Tek-Tips is the largest IT community on the Internet today!

Members share and learn making Tek-Tips Forums the best source of peer-reviewed technical information on the Internet!

Register Log in
  • Congratulations TugboatEng on being selected by the Eng-Tips community for having the most helpful posts in the forums last week. Way to Go!

Breaking a 2d cloud of data points into straight line segments

Status
Not open for further replies.
GregLocock

GregLocock

Automotive
Joined
Apr 10, 2001
Messages
23,892
Location
Orbiting a small yellow star
I recently found a couple of ways of doing this. They are not automatic, and i suspect they need some judgement in their use.

The first is from Matlab
and the second is the very neat SLM curve fitting toolbox
When i get matlab back then I'll be using these.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376
 
Here's a rather splendid piece of code that does most of what I need. That is, for a given set of knots in x0 it generates contiguous best fit straight lines for the x and y vectors. The result, p, is the y at the defined x0. What it doesn't do is measure the error, or attempt to move the knots to reduce the overall error. That of course, is what i need.

Code: 
function p = fitPiecewiseLinearFunction(x, y, x0)
%
% Fit a piecewise continuous function f(x) to the pairs of data points (x,y)
% such that the sum of squares of error is minimal.
%
% x0 - values of x that define ends of segments of function f(x)
%
% p - end points of the segments p = f(x0)
%  
% See also: [URL unfurl="true"]http://golovchenko.org/docs/ContinuousPiecewiseLinearFit.pdf[/URL]
%
% 4-May-2004 Nikolai Golovchenko.
%


numberOfParameters = length(x0);

% separate data in segments
j = {};
for i = 1 : numberOfParameters - 1
   j{i} = find(x > x0(i) & x <= x0(i + 1));
   
   if isempty(j{i})
      error('Insufficient amount of data points');
   end
   
end

% compute the matrices corresponding to the
% system of equations
A = zeros(numberOfParameters, numberOfParameters);
B = zeros(numberOfParameters, 1);

for i = 1:numberOfParameters
   if i ~= 1
      % first sum
      A(i, i-1) = A(i, i-1) - ...
         sum((x(j{i-1}) - x0(i-1)) .* (x(j{i-1}) - x0(i))) / (x0(i) - x0(i-1)) .^ 2;
      A(i, i) = A(i, i) + ...
         sum((x(j{i-1}) - x0(i-1)) .^ 2) / (x0(i) - x0(i-1)) .^ 2;
      
      B(i) = B(i) + ...
         (sum(x(j{i-1}) .* y(j{i-1})) - x0(i-1) * sum(y(j{i-1}))) / (x0(i) - x0(i-1));
   end
   if i ~= numberOfParameters
      % second sum
      A(i, i) = A(i, i) + ...
         sum((x(j{i}) - x0(i+1)) .^ 2) / (x0(i+1) - x0(i)) .^ 2;
      A(i, i+1) = A(i, i+1) - ...
         sum((x(j{i}) - x0(i)) .* (x(j{i}) - x0(i+1))) / (x0(i+1) - x0(i)) .^ 2;
      
      B(i) = B(i) + ...
         (-sum(x(j{i}) .* y(j{i})) + x0(i+1) * sum(y(j{i}))) / (x0(i+1) - x0(i));
   end
end


% find the parameters
p = A^-1 * B;

The black line is an eyeballed set of knots for the blue data. The circles are 11 year moving averages and the orange line is just a linear regression.

golov_f18vms.jpg



I looked at two built in functions. 'splinefit' tries to equalise the segment lengths. 'polyfit' doesn't guarantee that the lines are contiguous at the knots.

Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376
 
Try this. You can try several numbers of specified joints, and pick the 'Best' number based on rms error.

x=1:100;
y(1:25) = 0+rand(25,1);
y(26:50) = 1+rand(25,1);
y(51:75) = 2+rand(25,1);
y(76:100)= -1+rand(25,1);
figure
plot(x,y,'r.')
hold on

sp3=spap2(3,2,x,y) % 3 joints, 1st order( use a 2 for 1st order )
fnplt(sp3,'m')
 
 https://files.engineering.com/getfile.aspx?folder=20b527e5-015a-4ea2-89e6-7889d52fc5ea&file=Smoking_3_joints.JPG
Looks like elements derived from the Sunspot Cycle.
 
I should add I've got a rather horrible script that plots the error vs the number of knots and tries to optimise their location. it doesn't work very well






Cheers

Greg Locock


New here? Try reading these, they might help FAQ731-376
 
Settle on the number of knots the science seems to suggest, apply lsqcurvefit (Matlab) to the knot locations and turn the crank. I picked 11. Once you get the first solution, bootstrap it by perturbing the lsqcurvefit solution and send it back into the fire a few more times. I do this technique with Pacejka tire model fits and it works very well.
 
 https://files.engineering.com/getfile.aspx?folder=5231943f-49b1-4fde-893e-07c348f2b619&file=Knots_Landing.JPG
Status
Not open for further replies.

Similar threads

T
  • Locked
How do I change a measurment unit in a Simscape custom block?
Replies
0
Views
2K
tamsou
T
AitorKo
  • Locked
  • Question Question
Work in Matlab with a reduced model in Abaqus
Replies
1
Views
2K
GVDR
G
Arash Nasiri
  • Locked
  • Question Question
importing a prepared mesh (FEM) into Matlab
Replies
1
Views
981
Mohanlal0488
Mohanlal0488
udlondy
  • Locked
  • Question Question
How do I model cloud security in Matlab/Simulink
Replies
1
Views
243
IRstuff
IRstuff
TEIF-RO
  • Locked
  • Question Question
How to do a reccurent substitution in a symbolic matrix in matlab withor the ''FOR'' loop?
Replies
4
Views
1K
GregLocock
GregLocock

Part and Inventory Search

Sponsor

Back
Top