Convex hull / concave hull for multiple clusters in data

Question

I have done a lot of reading on drawing polygons around clusters and realized convhull maybe the best way forward. Basically I am looking for a elastic like polygon to wrap around my cluster points.

My data is matrix consisting of x (1st column) and y(2nd column) points which are grouped in clusters (3rd column). I have 700 such clusters hence not feasible to plot each separately.

Is there a way to perform convhull for each cluster separately and then plot each of them on a single chart.

EDIT

Code I have written until now which isn't able to run convex hull on each individual cluster...

    [ndata, text, alldata] =  xlsread(fullfile(source_dir));

       [~, y] = sort(ndata(:,end));
       As = ndata(y,:);

       lon = As(:,1); 
       lat = As(:,2);
       cluster = As(:,3);

       %% To find number of points in a cluster (repetitions)
   rep = zeros(size(cluster));

   for j = 1:length(cluster)
       rep(j) = sum(cluster==cluster(j));
   end

   %% Less than 3 points in a cluster are filtered out

   x = lon (rep>3);
   y = lat (rep>3);
   z = cluster (rep>3);

   %% convex hull for each cluster plotted ....hold....then display all.

   figure
   hold on

   clusters = unique(z);

       for i = 1:length(z)

          k=convhull(x(z==clusters(i)), y(z==clusters(i)));

          plot(x, y, 'b.'); %# plot cluster points
          plot(x(k),y(k),'r-'); %# plots only k indices, giving the convex hull


      end

Below is an image of what is being displayed;

If this question has already been asked I apologize for repetition but please do direct me to the answer you'll see fit.

Please can anyone help with this, however trivial I'm really struggling!

Answer 1

I would iterate through all the clusters and do what you already written, and use the hold on option to accumulate all the plots in the same plot. Something like this:

% Generate three clouds of points in 2D:
c1 = bsxfun(@plus, 0.5 * randn(50,2), [1 3]);
c2 = bsxfun(@plus, 0.6 * randn(20,2), [0 0]);
c3 = bsxfun(@plus, 0.4 * randn(20,2), [1 1]);

data = [c1, ones(50,1); ...
        c2, 2*ones(20,1); ...
        c3, 3*ones(20,1)];

% Plot the data points with different colors

clf
plot(c1(:,1), c1(:,2),'r+', 'LineWidth', 2);
hold on
plot(c2(:,1), c2(:,2),'k+', 'LineWidth', 2);
plot(c3(:,1), c3(:,2),'b+', 'LineWidth', 2);

x = data(:,1);
y = data(:,2);
cluster = data(:,3);

clusters = unique(cluster);

for i = 1:length(clusters)
    px = x(cluster == clusters(i));
    py = y(cluster == clusters(i));
    if length(px) > 2
        k = convhull(px, py);
        plot(px(k), py(k), '-');
    end
end

It gives the following result: