A k-segments algorithm for finding principal curves
Pattern Recognition LettersPublished 1 June 2002Open access
Jakob Verbeek, Nikos Vlassis, Ben Kröse
Citations111
Generate an AI Snapshot to get a quick, structured summary of this paper.
Study Snapshot
ObjectiveStudy objective
MethodsResearch methodology
PopulationPopulation studied
Sample sizeSample sizes
OutcomesStudy outcomes here
ResultsStudy results comes here
LimitationsResearch study limitations comes here
A concise AI-generated summary of the paper will appear here once you click Generate AI Snapshot.
TL;DR
An incremental method to find principal curves using line segments fitted and connected to form polygonal lines to meet a performance criterion is proposed.
Abstract
peer reviewed
Keywords
Computer ScienceEngineering
Springer series in information sciencesSelf-Organizing Maps
10,377 Citations1997Teuvo Kohonen
The mathematical preliminaries, background, basic ideas, and implications of the Self-Organising Map algorithm are expounded in a manner which is accessible without prior expert knowledge.
Vector Quantization and Signal Compression
7,039 Citations1992A. Gersho, Robert M. Gray
The author explains the design and implementation of the Levinson-Durbin Algorithm, which automates the very labor-intensive and therefore time-heavy and expensive process of designing and implementing a Quantizer.
Cambridge University Press eBooksPattern Recognition and Neural Networks
6,468 Citations1996B. D. Ripley
The Traveling Salesman Problem
1,622 Citations2019Lawrence Snyder, Zuo‐Jun Max Shen
Neural ComputationGTM: The Generative Topographic Mapping
1,389 Citations1998Chris Bishop, Markus Svensén +1 more
A form of nonlinear latent variable model called the generative topographic mapping, for which the parameters of the model can be determined using the expectation-maximization algorithm, is introduced.
Neural NetworksGrowing cell structures—A self-organizing network for unsupervised and supervised learning
1,263 Citations1994Bernd Fritzke
A new self-organizing neural network model that has two variants that performs unsupervised learning and can be used for data visualization, clustering, and vector quantization is presented and results on the two-spirals benchmark and a vowel classification problem are presented that are better than any results previously published.
Introduction to Graph Theory
933 Citations1972Robin Wilson
IEEE Transactions on Pattern Analysis and Machine IntelligenceLearning and design of principal curves
349 Citations2000Balázs Kégl, Adam Krzyżak +2 more
This work defines principal curves as continuous curves of a given length which minimize the expected squared distance between the curve and points of the space randomly chosen according to a given distribution, making it possible to theoretically analyze principal curve learning from training data and it also leads to a new practical construction.
Journal of the American Statistical AssociationPrincipal Curves
348 Citations1989Trevor Hastie, Werner Stuetzle
This article defines principal curves, an algorithm for their construction is given, some theoretical results are presented, and the procedure is compared to other generalizations ofprincipal components.
Statistics and ComputingPrincipal curves revisited
223 Citations1992Robert Tibshirani
An alternative definition of a principal curve is given, based on a mixture model, that is a generalization of linear principal components and carried out through an EM algorithm.
EcologyPRINCIPAL CURVES: A NEW TECHNIQUE FOR INDIRECT AND DIRECT GRADIENT ANALYSIS
104 Citations1999Glenn De’ath
Efficient greedy learning of Gaussian mixtures
8 Citations2001Jakob Verbeek, Nikos Vlassis +1 more
A deterministic greedy method to learn a mixture of Gaussians which runs in O(nk^2) time and which compares favorably to the standard EM with random initializations as well as to another existing greedy approach to learning Gaussian mixtures.