Heat map of 2-D scatter plot data

I have a n by 2 matrix called new_data, and I want to make a heat map plotting density of scatter distribution.

I want to add values varying from 0 to 1 to another array called z that has size of (xmax-xmin,ymax-ymin) in which value of 1 would be added to the z component that matches x and y coordinate and add values less than 1 as the distance from the coordinates increase (kind of like dropping ink on paper, and less ink with increasing distance from epicenter).

Here's my code til now:

x = new_data(:,1);
    y = new_data(:,2);
    z = zeros(round(max(x)) - round(min(x)), round(max(y)) - round(min(y)));
    for i = 1:size(new_data,1);
        x(i) = x(i) - min(x);
        y(i) = y(i) - min(y);
    end
    for i = 1:size(new_data,1);
        z(round(x(i)),round(y(i))) = z(round(x(i)),round(y(i))) + 1;
    end

Could anyone help me with this Gaussian value addition or provide any other ideas for plotting scatter density?

[per isakson]

See File Exchange

• heat map
• treemap

Answer 1

[Walter Roberson]

      for i = 1:size(new_data,1);
        d = sqrt((x(i) - round(x(i))).^2 + (y(i) - round(y(i)).^2);   %distance
        deltaz = exp(-d);   %gets exponentially less with increasing distance
        z(round(x(i)),round(y(i))) = z(round(x(i)),round(y(i))) + deltaz;
    end

[Kenny Kim]

I tried a modification of your code and it seems to work, except that my new_data has 27000 rows and thus would require 13 hours or more to process it. Changing x to x1 has nothing to do with this.

for i = 1:size(new_data,1);
        for j = 1:size(z,1);
            for k = 1:size(z,2);
            d = sqrt((j - x1(i)).^2 + (k - y1(i)).^2);   %distance
            if d <= 20
                deltaz = exp(-d);   %gets exponentially less with increasing distance
                z(j,k) = z(j,k) + deltaz;
            end
            end
        end
    end

[Walter Roberson]

Vectorize, Vectorize, Vectorize!

ndrow = size(new_data,1);
zrow = size(z,1);
zcol = size(z,2);
zcolvec = 1 : zcol;
for i = 1 : ndrow;
  x1i = x1(i);
  y1i = y1(i);
  for j = 1 : zrow;
    jdist2 = (j-x1i).^2;
    d = sqrt(jdist2 + (zcolvec - y1i).^2);
    deltaz = exp(-d);
    dinrange = d <= 20;
    z(j, dinrange) = z(j,dinrange) + deltaz(dinrange);
  end
end

Answer 2

[Image Analyst]

If you have the Image Processing Toolbox, perhaps one way is to use the distance transform:

numPoints = 30;
x = rand(1,numPoints);
y = rand(1, numPoints);
rows = 240;
columns = 320;
binaryImage = false(rows, columns);
for k = 1 : length(x);
  r = ceil(rows * y(k));
  c = ceil(columns * x(k));
  binaryImage(r, c) = true;
end
imshow(binaryImage);
edm = bwdist(binaryImage);
edmMax = max(edm(:));
edm = edmMax - edm;
imshow(edm, []);
colormap(hot(256));
colorbar;
hold on;
scatter(columns * x, rows * y, '*')