Databases
StackOverflow2013
Postsdbo
POFitting a curve "around" data points in R
 

Note that there are some explanatory texts on larger screens.

plurals
  1. POFitting a curve "around" data points in R
    primarykey
    data
    text
    <p>i have a data set consisting of a collection of points. the points are distributed on the plane in such a way that they can be roughly bounded by a parabola. i am trying to find a way of fitting a parabola to the boundary of the points.</p> <p>this is what i have at present:</p> <pre><code>a = 1 b = 2 c = 3 parabola &lt;- function(x) { a * x^2 + b * x + c } N = 10000 x &lt;- runif(N, -4, 3) y &lt;- runif(N, 0, 10) data &lt;- data.frame(x, y) data &lt;- subset(data, y &gt;= parabola(x)) plot(data, xlim = c(-5, 5), ylim = c(0, 10), col = "grey") fr &lt;- function(x) { PAR = x[1] * data$x^2 + x[2] * data$x + x[3] # sum((PAR - data$y)^2 + 100 * plogis(PAR - data$y, scale = 0.00001)) } par = optim(c(0, 0, 0), fr)$par a = par[1] b = par[2] c = par[3] curve(parabola, add = TRUE, lty = "dashed") </code></pre> <p>this creates a sample data set and then fits a curve to the boundary. the objective function consists of a "normal" squared error term, which fits a parabola to the data as well as a second logistic term which penalizes points which live below the parabola. the parameters (100 and 0.00001) of this second term were determined by trial and error.</p> <p>the code plots the points as well as the fitted parabola.</p> <p>now this system works... but only some of the time. sometimes it produces a fit that is completely wrong and i guess that in these instances the parameters for the logistic term are just inappropriate. run the code a few times to see what i mean.</p> <p>i am sure that there must be a more robust way of solving this problem. ideas and suggestions?</p> <p>.</p>
    singulars
    1. PO
      singulars
      1. PTAnswer
    1. This table or related slice is empty.
    1. PTQuestion
    1. USmnel
    1. USDataWookie
    plurals
    1. This table or related slice is empty.
    1. This table or related slice is empty.
    1. This table or related slice is empty.
    1. PO
      singulars
      1. PTAnswer
    2. PO
      singulars
      1. PTAnswer
    1. VO
      singulars
      1. POFitting a curve "around" data points in R
      1. This table or related slice is empty.
      1. VTUpMod
    2. VO
      singulars
      1. POFitting a curve "around" data points in R
      1. This table or related slice is empty.
      1. VTUpMod
    3. VO
      singulars
      1. POFitting a curve "around" data points in R
      1. This table or related slice is empty.
      1. VTUpMod
    1. COThe default algorithm in `optim` isn't very good. Try specifying `method="BFGS"` or `method="L-BFGS-B"`.
      singulars
      1. POFitting a curve "around" data points in R
      1. USHong Ooi
    2. COSet the random number seed to get a reproducible example of your problem. If I do `set.seed(999)` and run your code, is that an example of a wrong fit? Gives us something to work with! In this case, `method="BFGS"` produces a much better fit...
      singulars
      1. POFitting a curve "around" data points in R
      1. USSpacedman
    3. COyes, precisely: with a seed of 999 it fails but with a seed of 1 it works fine.
      singulars
      1. POFitting a curve "around" data points in R
      1. USDataWookie
 

Querying!

 
Guidance
A row detail

Detail views are divided into sections. All the information in the data section comes from columns in the selected row. The other sections display data from other, related rows.

Related data can be related in a to-one or a to-many fashion. Captions of data related in a to-many fashion link to a list view showing a filtered view of the table.

Try moving around until you find a non-empty to-many entry and click on the label to get to one. You can move back to the root by clicking on the database name in the header.

SQuiL has stopped working due to an internal error.

If you are curious you may find further information in the browser console, which is accessible through the devtools (F12).

Reload