Local principal curves

Authors:
Jochen Einbeck;Gerhard Tutz;Ludger Evers
Affiliations:
Department of Mathematics, National University of Ireland, Galway, Ireland;Institut für Statistik, München, Germany 80799;Department of Statistics, University of Oxford, Oxford, UK OX1 3TG
Venue:
Statistics and Computing
Year:
2005

Citing 6
Cited 5

Dimension reduction by local principal component analysis

Neural Computation
Nonlinear component analysis as a kernel eigenvalue problem

Neural Computation
Learning and Design of Principal Curves

IEEE Transactions on Pattern Analysis and Machine Intelligence
Another look at principal curves and surfaces

Journal of Multivariate Analysis
Piecewise Linear Skeletonization Using Principal Curves

IEEE Transactions on Pattern Analysis and Machine Intelligence
Mean Shift: A Robust Approach Toward Feature Space Analysis

IEEE Transactions on Pattern Analysis and Machine Intelligence

Similarity preserving principal curve: an optimal 1-D feature extractor for data representation

IEEE Transactions on Neural Networks
Fast communication: Connectivity of projected high dimensional data charts on one-dimensional curves

Signal Processing
Exploring US Business Cycles with Bivariate Loops Using Penalized Spline Regression

Computational Economics
Nonlinearities and adaptation of color vision from sequential principal curves analysis

Neural Computation
A global structure-based algorithm for detecting the principal graph from complex data

Pattern Recognition

Quantified Score

Hi-index	0.00

Visualization

Abstract

Principal components are a well established tool in dimension reduction. The extension to principal curves allows for general smooth curves which pass through the middle of a multidimensional data cloud. In this paper local principal curves are introduced, which are based on the localization of principal component analysis. The proposed algorithm is able to identify closed curves as well as multiple curves which may or may not be connected. For the evaluation of the performance of principal curves as tool for data reduction a measure of coverage is suggested. By use of simulated and real data sets the approach is compared to various alternative concepts of principal curves.