How to segment a curve into linear and nonlinear pieces
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I have a dataset which looks linear at the beginning (up to ~3.5 along x-axis) and then it shows and upward climb. I want to locate an ideal point uptill where the data is linear at the beginning and fit a line. Thanks a lot. The data is attached (1st column is X and 2nd column is Y).
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Bruno Luong
2023년 7월 19일
linear about 3.5 ? When I zoom in it is not clear where the linear starts. Not 3.5, not 2, may be on the interval (0,1)
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Chunru
2023년 7월 19일
load(websave("DatasetXY.mat", "https://www.mathworks.com/matlabcentral/answers/uploaded_files/1437433/DatasetXY.mat"));
whos
[~, ia] = unique(XY(:, 1)); % remove the duplicated points
XY = XY(ia, :);
plot(XY(:,1), XY(:,2));
gg = gradient(gradient(XY(:, 2), XY(:, 1)), XY(:, 1)); % 2nd derivative
gg = movmedian(gg, 20); % to remove some spikes
hold on;
whos
% ignore some initial points
ip = 20; % 20 points
gg((ip+1):end)
i = find(abs(gg((ip+1):end))>20, 1, 'first'); % 2000 as a threshod (adjust it)
i = ip+i
plot(XY(i,1), XY(i, 2), 'ro');
%xlim([2 3])
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Bruno Luong
2023년 7월 19일
편집: Bruno Luong
2023년 7월 19일
Ths produces kind of "arbitrary" choice of the breakpoint, consider fitting the global curve with few line segments
load(websave("DatasetXY.mat", "https://www.mathworks.com/matlabcentral/answers/uploaded_files/1437433/DatasetXY.mat"));
X=XY(:,1);
Y=XY(:,2);
% FEX https://uk.mathworks.com/matlabcentral/fileexchange/25872-free-knot-spline-approximation
% it takes a dozain of seconds here
pp = BSFK(X,Y,2,[],[],struct('Animation',true))
xbreaks=pp.breaks(2)
ybreaks=ppval(pp,xbreaks)
plot(xbreaks,ybreaks,'or','MarkerSize',15)
댓글 수: 1
Bruno Luong
2023년 7월 19일
If I crop the data up to X <= 4 it finds the break at
xbreaks=2.3085
As I said it's a mmoving target. The data is more or less exponetial everywhere. It is just a question of scaling, totally subjective.
load(websave("DatasetXY.mat", "https://www.mathworks.com/matlabcentral/answers/uploaded_files/1437433/DatasetXY.mat"));
X=XY(:,1);
Y=XY(:,2);
b = X < 4
% FEX https://uk.mathworks.com/matlabcentral/fileexchange/25872-free-knot-spline-approximation
% it takes a dozain of seconds here
pp = BSFK(X(b),Y(b),2,[],[],struct('Animation',true))
xbreaks=pp.breaks(2)
ybreaks=ppval(pp,xbreaks)
plot(xbreaks,ybreaks,'or','MarkerSize',15)
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