How to remove outliers from a linear fit?

Hi all!

I have points P(xi,yi)and the linear fit y=ax+b. I want to remove the maximum outlier from the linear fit and I will do a new linear fit. Then to remove the maximum outlier and a new linear fit and so on, until I have the 50% of points P(xi,yi). Any ideas?

Thank you!

Answer 1

[Star Strider]

My idea:

x = 1:100;                                                      % Create Data
y = randi(99, 1, 100);                                          % Create Data
nr_pts_to_remove = fix(length(x)/2);
for k1 = 1:nr_pts_to_remove
    dm = [ones(size(x(:))) x(:)];                               % Design Matrix
    b = dm\y(:);                                                % Estimate Parameters
    yfit = dm*b;                                                % Fit Data
    [~,idx] = max(abs(y(:) - yfit));                            % Index Of Maximum Residual
    x(idx) = [];                                                % Remove Maximum ‘x’
    y(idx) = [];                                                % Remove Maximum ‘y’
end

xv = linspace(min(x), max(x));                                  % Create Vectors For Plot
yv = [ones(size(xv(:))) xv(:)]*b;                               % Create Vectors For Plot

figure(1)
plot(x, y, 'pg', 'MarkerFaceColor','g')
hold on
plot(xv, yv, '-r')
hold off
grid

The ‘(:)’ creates column vectors for all data and other variables.

[Thar]

I agree with it. I need also to save as .fig all the figures and the first figure with all points (100).

Thank you!

[Image Analyst]

Just an FYI, Thodoris: have you seen or heard about RANSAC? https://en.wikipedia.org/wiki/Random_sample_consensus

[Star Strider]

@Thodoris —

My pleasure!

Image Analyst’s observation is certainly worth considering.

To save your figures as a ‘.fig’ file use the savefig function. This also saves all your data and all the figure, axis, line, and other properties so that they can be retrieved later. The disadvantage is that you have to have MATLAB open to load and read them.

If you only want to save the image of the plot itself, the easiest way is to use the ‘File’—>‘Save’ on the menu (or the floppy disk icon in the toolbar) in the plot figure window, and the best format is PNG. The advantage is that any image reader can display them. The disadvantage is that they do not contain any information about the data or figure properties that produced them.

Another option is to use the print function to save the image (without the other data) as a file, or print it out on a printer. (I’ve not used print in a while.)

[Thar]

Hi!

I need all properties of the figures, so I must save them as .fig. I use the function savefig but for one graph. I need to save more graphs.

[Star Strider]

I am not certain what you intend by ‘I need to save more graphs.’ If you need to plot several plots in the same figure and then save the figure, use the subplot function to plot them, then savefig as with the others.

[Thar]

I mean that i have a loop and gave me 22 graphs. I want to save it automatic and not one by one. The function savefig save the first graph only.

Thank you!

[Star Strider]

If you plot them with subplot, it should save all of them as the same figure. It would be crowded to look at, but all the information would be available.

[Thar]

I want to save them in different figures. I wrote savefig('graphk1.fig'),but save the first graph only.

[Star Strider]

You have two options, to save them all in the same file:

H(1) = figure(1)
plot( . . . )
    . . .
H(22) = figure(22)
plot( . . . )

savefig(H,'graphk.fig')

or to save every figure individually:

savefig('graphk01.fig')
savefig('graphk02.fig')
       . . .
savefig('graphk22.fig')

I would save them all in the same file (the first option). See the documentation for savefig for details. The documentation says it was ‘Introduced in R2013b’, so if you have that or a later version, you should be able to do this.