what kind of plot is useful for comparing two matrices?

I have two 5*5 matrices. I want to use a plot to show that they are close element-wise.

What plot is suitable?

I think the plot should be transparent.

It is of course doable if we reshape the matrices into vectors, and use a 2d plot. But that is not intuitive.

Answer 1

[Star Strider]

I am not certain that there is any built-in functtion for this sort of problem.

One approach —

M1 = randn(5)

M1 = 5x5

1.0335 0.3537 0.1255 0.0657 0.1121 -1.0280 0.0115 -0.0957 -0.4548 -0.6092 0.1566 0.3970 1.2606 -0.1277 -0.1152 -1.2395 -0.4992 -0.2599 0.6389 -0.0945 -0.4119 -0.1545 0.6857 -3.2695 0.0717

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M2 = M1 + randn(5)/10

M2 = 5x5

1.0987 0.3445 0.0749 -0.0346 0.0453 -0.9348 -0.1396 -0.2144 -0.2877 -0.6895 0.2739 0.4181 1.3805 -0.1310 -0.1254 -1.3055 -0.5989 -0.3736 0.6637 -0.0121 -0.3835 -0.3049 0.7109 -3.2123 0.2489

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Mcomp = sqrt((M1-M2).^2/numel(M1));

ms = fitdist(Mcomp(:),'lognormal')

ms = 
  LognormalDistribution

  Lognormal distribution
       mu = -4.47506   [-4.8949, -4.05523]
    sigma =  1.01709   [0.794171, 1.41492]

lognparms = @(mu,sigma) [exp(mu + sigma^2/2); exp(2*mu + sigma^2) * (exp(sigma^2)-1); sqrt(exp(2*mu + sigma^2) * (exp(sigma^2)-1))];    % [mean; var; std]
lnparms = lognparms(ms.mu, ms.sigma);
fprintf(1,'\nMean = %.6f\nVar  = %.6f\nStDv = %.6f\n',lnparms)

Mean = 0.019105
Var  = 0.000662
StDv = 0.025728

[X,Y] = meshgrid(1:5);

figure
stem3(Mcomp)
hold on
scatter3(X(:), Y(:), Mcomp(:), 50, Mcomp(:), 'filled')
patch([xlim flip(xlim)], [1 1 5 5], ones(1,4)*lnparms(1), 'k', 'FaceAlpha',0.25, 'EdgeColor','none')
hold off
colormap(turbo)
colorbar
axis('padded')
zlabel(["‘Mcomp’ Values For Each" "Comparison Matrix Element"])

The comparison value ‘Mcomp’ is a ‘sort of’ root-mean-square value. (It can be anything, providing it returns a matrix equal to the original matrices.) Since the ‘Mcomp’ calculation I chose can never be negative (and would likely be strictly positive, so non-zero as well), I chose the lognormal distribution to calculate its parameters. If you choose a different calculation, choose an appropriate distribution if you want to calculate its parameters. The gray patch is the mean of the ‘Mcomp’ values, as calculated from the lognormal distribution parameters.

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[min lee]

This is very fancy. However, first of all, I want to display the matrices, not just the difference.

[Image Analyst]

You can use imshow. Did you even see my answer below? You got two answers you know.

[Star Strider]

I am not certain what you want to display.

Again using the stem3 and scatter3 plots, perhaps something like this —

M1 = randn(5)

M1 = 5x5

0.8335 -0.2427 0.3680 0.1094 0.1555 -0.1843 1.0874 0.4701 -2.5072 -0.8886 -1.3167 -0.1393 1.2380 0.4200 0.9833 -0.2696 -1.4628 -0.0306 1.1420 1.0060 0.6801 1.2758 1.2581 0.5490 1.3376

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M2 = M1 + randn(5)/10

M2 = 5x5

0.7674 -0.0564 0.3669 -0.0045 0.2466 -0.1661 0.9544 0.4437 -2.3242 -0.9988 -1.3776 0.0203 1.2589 0.3516 0.9044 -0.4236 -1.5446 -0.1221 1.1511 1.0160 0.7621 1.4024 1.3415 0.4807 1.2261

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[X,Y] = meshgrid(1:5);

figure
stem3(M1,'b')
hold on
hs3(1) = scatter3(X(:), Y(:), M1(:), 'r', 'filled', 'DisplayName','Matrix 1');
stem3(M2,'b')
hs3(2) = scatter3(X(:), Y(:), M2(:), 'g', 'filled', 'DisplayName','Matrix 2');
patch([xlim flip(xlim)], [1 1 5 5], zeros(1,4), 'k', 'FaceAlpha',0.25, 'EdgeColor','none')
hold off
axis('padded')
legend(hs3, 'Location','best')

I am not certain what your matrices are, however if you want to display the differences between them, and you do not want the differences themselves calculated, this would appear to work.

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[min lee]

Ah, I think this is what I want! Thank you very much!

[Star Strider]

My pleasure!

Answer 2

[Image Analyst]

Why a plot and not a 2-D image showing differences? What would your x axis represent?

If you treat your matrix as an image there are lots of ways to compare images. For example imabsdiff, immse, psnr, etc. For example you could use imabsdiff and color code the magnitude of the differences in an image, or you could count the number of matches and mismatches. You could also make a histogram of the differences - that's a plot.

immse and psnr give single numbers gauging how close the matrices are to each other.

Here's some code

% Create two matrices
m1 = uint8(randi(255, 5, 5))

m1 = 5x5

2 151 230 193 31 188 128 17 133 172 84 164 69 28 168 30 162 145 124 116 190 220 77 212 194

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m2 = uint8(randi(255, 5, 5))

m2 = 5x5

97 14 248 53 201 225 50 103 219 151 12 24 155 251 182 57 240 80 181 76 254 201 58 19 92

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% Compute difference.
diffMatrix = imabsdiff(m1, m2)

diffMatrix = 5x5

95 137 18 140 170 37 78 86 86 21 72 140 86 223 14 27 78 65 57 40 64 19 19 193 102

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% Display m1
subplot(2, 2, 1);
imshow(m1)
title('m1');
% Display m2
subplot(2, 2, 2);
imshow(m2)
title('m2');
% Display diffMatrix
p3 = subplot(2, 2, 3);
imshow(diffMatrix)
title('diffMatrix');
colorbar(p3)
colormap(p3, 'turbo')