How To Create A Persistence Plot

I have quite a large data set that I want to visulaise by overlaying all the traces on one plot, with the traces only using one colour & the opacity/brightness of the resulting trace determined by how many instances of a particular value occur at each point - the only thing I can think to compare it to would be persistence on an old school oscilloscope.

Can someone point me to the correct plot type to achieve this or help me out with some code?

Thanks

[dpb]

Just plot with hold on and selected color to put the points on the screen -- histcounts() will let you bin the observatons by whatever resolution you have to sufficiently have multiple counts; you can set a colormap based on those counts by bin location...

Without trying to make up data...

[DrEamonn]

Thanks dpb

The data is just 1000+ similar but slightly different x^2 type traces. I would like to show the bounds of all the data with some sort of highlighted border, & then the range of the data shaded with areas of common data points denser/more opaque thean areas of less occurance - similar to how pulse info is displayed in the Google Fit app.

[Adam Danz]

An example image would help.

It sounds like you have you have to compute the outter boundaries of the data and then use patch or fill to plot the shape of the data.

[DrEamonn]

This is similar to what I had in mind.

The main difference between the above & what I would like to achieve is that I would like the opacity to vary depending on denisty of values i.e. simialr to an old school oscilloscope display with persistence.

[Adam Danz]

As far as I know you cannot vary the transparency within a patch. However, you can adjust the color (ie, shades of blue) and then set a constant transparency value.

Here's some background info on controlling the color transitions of a patch by setting the CData property of a patch object. You can set a colormap from light blue to dark blue.

https://www.mathworks.com/help/matlab/creating_plots/how-patch-data-relates-to-a-colormap.html

Answer 1

[Star Strider]

Perhaps something like this:

x = linspace(0, 10, 250);                                                                       % Create Data
y = randn(10,1) .* sin(2*pi*x + randn(10,1));                                                   % Create Data

figure
plot(x, y)                                                                                      % Original Waveforms
grid

colMin = min(y);
colMax = max(y);
colMean = mean(y);

figure
plot(x, colMean)                                                                                % Data Mean
hold on
patch([x fliplr(x)], [colMin fliplr(colMax)], 'b', 'FaceAlpha',0.2, 'EdgeColor','none')         % Shaded Range
hold off
grid

producing:

This can likely be changed to show other results.

.

[DrEamonn]

That's sooo close to what I'm looking for.

Is there a way of applying a colormap or contour to the patch based on data density?

[dpb]

Yeah, but you've got to develop a density variable similarly to how I described earlier to use as the variate.

[Star Strider]

Try this:

x = linspace(0, 10, 250);                                                                       % Create Data
y = randn(10,1) .* sin(2*pi*x + randn(10,1));                                                   % Create Data

figure
plot(x, y)                                                                                      % Original Waveforms
grid

colMin = min(y);
colMax = max(y);
colMean = mean(y);
colStd = std(y);
stdMult = (-3:0.5:3);
colData = colMean + stdMult(:)*colStd;

figure                
klen = numel(stdMult);
hold on
for k = 1:size(colData,1)
    FaceAlfa(k) = (1-abs(stdMult(k)/3.1))*0.2;                                                      % Alpha Value For This Face
    vflip = klen-k+1;
    patch([x fliplr(x)], [colData(k,:) fliplr(colData(vflip,:))], 'b', 'FaceAlpha',FaceAlfa(k), 'EdgeColor','none')         % Shaded Range
end
plot(x, colMean,'-r')                                                                           % Data Mean
hold off
grid

producing (for example, since each run is random):

This calculates the standard deviation ‘bands’ (set in ‘stdMult’) and then creates a separate patch object for each one. Here the ‘FaceAlfa’ vector calculates an alpha value for each face, and ‘k’ and ‘vflip’ sets the y-direction boundaries for each face.

.

[DrEamonn]

That's exactly what I was look ing for - thanks Star Strider

[Star Strider]

My pleasure!

If my Answer helped you solve your problem, please Accept it!

.

[dpb]

Nice thought w/ the std, SS. Maybe if used the positions and values could make into a single patch and then use the std array as CData to get the smooth color gradient?

[Star Strider]

I explored that, however it wasn’t obvious to me how to make any colour interpolation scheme (including CData and FaceVertexData) work for this plot. So, I went with what I know, and it appears to work reasonably well.

[dpb]

Ah. If "wasn't obvious" to you, then it certainly isn't to me! I never could much fathom CData anyways; just thought perhaps you hadn't thought to look--but, that is also not a likely event either. :)

[DrEamonn]

I have run some experiements & have a question:

The first plot shows the data plotted using 'plot()'

The second shows the same data plotted using the Start Strider's code:

Why is the highest value on the second plot higher than the first if it is plotted using the same data?

[Star Strider]

‘Why is the highest value on the second plot higher than the first if it is plotted using the same data?’

My code creates the gradients with reference to the standard deviations of the data, going from -3 to +3, corresponding to probabilities of the data being in that range of 0.0013499 to 0.9986501, so a probability of 0.005 that the data will be included within those limits. If you prefer that they have different limits, set ‘stdMult’ to a different range, perhaps using linspace:

stdMult = linspace(-2, 2, 15);

The limits must be symmetrical, and an odd number of elements appears to work best. You can experiment with and design the probabilities using normcdf (that will produce the associated probabilities from the elements of ‘stdMult’) and norminv (that will produce the limits for ‘stdMult’ from the chosen probability).