# unevenly spaced data

Suppose I have a (very large) noisy data set of points $(x_i, y_i)$ and I want to smooth it. Mathematica seems to have a number of smoothing schemes (EstimatedBackground[], ListConvolve[], etc) but they all seem to have the underlying assumption that the data is sampled at regular intervals (and thus, usually takes a flat list of numbers as input), which is not my case (nor, I suspect, is it the case particularly frequently). Is there some more or less standard way to deal with this?

• But you need some assumption about the underlying relation and the noise. Otherwise your perceived "noise" could be your signal. Oct 6 '14 at 16:17
• @Belisarius Of course. In my case I am doing a computational experiment where I am computing spectral invariants of random (in a certain sense) matrices (so, I have a list of pairs of the form (eigenvalue, some_function_of_eigenvector) of my matrices, which, to make things more annoying, are not precisely the same size. If I do the experiment 1000 times, and compute the mean of my function, and plot it vs the ordinal number of eigenvector, all is well, and the curve is smooth. If I want to plot it against the corresponding eigenvalue, lots of noise. Moving average does sort of work, but... Oct 6 '14 at 16:23
• ... is not clearly the right thing. In any case, there is the actual mathematical/scientific problem, and then there is the functionality provided by mathematica, which seems to not be quite what is needed (of course, I can write my own Gauss convolver, or whatever, but this will be actual work and run slowly, too boot :() Oct 6 '14 at 16:24
• @IgorRivin Can you supply a sample data set or should I experiment on one of my own ? Oct 6 '14 at 16:35
• @Sektor Sure, watch this space for the Dropbox link. Oct 6 '14 at 16:36

Mathematica 10 has new interesting functions for irregularly spaced data like MovingMap

data = RandomReal[1, {1000, 2}];

ListLinePlot[MovingMap[Mean, data, {{0.1}}]]


• Aha! That could be what I am looking for, I will check it out and report! Oct 6 '14 at 19:07
• But wait, this is just a generalized MovingAverage[] Oct 6 '14 at 19:09
• @IgorRivin, what functionality were you expecting? Oct 24 '14 at 19:11
Show[
ListPlot[#,
DataRange -> {0, 6 Pi},
PlotTheme -> "Detailed",
PlotStyle -> PointSize[Tiny]],

ListLinePlot[
MovingMap[Mean, #, {{250}, Center}, 0],
PlotStyle -> {Thick, Blue},
DataRange -> {0, 6 Pi}]] & [Table[Cos[x] + RandomReal[{-1, 1}], {x, 0, 6 Pi, 0.01}]]


• I will try with my data, and report. Oct 6 '14 at 20:19
• On second thought, your data is actually regularly spaced (and so, just like the built-in stuff, you are not using the abscissas...) Oct 6 '14 at 21:04