Local principal curve methods

Description

Fitting multivariate data patterns with local principal curves; including simple tools for data compression (projection), bandwidth selection, and measuring goodness-of-fit.

This package implements the techniques introduced in Einbeck, Tutz & Evers (2005), and successive related papers.

The main functions to be called by the user are

• lpc, for the estimation of the local centers of mass which make up the principal curve;

• lpc.spline, which is a smooth and fully parametrized cubic spline respresentation of the latter;

• lpc.project, which enables to compress data by projecting them orthogonally onto the curve;

• lpc.coverage and Rc for assessing goodness-of-fit;

• lpc.self.coverage for bandwidth selection;

• the generic plot and print methods for objects of class lpc and lpc.spline.

This package also contains some code for density mode detection (‘local principal points’) and mean shift clustering (as well as bandwidth selection in this context), which implements the methods presented in Einbeck (2011). See the help file for ms.

A second R package which will implement the extension of local principal curves to local principal surfaces and manifolds, as proposed in Einbeck, Evers & Powell (2010), is in preparation.

Details

Acknowledgements

Contributions (in form of pieces of code, or useful suggestions for improvements) by Jo Dwyer, Mohammad Zayed, and Ben Oakley are gratefully acknowledged.

Author(s)

Jochen Einbeck and Ludger Evers

Maintainer: Jochen Einbeck <jochen.einbeck@durham.ac.uk>

References

Einbeck, J., Tutz, G., & Evers, L. (2005): Local principal curves, Statistics and Computing 15, 301-313.

Einbeck, J., Evers, L., & Powell, B. (2010): Data compression and regression through local principal curves and surfaces, International Journal of Neural Systems, 20, 177-192.

Einbeck, J. (2011): Bandwidth selection for nonparametric unsupervised learning techniques – a unified approach via self-coverage. Journal of Pattern Recognition Research 6, 175-192.

See Also

pcurve, princurve

Results