognition Lett. 23, 1009–1017] for computing principal curves. In particular an autoHastie and Stuetzle (1989) ..."
Abstract
 Add to MetaCart
e 8 d b This paper studies the ksegments algorithm proposed by Verbeek et al. [Verbeek, J.J., Vlassis, N., Krose, B., 2002. A ksegments algorithm for finding principal curves, Pattern Recognition Lett. 23, 1009–1017] for computing principal curves. In particular an autoHastie and Stuetzle (1989
Principal Curves and Principal Oriented Points
, 1998
"... Principal curves have been de#ned #Hastie and Stuetzle 1989# as smooth curves passing through the middle of a multidimensional data set. They are nonlinear generalizations of the #rst principal component, a charazterization of which is the basis for the principal curves de#nition. In this paper we p ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
Principal curves have been de#ned #Hastie and Stuetzle 1989# as smooth curves passing through the middle of a multidimensional data set. They are nonlinear generalizations of the #rst principal component, a charazterization of which is the basis for the principal curves de#nition. In this paper we
Results 1  10
of
38