Set marker alpha transparency based on point density for scatter plot

Hi everyone,

I am using a custom function to calculate the density of point for a scatter plot based on the bin size. Below is the example of the plot generated by the code.

In the above code, the color is set such that point around the center of bin with high point density will be colored brownm, and the lower desity will be blue. The point in the bithween will be colored in accordance to the heatmap gradiente.

Problem:

1. Similarly to setting the color as a function fo the point density, I would like to set the alpha trasnparency of the marker edges and faces based on the point density. So the plot would like somewhat like below. Basically, what I want to accomplishe is that as the marker color gravitates towards the blue color, I would like to the decrease the transparency level of the marker, at the same time that the marker taht are Brown will be 100% opaque. So, simply put, I would like to change the 'MarkerEdgeAlpha' as a function of the point count density.

2. Change point cound density to relative frequency. Below is a figure where this is exemplified (Source Fig. 2 in Nature Paper).

Following is my script, which contain the in file function. This is a modification of the file prepared by @Lukas and shared at Original File.

clear all
close all
function outfile = heatscatter(X, Y, outpath, outname, numbins, markersize, marker, plot_colorbar, plot_lsf, xlab, ylab, title)

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%% heatscatter(X, Y, outpath, outname, numbins, markersize, marker, plot_colorbar, plot_lsf, xlab, ylab, title)
% mandatory:
%            X                  [x,1] array containing variable X
%            Y                  [y,1] array containing variable Y
%            outpath            path where the output-file should be saved.
%                                leave blank for current working directory
%            outname            name of the output-file. if outname contains
%                                filetype (e.g. png), this type will be used.
%                                Otherwise, a pdf-file will be generated
% optional:
%            numbins            [double], default 50
%                                number if bins used for the
%                                heat3-calculation, thus the coloring
%            markersize         [double], default 10
%                                size of the marker used in the scatter-plot
%            marker             [char], default 'o'
%                                type of the marker used in the scatter-plot
%            plot_colorbar      [double], boolean 0/1, default 1
%                                set whether the colorbar should be plotted
%                                or not
%            plot_lsf           [double], boolean 0/1, default 1
%                                set whether the least-square-fit line
%                                should be plotted or not (together with
%                                the correlation/p-value of the data
%            xlab               [char], default ''
%                                lable for the x-axis
%            ylab               [char], default ''
%                                lable for the y-axis
%            title              [char], default ''
%                                title of the figure
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

    %%%% mandatory
    if ~exist('X','var') || isempty(X)
        error('Param X is mandatory! --> EXIT!');
    end
    if ~exist('Y','var') || isempty(Y)
        error('Param Y is mandatory! --> EXIT!');
    end
    if ~exist('outpath','var')
        error('Param outpath is mandatory! --> EXIT!');
    end
    if ~exist('outname','var') || isempty(outname)
        error('Param outname is mandatory! --> EXIT!');
    end
    
    %%%% optional
    if ~exist('numbins','var') || isempty(numbins)
        numbins = 50;
    else
        % force number, not char input
        numbins = str2double(numbins);
    end
    if ~exist('markersize','var') || isempty(markersize)
        markersize = 10;
    else
        % force number, not char input
        markersize = str2double(markersize);
    end
    if ~exist('marker','var') || isempty(marker)
        marker = 'o';
    end
    if ~exist('plot_colorbar','var') || isempty(plot_colorbar)
        plot_colorbar = 1;
    end
    if ~exist('plot_lsf','var') || isempty(plot_lsf)
        plot_lsf = 1;
    end
    if ~exist('xlab','var') || isempty(xlab)
        xlab = '';
    end
    if ~exist('ylab','var') || isempty(ylab)
        ylab = '';
    end
    if ~exist('title','var') || isempty(title)
        title = '';
    end
    
    [values, centers] = hist3([X Y], [numbins numbins]);

    centers_X = centers{1,1};
    centers_Y = centers{1,2};

    binsize_X = abs(centers_X(2) - centers_X(1)) / 2;
    binsize_Y = abs(centers_Y(2) - centers_Y(1)) / 2;
    bins_X = zeros(numbins, 2);
    bins_Y = zeros(numbins, 2);

    for i = 1:numbins
        bins_X(i, 1) = centers_X(i) - binsize_X;
        bins_X(i, 2) = centers_X(i) + binsize_X;
        bins_Y(i, 1) = centers_Y(i) - binsize_Y;
        bins_Y(i, 2) = centers_Y(i) + binsize_Y;
    end

    scatter_COL = zeros(length(X), 1);

    onepercent = round(length(X) / 100);
    
    for i = 1:length(X)

        if (mod(i,onepercent) == 0)
            fprintf('.');
        end            

        last_lower_X = NaN;
        last_higher_X = NaN;
        id_X = NaN;

        c_X = X(i);
        last_lower_X = find(c_X >= bins_X(:,1));
        if (~isempty(last_lower_X))
            last_lower_X = last_lower_X(end);
        else
            last_higher_X = find(c_X <= bins_X(:,2));
            if (~isempty(last_higher_X))
                last_higher_X = last_higher_X(1);
            end
        end
        if (~isnan(last_lower_X))
            id_X = last_lower_X;
        else
            if (~isnan(last_higher_X))
                id_X = last_higher_X;
            end
        end

        last_lower_Y = NaN;
        last_higher_Y = NaN;
        id_Y = NaN;

        c_Y = Y(i);
        last_lower_Y = find(c_Y >= bins_Y(:,1));
        if (~isempty(last_lower_Y))
            last_lower_Y = last_lower_Y(end);
        else
            last_higher_Y = find(c_Y <= bins_Y(:,2));
            if (~isempty(last_higher_Y))
                last_higher_Y = last_higher_Y(1);
            end
        end
        if (~isnan(last_lower_Y))
            id_Y = last_lower_Y;
        else
            if (~isnan(last_higher_Y))
                id_Y = last_higher_Y;
            end
        end

        scatter_COL(i) = values(id_X, id_Y);
        alpha_COL(i) = sqrt(values(id_X)^2+values(id_Y)^2);
    
    end

    f = figure();
    sct=scatter(X, Y, markersize, scatter_COL,"filled");

    if (plot_colorbar)
        colorbar;
    end
    
    if (plot_lsf)
        [r,p] = corr(X, Y);
        str = {sprintf('corr: %.3f', r), sprintf('pval: %d', p)};
        l = lsline;
        set(l, 'Color', 'k');
        annotation('textbox', [0.14 0.80 0.1 0.1], 'String', str, 'EdgeColor', 'none');
    end
    
    if (~isempty(xlab))
        xlabel(xlab);
    end
    if (~isempty(ylab))
        ylabel(ylab);
    end
    if (~isempty(title))
        title(title);
    end
    
    [p,n,r] = fileparts(outname);
    if (isempty(r))
        r = '';
    end
    set(gca,'FontSize',12,'fontname','Samsung Sans','color','w')
    outname = strcat(p,n,r);
    f.Position = [100 100 400 400];
    set(gcf, 'PaperSize', [2 4]);
    set(gcf,'windowstyle','docked') % or use a specific fig handle
    colormap jet(64)
    cb = colorbar;
    cb.Label.String = 'Density by Point Count';
    cb.FontName = 'Samsung Sans';
    cb.Label.FontSize = 12;

    figname = [num2str(outname) 'Oscilogram.jpg'];
    exportgraphics(f,figname,'Resolution',600);

    outfile = fullfile(outpath, outname);
    % saveas(f, outfile);
end

X1=randn(10000,1);
X2=randn(10000,1);
X3=randn(10000,1);
X=X1.^2+X2.*X3;
Y=randn(10000,1);

numbinss=80;

f=heatscatter(X,Y,"C:\",'X-Y Scatter Variable Alpha',num2str(numbinss),'15','o',1,0,'X-axis','Y-axis');

Please let me know if more clarification is required and I will be happy to provide.

Thank you so much for the help.

Answer 1

[Tony]

Not sure about changing marker transparency, but an indirect way is to change the 'lightness' of the marker color

c_max = [0 0 1];
LIGHTNESS_MAX = 0.9; % 1 will be white, and potentially hard to see
pt_values = 0:0.1:1;
pt_min = min(pt_values);
pt_max = max(pt_values);
pt_colours = 1 - (1 - LIGHTNESS_MAX * (pt_max - pt_values') / (pt_max - pt_min)) * (1 - c_max); % range of base color with lightness varying from base color to max lightness parameter
figure(); hold on;
for i = 1:numel(pt_values)
    plot(pt_values(i), pt_values(i), 'Color', pt_colours(i,:), 'Marker', '.', 'MarkerSize', 16);
end

[Emanuel Santos]

Hi Tony, thank you for your input. I am not being able to translate that into my scatter plot. Still strugling to get it as I would like.