predict.prcurve: Predict new locations & fitted values on a principal curve

Description

Locations on a fitted principal curve are predicted by projecting the new observations in \(m\) dimensions on to the corresponding closest point on the curve. Fitted values for data used to fit the curve are available with respect to the principal curve or to the individual smooth functions.

Usage

# S3 method for prcurve
predict(object, newdata, ...)
# S3 method for prcurve
fitted(object, type = c("curve","smooths"), ...)

Value

A matrix of points in the space of the original data. Rows correspond to the new samples and columns to the variables (ordered as per the original data used to fit the curve).

How these points are ordered along the fitted curve is contained in attributed tag.

Arguments

object: an object of class prcurve.
newdata: a matrix or data frame of new observations within the space of the orginal data. Variables are matched against those of the original data via their names or colnames. If a data frame is supplied, it is converted to a matrix via data.matrix.
type: character; the type of fitted values to return.
...: other arguments passed to other methods. Not currently used.

Author

Gavin L. Simpson

Details

Fitting a principal curve involves two procedures. In one, the current curve is bent towards the data via the fitting of spline functions with distance along the curve as the predictor variable and each variable in turn as the response. The second procedure, a projection step, involves projecting the observed points in \(m\) dimensions on to locations along the current curve to which they are closest in the hyperspace.

Given a fitted curve, the projection step can be used to find new points on the fitted curve by projecting the new points located in the hyperspace on to points on the curve to which they are closest.