R functions for local principal curves

• The file lpc.r (updated 16/10/2007, version 0.32) contains the function lpc and some other auxiliary functions, which can be used to fit Local Principal Curves [1,2] for arbitrary dimensions [1], and for finding branches of at most third depth [2].
  New features in version 0.32:
  • A bug relating the initialization of multiple random starting points was fixed.
  • For all dimensions d ≥ 2, the (unit-speed) parameterization is now accessible in the fitted lpc object.
  
  New features in version 0.31:
  • Default settings for all tuning parameters.
  • An arbitrary number of starting points can be specified by hand.
  • The possibility to scale the data automatically onto the [0,1] range in each direction, facilitating bandwidth selection.
• The file letters.r contains R-code for the simulation and estimation of letters as in [2].
• The file leicester-talk.r contains R-code for all real data examples presented in my talk at the Workshop Principal manifolds for data cartography and dimension reduction , Leicester, UK, August 24-26, 2006.
• R-code for [3].
• Additional R functions which enable to fit a spline through the fitted LPC and to project data points onto it (this is useful when LPCs shall be used as nonparametric tool for data compression) can be obtained on request from the authors: jochen.einbeck ``at'' durham.ac.uk

Data sets

• Pennsylvania Floodplain Data (Source: Office of Remote Sensing for Earth Resources, Pennsylvania State University).
• European Coastal resorts (Source: Diercke Weltatlas, 1984).
• Bladder cancer microarray data
• Speed-flow data for [3].

References

[1] Local Principal Curves (Einbeck, Tutz & Evers, 2005), Statistics and Computing 15, 301-313.

[2] Exploring Multivariate Data Structures with Local Principal Curves (Einbeck, Tutz & Evers, 2005), Proceedings of the GfKl 2004.

[3] A catalogue of speed-flow diagrams based on local principal curves (Einbeck & Dwyer, 2008). Preprint, Durham University.