LPCM (version 0.44-5)

lpc.spline: Representing local principal curves through a cubic spline.

Description

Fis a natural cubic spline component-wise through the series of local centers of mass. This provides a continuous parametrization in terms of arc length distance, which can be used to compute a projection index for the original or new data points.

Usage

lpc.spline(lpcobject, optimize = TRUE, compute.Rc=FALSE,
     project=FALSE, ...)

Arguments

lpcobject

Object of class lpc.

optimize

Boolean. If TRUE, optimize is used to find the point on the curve with minimum distance. Otherwise, data points are only projected onto the closest knot.

compute.Rc

Boolean. If TRUE, the goodness-of-fit measure $R_C$ suggested in [1] is computed and returned (using the scaled data, if scaled=TRUE in lpcobject).

project

Boolean. If TRUE, projections onto curve are computed.

...

Additional arguments to be passed to lpc.project.spline

Value

• knots.pi
  LPC parameters (in cubic spline parametrization) at position of the knots of the spline function (these are not identical to the LPC mass points!)
• knots.coords
  Coordinates of the spline knots.
• closest.pi
  Parameter of the projected data points.
• closest.coords
  Coordinates of projected data points.
• closest.dist
  Euclidean distance between original and projected data point.
• closest.branch
  ID Number of the branch on which the data point was projected (the IDs are given in the output of function lpc).
• Rc
  Value of $R_C$.
• project
  repeats the input value of project.
• lpcobject
  returns the provided object lpcobject.
• splinefun
  returns the cubic spline function (generated by lpc.splinefun).

Warning

Careful with options project and compute.Rc - they can take rather long if the data set is large!

Details

See reference [2].

References

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

[2] Einbeck, J., Evers, L. & Hinchliff, K. (2010): Data compression and regression based on local principal curves. In A. Fink, B. Lausen, W. Seidel, and A. Ultsch (Eds), Advances in Data Analysis, Data Handling, and Business Intelligence, Heidelberg, pp. 701--712, Springer.

See Also

lpc

Examples

data(gvessel)
gvessel.lpc <- lpc(gvessel[,c(2,4,5)],   h=0.11,  x0=c(35, 1870, 6.3))
gvessel.spline  <- lpc.spline(gvessel.lpc)
plot(gvessel.spline, lwd=2)