# Find parametric representation of cluster surface [closed]

I have a large set of records with each record containing $N$ variables $v_i$ (say $N=20$).

I can transform these variables $v_i$ to be in the range [0,1] and am able to use a simple loss function $L = \sum_i v_i^2$. After that I know that there are two large clusters of points with small $L$ and large $L$. There are also few points in between these clusters. I can successfully assign records to these clusters.

But what R functionality would I use to get a parametric representation (in the variables $v_i$) of the surface of the "large $L$ cluster", preferably as a function of $L$?

(I know I could train a neural network on my data to give me a similar answer, but I would like to stay away from that for this application.)

-
(1) Are these clusters in L alone or clusters in N -dimensional space? (2) The penultimate remark about "a function of L " may be confusing, because it seems to conflict with what a "parametric representation ... in ...v[i]" would be (namely, a smooth map from an M << N dimensional space into N dimensional space whose image closely approximates most of the records). – whuber Aug 18 '10 at 18:53
@whuber: (1) The points are in both in L and the N-dimensional space of the v_i. However since I have more than a few variables most points lie near the surface and using simple box cuts e.g. v_i>0.5 would miss a lot of points that would have a "good enough" L. (2) Think of L as the onion layer I would be sitting on. – honk Aug 18 '10 at 19:47
I'm still confused by the question, because it uses some words in ways that are inconsistent with the definitions I know. A "parametric representation" of a (hyper)surface in $N$ dimensions is a function of $N-1$ variables, for instance. A "function of $L$" couldn't do anything for you in this regard. I'm thinking that perhaps you're looking for $L$ itself to be a function of $N-1$ angular parameters. Could you perhaps clarify this or give an example of what you're looking for as a solution? – whuber Sep 16 '10 at 3:12
@Honk answers to whuber's questions are crucial to being able to answer this question, I notice you regularly pop by after a few months of absence and were even a beta participant, so I'll leave this for a while, but if you are not able to improve the question, I think we have to close this question as unanswerable. – Corone Feb 17 at 19:49
@Corone: Thanks for wrangling old questions. I tried to answer whuber's questions earlier and wasn't able to add to what I had said. However, this question is specifically tied to how R internally parametrizes clusters, and given the many different algorithms giving a generally correct answer might be impossible. If you think this question should be closed and have no issue with that. – honk Feb 17 at 21:03

## closed as not a real question by gung, Macro, whuber♦Feb 18 at 17:59

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, see the FAQ.