[R] Fitting Hastie's principal surfaces in R

[David Winsemius]

> On Jan 1, 2017, at 12:26 PM, Bert Gunter <bgunter.4567 at gmail.com> wrote:
> 
> I couldn't find anything, but you might try searching on "thin plate
> splines" on rseek.org. I realize these are different than principal
> surfaces, but they might nevertheless be useful to you.   Or not.
> 
> Cheers,
> Bert
> 
> 
> Bert Gunter
> 
> "The trouble with having an open mind is that people keep coming along
> and sticking things into it."
> -- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )
> 
> 
> On Sun, Jan 1, 2017 at 2:56 AM, Neverstop . <neverstop at hotmail.it> wrote:
>> Hello,
>> 
>> I need to summarize a three-dimensional dataset through a principal surface that passes through the middle of the data. Principal surfaces are non-linear generalization of the plane created by the first two principal components and provide a non-linear summary of p-dimensional dataset. Principal surfaces are described in this 1989 article by Hastie and Stuetzle: https://web.stanford.edu/~hastie/Papers/Principal_Curves.pdf . They were introduced by Trevor Hastie in his Ph.D dissertation: http://www.slac.stanford.edu/cgi-wrap/getdoc/slac-r-276.pdf
>> 
>> I'm looking for a package to fit principal surfaces with R.
>> I've come across the package princurve created by TrevorHastie, but it allows to fit principal curves only. How can I fit two-dimensional principal surfaces in R?

What are the operational requirements for satisfaction with this assignment? I wonder if a regression "surface" of some other sort would be sufficient?  Assuming the three dimensions are X,Y, Z, then a loess (or locfit) "surface" or a regression estimate that used a spline surface for  Z ~ X+Y would not be a principal surface, but should satisfy some of your other requirements. This question would become clearer if you would offer data for analysis (the lack of which is one reason that duplicates of this question were closed as off-topic at both CrossValidated.com and StackOverflow.)


>> 
>> Thank you.
>> 
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David Winsemius
Alameda, CA, USA