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1,578
Principal Curves
, 1989
"... Principal curves are smooth onedimensional curves that pass through the middle of a pdimensional data set, providing a nonlinear summary of the data. They are nonparametric, and their shape is suggested by the data. The algorithm for constructing principal curve starts with some prior summary, suc ..."
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Cited by 394 (1 self)
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Principal curves are smooth onedimensional curves that pass through the middle of a pdimensional data set, providing a nonlinear summary of the data. They are nonparametric, and their shape is suggested by the data. The algorithm for constructing principal curve starts with some prior summary
Learning and Design of Principal Curves
, 2000
"... Principal curves have been defined as ``self consistent'' smooth curves which pass through the ``middle'' of a $d$dimensional probability distribution or data cloud. They give a summary of the data and also serve as an efficient feature extraction tool. We take a new approach by ..."
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Cited by 105 (4 self)
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Principal curves have been defined as ``self consistent'' smooth curves which pass through the ``middle'' of a $d$dimensional probability distribution or data cloud. They give a summary of the data and also serve as an efficient feature extraction tool. We take a new approach
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 ..."
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Cited by 67 (0 self)
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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
Principal Curves With Bounded Turn
, 2002
"... 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 ..."
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Cited by 16 (0 self)
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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
The Geometry of Principal Curves in the Plane
 Proceedings of the Third International Conference on Rewriting Techniques and Applications (Chapel Hill, NC
, 1993
"... ABSTRACT. Principal curves were introduced to formalize the notion of "a curve passing through the middle of a dataset". Vaguely speaking, a curve is said to pass through the middle of a dataset, if every point on the curve is the average of the observations projecting onto it. This idea c ..."
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Cited by 1 (0 self)
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ABSTRACT. Principal curves were introduced to formalize the notion of "a curve passing through the middle of a dataset". Vaguely speaking, a curve is said to pass through the middle of a dataset, if every point on the curve is the average of the observations projecting onto it. This idea
Principal curve sonification
 In: Proceedings of International Conference on Auditory Display
, 2000
"... This paper describes a new approach to render sonifications for highdimensional data, allowing the user to perceive the “main” structure of the data distribution. This is achieved by computing the principal curve of the data set, which is a trajectory that passes through the “middle ” of the data a ..."
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Cited by 18 (1 self)
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This paper describes a new approach to render sonifications for highdimensional data, allowing the user to perceive the “main” structure of the data distribution. This is achieved by computing the principal curve of the data set, which is a trajectory that passes through the “middle ” of the data
Principal Curve Sonification
 In Proceedings of ICAD 2000
, 2000
"... This paper describes a new approach to render sonifications for highdimensional data, allowing the user to perceive the "main" structure of the data distribution. This is achieved by computing the principal curve of the data set, which is a trajectory that passes through the "middle& ..."
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This paper describes a new approach to render sonifications for highdimensional data, allowing the user to perceive the "main" structure of the data distribution. This is achieved by computing the principal curve of the data set, which is a trajectory that passes through the "
Parameter Selection for Principal Curves
, 2011
"... Abstract – Principal curves are nonlinear generalizations of the notion of first principal component. Roughly, a principal curve is a parameterized curve in R d which passes through the “middle ” of a data cloud drawn from some unknown probability distribution. Depending on the definition, a princip ..."
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Cited by 6 (1 self)
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Abstract – Principal curves are nonlinear generalizations of the notion of first principal component. Roughly, a principal curve is a parameterized curve in R d which passes through the “middle ” of a data cloud drawn from some unknown probability distribution. Depending on the definition, a
Principal Curves: Learning and Convergence
, 1998
"... Principal curves have been defined as "self consistent" smooth curves which pass through the "middle" of a ddimensional probability distribution or data cloud. We generalize a property of first principal component lines and this leads to a new definition. Specifically, we define ..."
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Cited by 6 (4 self)
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Principal curves have been defined as "self consistent" smooth curves which pass through the "middle" of a ddimensional probability distribution or data cloud. We generalize a property of first principal component lines and this leads to a new definition. Specifically, we
Principal curve clustering with noise
, 1997
"... was supported by ONR grants N000149610192 and N000149610330. The authors are Clustering on principal curves combines parametric modeling of noise with nonparametric modeling of feature shape. This is useful for detecting curvilinear features in spatial point patterns, with or without backgroun ..."
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Cited by 21 (4 self)
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was supported by ONR grants N000149610192 and N000149610330. The authors are Clustering on principal curves combines parametric modeling of noise with nonparametric modeling of feature shape. This is useful for detecting curvilinear features in spatial point patterns, with or without
Results 1  10
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1,578