lpc.spline {LPCM} | R Documentation |
Representing local principal curves through a cubic spline.
Description
Fits 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 |
optimize |
Boolean. If TRUE, |
compute.Rc |
Boolean. If TRUE, the goodness-of-fit measure
|
project |
Boolean. If TRUE, projections onto curve are computed. |
... |
Additional arguments to be passed to |
Details
See reference [2].
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 |
Rc |
Value of |
project |
repeats the input value of |
lpcobject |
returns the provided object |
splinefun |
returns the cubic spline function (generated by
|
Warning
Careful with options project
and compute.Rc
- they can take rather long
if the data set is large!
Note
The parametrization of the cubic spline function is not exactly the same as that of the original LPC. The reason is that the latter uses Euclidean distances between centers of masses, while the former uses the arc length along the cubic spline. However, the differences are normally quite small.
Author(s)
J. Einbeck and L. Evers
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
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)