How to make a heatmap with density of points

Hello!

I have two vectors ( x_vector and y_vector) which correspond with the different points obtained on my simulation. The point is that I want to make a kind of heatmap with the density of the repetition of those points. I have tried with different functions such as imagesc or histogram2, but I didn't get to achieve what I wanted.

Thank you.

Answer 1

[jonas]

See this thread on density plots using hist3 and contourf

https://se.mathworks.com/matlabcentral/answers/409660-can-i-use-contourf-with-two-matrices

[Ángel González]

Thank you, but in this thread they are using matrix instead of vectors (as in my case, which are vectors of 1xN)

[jonas]

Did you try it? The syntax X(:) makes the matrix into a vector, so it works for both.

[Ángel González]

Okey, I tried it and it works. Thank you so much. One more thing, when i plot the histogram..I want all the figure to be coloured, but there are some margins that don't appear that way. Any idea on how to fix this?

[jonas]

Great!

axis tight

should fix it. If not, please upload an image describing the issue.

[Ángel González]

I'll explain with more detail the full issue.

I'm using an eyetracker to get x and y coordinates of where I'm looking at. My goal is to create a heatmap with those coordinates, which I have stored in two vectors (files attached).

My screen is 1920x1080...so I want the axis to have that length fixed. This is the code I'm using to create the heatmap:

figure()
nbins = [60 60];
hist3([x_vector(:), y_vector(:)], nbins, 'CdataMode','auto', 'EdgeColor', 'interp')
axis([0 1920 0 1080]);
xticks([0:240:1920])
yticks([0:135:1080])
set(gca, 'ydir', 'reverse', 'xaxislocation', 'top')

And this is the result I got:

The point is that I would like that space at the bottom of the figure to be filled as well.

Thank you for your help!

[jonas]

Instead of bin amount, you can define the grid, using edges argument

hist3([x_vector(:), y_vector(:)],'CdataMode','auto', 'EdgeColor', 'interp','edges',{linspace(0,1920,nbins(1)) linspace(0,1080,nbins(2))})

I wrote it so that your code still works when you replace the hist3 line. The edges argument is a 1x2 cell array.

Don't forget to try some alternative surface plots. In my opinion they are more visually appealing. Here's a surf with the magma colormap

You just need to specify the output from hist3 and then use that as input to surf, contour, mesh etc...

[N,C]=hist3(...)
surf(C{1},C{2},N)

[Ángel González]

Thank you so much, I'll take a look at those colormaps you linked. But...when I use countourf with the outputs of the hist3 you suggested, there's a new margin unfilled:

[jonas]

You are correct! The surface also extends beyond the axes limits. I havn't noticed this before but it becomes abundantly clear when the bin count is low. This is probably because the output X/Y-data from hist refer to the bin centers, so everything is shifted half a bin width/height to the right/bottom. Add these two lines after [C,N]=hist3(...) to adjust for this:

C{1}=C{1}-min(C{1});
C{2}=C{2}-min(C{2});

[Ángel González]

Yes, that lines fixed the problem, but I have represented the points of the vectors over the heatmap...and I think it is not very accurate:

[jonas]

The hist3 plot looks OK but the surf has been rotated. Try transposing N

surf(C{1},C{2},N')

Sorry for the many bugs :)

This looks quite neat:

contourf(C{1},C{2},N','levelstep',1,'edgecolor','none')
colormap(magma)

[Ángel González]

Hi Jonas! Thank you so much for your help. Everything works fine now. I have a little doubt about how this lines corrected the problem I had:

C{1}=C{1}-min(C{1});
C{2}=C{2}-min(C{2});

I understand that it is to correct the shifting, what I don't understand is why we have to subtract min(C{1})

[jonas]

C{1} describe the x-coordinates and C{2} describe the y-coordinates. I drew a picture to show you the rationale, using a much courser grid so that the offset becomes significantly larger. In short, we move the entire grid so that [min(C{1}) ; min(C{2})] is located at the origin.

[Ángel González]

Ahhhhh okey okey, I didn't know that min(C{2}) meant C{2}(1). I supposed that it would return the minimum value of that array.

Thank you!!

[jonas]

Well you were not incorrect, min(C{2}) does not always equal C{2}(1). However, in this specific case C{2}(1) is the minimum value of C{2}. It works both ways.

Sorry for the confusing code ;)

Answer 2

[Walter Roberson]

https://www.mathworks.com/matlabcentral/answers/224454-creating-a-heatmap-to-visualize-denisity-of-2d-point-data#answer_183261

Or Malcolm's https://www.mathworks.com/matlabcentral/fileexchange/31726-data-density-plot

[Michael King]

Great answer to this question! I'd like to ask a follow up question. Can a number be extracted to indicate the extent of density in a data set? i.e. how focused is a heatmap?

[Walter Roberson]

If you use Malcolm's contribution, then his dataDensity() function calculates those numbers.