Measuring goodness-of-fit for principal objects.
These functions compute the ‘coverage coefficient’ R_c for local principal curves, local principal points (i.e., kernel density estimates obtained through iterated mean shift), and other principal objects.
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an object used to select a method.
Further arguments passed to or from other methods (not needed yet).
A data matrix.
A matrix of coordinates of the projected data.
For principal curves, don't modify. For principal points, set "points".
Rc computes the coverage coefficient R_c, a quantity which
estimates the goodness-of-fit of a fitted principal object. This
quantity can be interpreted similar to the coeffient of determination in
regression analysis: Values close to 1 indicate a good fit, while values
close to 0 indicate a ‘bad’ fit (corresponding to linear PCA).
For objects of type
ms, S3 methods are available which use the generic function
Rc. This, in turn, calls the base function
can also be used manually if the fitted object is of another class.
In principle, function
base.Rc can be used for assessing
goodness-of-fit of any principal object provided that
the coordinates (
closest.coords) of the projected data are
available. For instance, for HS principal curves fitted via
princurve, this information is contained in component
and for a a k-means object, say
fitk, this information can be
the latter case.
Rc attempts to compute all missing information, so
computation will take the longer the less informative the given
x is. Note also,
Rc looks up the option
scaled in the fitted
object, and accounts for the scaling automatically. Important: If the data
were scaled, then do NOT unscale the results by hand in order to feed
the unscaled version into
base.Rc, this will give a wrong result.
In terms of methodology, these functions compute R_c directly through the mean reduction of absolute residual length, rather than through the area above the coverage curve.
These functions do currently not account for observation weights, i.e. R_c is computed through the unweighted mean reduction in absolute residual length (even if weights have been used for the curve fitting).
Contributions (in form of pieces of code, or useful suggestions for improvements) by Jo Dwyer, Mohammad Zayed, and Ben Oakley are gratefully acknowledged.
J. Einbeck and L. Evers.
Einbeck, Tutz, and Evers (2005). Local principal curves. Statistics and Computing 15, 301-313.
Einbeck (2011). Bandwidth selection for nonparametric unsupervised learning techniques – a unified approach via self-coverage. Journal of Pattern Recognition Research 6, 175-192.
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