Data Normalization

Question

I am having trouble selecting certain region from the data. I have data such that,

where A and B are the transparent region.

I want to normalize data by setting these transparent regions to 1, so I want to first fit the linear function f[x] by using data from region A and B such that

If I can find the function, then it is easy to normalize the data,

Table[data2[[i]]/f[i],{i,1,Length[data2]}].

However, it is hard to select the date in arbitrary transparent region. Any one can give me any idea to find this region?

Thank you!

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Julien Kluge · Accepted Answer · 2016-09-29 21:55:35Z

I would say, you would be the best to detect such regions and select them manually but hey, thats not so much fun so lets try:

A straightforward (and sadly good way) is it to select the datapoints within a thereshold of the maximum. I've choosen 5% and got that:

thereshold=0.95;
maxData=thereshold*Max[data];
pData=DeleteCases[Table[If[maxData<data[[i]],{i,data[[i]]},Null],{i,1,Length[data]}],Null];
fit=LinearModelFit[pData,{1,x},x];
Show[ListPlot[data],Plot[fit["BestFit"],{x,0,2000},PlotStyle->Blue],ListPlot[pData,PlotStyle->Black]]

Another approach is a little more difficult. We smoothing out the data with a GaussianFilter. Then we select all points, where the neighborhood is only a special thereshold away in total difference to our startpoint. Sadly the result is a little bit more innacurate imo.

l=10;
smoothData=GaussianFilter[data,4l];
s=Flatten[DeleteCases[Reap[If[Total@Abs@Differences[smoothData[[#;;#+l]]]<0.0002,Sow[{#,smoothData[[#]]}]]&/@Range[1,Length[smoothData]-l]][[2]],Null],1];
fit=LinearModelFit[s,{1,x},x];
Show[ListPlot[data,ImageSize->Medium],Plot[fit["BestFit"],{x,0,2000},PlotStyle->Blue],ListPlot[s,PlotStyle->Black]]

Interesting task nevertheless. I'm sure someone better than me, will post a better code though.

Thank you Julien! I think Gaussian Filter will be very useful for me. Thank you for introducing me great code! :D — Saesun Kim, 6 hours ago

mikado · Answer 2 · 2016-09-29 22:25:17Z

up vote 3 down vote

You could try Quantile Regression. The following regresses on the 90% quantile (other choices might be better), that is, it finds a line with 90% of the data below it.

Import["https://raw.githubusercontent.com/antononcube/MathematicaForPrediction/master/QuantileRegression.m"]
fit = QuantileRegressionFit[Transpose[{Range[Length[data2]], data2}], {x, 1}, x, {0.9}]
(* {0.761387 + 0.0000220083 x} *)

ListPlot[{data2, Flatten[fit /. x -> Range[Length[data2]]]}]

answered 6 hours ago

mikado

3,4551220

Thank you for your code! I think I can use this as well! – Saesun Kim 4 hours ago

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