How to segment a curve into linear and nonlinear pieces

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Ahmed Zohaib
Ahmed Zohaib 2023-7-19
评论： Bruno Luong 2023-7-19
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).
  2 个评论
Bruno Luong
Bruno Luong 2023-7-19
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)
Ahmed Zohaib
Ahmed Zohaib 2023-7-19
Thanks for the feedback. Okay, how do I locate the exact point where it loses linearity in between [0 1]?

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采纳的回答

Chunru
Chunru 2023-7-19
Ran in:
load(websave("DatasetXY.mat", "https://www.mathworks.com/matlabcentral/answers/uploaded_files/1437433/DatasetXY.mat"));
whos
Name Size Bytes Class Attributes XY 52651x2 842416 double cmdout 1x33 66 char
[~, 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
Name Size Bytes Class Attributes XY 818x2 13088 double cmdout 1x33 66 char gg 818x1 6544 double ia 818x1 6544 double
% ignore some initial points
ip = 20; % 20 points
gg((ip+1):end)
ans = 798×1
0 0 0 0 0 0 0 0 0 0
i = find(abs(gg((ip+1):end))>20, 1, 'first'); % 2000 as a threshod (adjust it)
i = ip+i
i = 301
plot(XY(i,1), XY(i, 2), 'ro');
%xlim([2 3])

更多回答（1 个）

Bruno Luong
Bruno Luong 2023-7-19
编辑：Bruno Luong 2023-7-19
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)
  1 个评论
Bruno Luong
Bruno Luong 2023-7-19
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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