Fis a natural cubic spline componentwise 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.
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lpcobject 
Object of class 
optimize 
Boolean. If TRUE, 
compute.Rc 
Boolean. If TRUE, the goodnessoffit measure
R_c suggested in [1] is computed and returned (using the scaled data, if 
project 
Boolean. If TRUE, projections onto curve are computed. 
... 
Additional arguments to be passed to 
See reference [2].
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 R_c. 
project 
repeats the input value of 
lpcobject 
returns the provided object 
splinefun 
returns the cubic spline function (generated by

Careful with options project
and compute.Rc
 they can take rather long
if the data set is large!
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.
J. Einbeck and L. Evers
[1] Einbeck, J., Tutz, G., and Evers, L. (2005). Local principal curves. Statistics and Computing 15, 301313.
[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.
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