Fit a principal curve which describes a smooth curve that passes through the middle
of the data x in an orthogonal sense. This curve is a non-parametric generalization
of a linear principal component. If a closed curve is fit (using smoother = "periodic_lowess")
then the starting curve defaults to a circle, and each fit is followed by a bias correction
suggested by Jeff Banfield.
Hastie, T. and Stuetzle, W., Principal Curves, JASA, Vol. 84, No. 406 (Jun., 1989), pp. 502-516, 10.2307/2289936 (PDF).
See also Banfield and Raftery (JASA, 1992).