Plot overlapped points (Matlab 2020a)

Hi,

I have a scatter plot (see the picture and code below) comparing the true values with the estimation results from 3 methods. The issue with this plot is that there are many overlapped points, making it hard to see.

My question is: How can we make the overlapped points to be seen? I am using Matlab 2020a. Thank you very much in advance !

Edit: Some suggested reducing the size of the points (Thank you for giving this suggestion). However, I actually do not want to reduce the Linewidth because there will be 4 plots like this one displayed in a figure. Also, I need to show all the points.

min_x = min(true_value(:));
max_x = max(true_value(:));
x = linspace(min_x -1,max_x+1,200);
figure(1)
hold on;

for k = 1:K
    Estimates = mean(methods{k,1}.alpha,3);
    plot(Estimates(:),true_value(:),shape{k},'LineWidth',2.5);
end
set(gca,'fontsize',12) % 
xlabel('Estimates');
ylabel('True values');
legend({'method 1','method 2','method 3',},'Location','northwest','Interpreter',"latex");
plot(x,x,'r--','LineWidth',1,'HandleVisibility','off');
hold off;

Answer 1

[Meg Noah]

Just some ideas:

npts = 200;
true_value = randn(npts,1);
Estimates1 = true_value + 0.01*randn(npts,1);
Estimates2 = true_value + 0.08*randn(npts,1);
Estimates3 = true_value - 0.15*randn(npts,1);

figure()
subplot(2,1,1)
s1 = scatter(Estimates1,true_value,20,'filled','DisplayName','Estimates1');
alpha(s1,0.95);
s1.MarkerFaceColor = '#0072BD';
s1.MarkerEdgeColor = 'None';
hold on
s2 = scatter(Estimates2,true_value,20,'filled','DisplayName','Estimates2');
alpha(s2,0.35);
s2.MarkerFaceColor = '#EDB120';
s2.MarkerEdgeColor = 'None';
s3 = scatter(Estimates3,true_value,20,'filled','DisplayName','Estimates3');
alpha(s3,0.15);
s3.MarkerFaceColor = '#A2142F';
s3.MarkerEdgeColor = 'None';
grid on
legend('location','northwest');
xlim([-4 4]);
ylim([-4 4]);

subplot(2,1,2)
s1 = scatter3(Estimates1,3*ones(npts,1),true_value,'r','filled','SizeData',20);
alpha(s1,0.25);
hold on
s2 = scatter3(Estimates2,2*ones(npts,1),true_value,'y','filled','SizeData',20);
alpha(s2,0.25);
s3 = scatter3(Estimates3,1*ones(npts,1),true_value,'b','filled','SizeData',20);
alpha(s3,0.25);
grid on
xlim([-4 4]);
ylim([0 4]);
zlim([-4 4]);

[Hung Dao]

Thank you so much ! This is exactly what I am looking for.

Answer 2

[Sulaymon Eshkabilov]

Use smaller line width within the loop, e.g.:

...
plot(Estimates(:),true_value(:),shape{k},'LineWidth',1.25);
...

[Hung Dao]

Thank you for your suggestion. Is it possible to not reducing the linewidth?

Answer 3

[Image Analyst]

You probably don't need to plot so many points to get an idea of what's going on. Pick a subset of them, like 10 perent of the points or something. And reduce the LineWidth;

pct = 10;
numPointsToDisplay = round(pct * length(Estimates) / 100);
randomIndexes = randperm(length(Estimates), numPointsToDisplay);
plot(Estimates(randomIndexes), true_value(randomIndexes), shape{k}, 'LineWidth', 1);

[Hung Dao]

Thank you for the suggestion, but I actually do not want to reduce the linewidth because it would be too small to see, especially there will be 4 subplots like this one. Also, I need to show all the points.

[Image Analyst]

If the line width is too big, many of the later-plotted markers will overlap and totally obscure the underlying markers so you won't see them anyway. Just look at your plot. The upper layer is just a solid mass of yellow. You're not seeing individual points, if that's what you (incorrectly) think.