Minimize distance between curves

2 Ansichten (letzte 30 Tage)
Deepa Maheshvare
Deepa Maheshvare am 4 Jul. 2022
I have a dataset with values of multiple curves. An example plot is shown below. I want to scale the curves so that all curves overlap or get closer to the target curve. The following is the plot of a sample dataset
I want to scale the function values in the curves so that all curves overlap. Say, green curve is the target (g) and I want to move the other curves (f) towards target curve by scaling (scale facotor is a).
The function that I want to minimize is:
Expected result:
Data:
data = {{{157, 60}, {140, 57}, {121, 52}, {103, 47}, {86, 39}, {67, 28}, {50,21}, {32, 15}}, {{159, 70}, {140, 67}, {122, 63}, {105, 58}, {85, 45}, {68, 42}, {50, 34}, {33, 29}}, {{157, 74}, {140, 71}, {121, 70}, {105, 65}, {86, 55}, {69, 52}, {52, 43}, {32, 37}}, {{158, 100}, {141, 100}, {123, 95}, {105, 90}, {88, 78}, {69, 72}, {51, 57}, {33, 46}}, {{160, 143}, {140, 146}, {123, 146}, {105, 145}, {86, 136}, {70, 121}, {51, 97}, {34, 60}}}
Could someone please help me with the function that has to be used for solving this problem in MATLAB ?

Akzeptierte Antwort

Torsten
Torsten am 4 Jul. 2022
Bearbeitet: Torsten am 4 Jul. 2022
Differentiating with respect to a, setting the derivative to 0 and solving for "a" gives
a = sum_i (f_i*g_i) / sum_i (f_i^2)
I leave it to you to insert the data points.
  3 Kommentare
Torsten
Torsten am 6 Jul. 2022
Bearbeitet: Torsten am 6 Jul. 2022
What is the "absolute error" ?
sum_i abs(a*f_i - g_i)
?
If this is the case, use "linprog" to solve
min: sum_i u_i
s.c.
f_i * a - u_i <= g_i
-f_i * a - u_i <= -g_i
with unknowns a and u_i (i=1,...,number of data points).
Deepa Maheshvare
Deepa Maheshvare am 7 Jul. 2022
Thanks so much. Yes, I mean sum_i abs(a*f_i - g_i)
% Loss Function (absolute error loss)
%% input curves
scale = 1.5;
x1 = [0,4,6,10,15,20]*scale;
y1 = [18,17.5,13,12,8,10];
x2 = [0,10.5,28]*scale;
y2= [18.2,10.6,10.3];
%% y2 is the target function and y1 is the function to be shifted
f = y1;
g = interp1(x2,y2,x1);
%% linprog inputs
% x = linprog(f,A,b)
% i = 1:length(x1)
A = [fi - 1; -fi -1];
x = [a ui];
b = [gi -gi];
% obj = sum_i u_i (function to minimize)
%% solve system
I am not sure how to set this up in MATLAB's linprog
Could you please help?

Melden Sie sich an, um zu kommentieren.

Weitere Antworten (0)

Kategorien

Mehr zu Get Started with Curve Fitting Toolbox finden Sie in Help Center und File Exchange

Produkte


Version

R2021a

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by