Assign 3d points to multiple cluster when their coordinates meet certain conditions

Hi all,

I am trying to assign each point of the 3D dataset I have to the "correct" cluster based on certain conditions. The code below shows the 3D dataset I have with 15 data points. Here I have 4 clusters to assign these 15 points to. The challenge here is the following:

1. I want to test the distance between the x cooridnate of the point and the x cooridnate of the initial centroid and the distance should be equal or less some value. The same goes for the y cooridnate.
2. If the previous condition is met, test the z coordinate in the same way.
3. If the previous two conditions are met, assign this point to the "correct" cluster. I think the final index matrix should be 15x4 where the rows corrspond to the number of points, the first column is the x coordinates, the second column is the y coorindtaes, the third column is the z coordinates, and the fourth clumn correspnds to the cluster index.

clear all;
close all;

%3D dataset
X = [0.6820   -0.4255    0.4255
    0.6820    0.8088    0.5881
    0.6820   -0.9337   -0.3580
    0.6820    0.5513    0.8343
    0.6820   -0.4142    0.4142
    0.6820    0.5281    0.8492
    0.6820   -0.9234   -0.3838
    0.6820   -0.2950    0.2950
    0.6820   -0.3111    0.3111
    0.6820   -0.7517   -0.6595
    0.6820    0.3220    0.9467
    0.6820   -0.3805    0.3805
    0.6820    0.6108    0.7918
    0.6820   -0.2954    0.2954
    0.6820    0.9530    0.3029];

%number of lcusters
NoCluster = 4;

%initial random centroids
xmin = 1 ; xmax = 4;
ymin = -1; ymax = 1;
zmin = -1; zmax = 1;
initial_centroids = [xmin+(xmax-xmin).*rand(NoCluster,1)...
    ymin+(ymax-ymin).*rand(NoCluster,1)...
    zmin+(zmax-zmin).*rand(NoCluster,1)];

%calculate the distance betweene each point and each centorid
%go through all points
for isp = 1:size(X,1)
    %go through all clusters
    for ic = 1:size(initial_centroids,1)
        %measure the distance between each to each of the
        %preivously determined centroids
        Dist_x(isp,ic) = abs(X(isp,1)-initial_centroids(ic,1));
        Dist_y(isp,ic) = abs(X(isp,2)-initial_centroids(ic,2));
        Dist_z(isp,ic)  = abs(X(isp,3)-initial_centroids(ic,3));
    end
end

%go through all calculated distances for testing
for idist = 1:size(Dist_x,1)
    %go throguh all clusters
    for icc = 1:size(initial_centroids,1)
        %test x and y
        if Dist_x(idist,icc) <= 0.01 && ...
                Dist_y(idist,icc) <= 0.01
            %if the previous condiiton is met, test the
            %corresponding z point
            if Dist_z(idist,icc) <= 0.01
                %if the previous two conditions are met,
                %assign this point to the current cluster and save
                %its cluster index
                [~ , ~ , ~ , cluster_indices] = ; %what to write here?
            end

        end
    end
end

Any help would be appreciated.

Thanks.

Answer 1

[Yatharth]

Hi LH,

I understand that you're aiming to assign each point in the 3D dataset to a cluster based on specific conditions, as outlined in your question and provided code.

After setting initial centroids, consider using this code snippet instead:

threshold_x = 1.5;
threshold_y = 1.5;
threshold_z = 1.5;

% Initialize the cluster assignment matrix
cluster_assignments = zeros(size(X,1), 4);

for i = 1:size(X,1)
    for j = 1:NoCluster
        % Calculate the distance between the point and the centroid
        dist_x = abs(X(i,1) - initial_centroids(j,1));
        dist_y = abs(X(i,2) - initial_centroids(j,2));
        dist_z = abs(X(i,3) - initial_centroids(j,3));
        
        % Check if the point meets the conditions for all coordinates
        if dist_x <= threshold_x && dist_y <= threshold_y && dist_z <= threshold_z
            % Assign the point to this cluster
            cluster_assignments(i,:) = [X(i,:), j];
            break; % Break the loop once the point is assigned to a cluster
        end
    end
end

% Display the final cluster assignments
disp(cluster_assignments);

I hope this is what you were looking for.

[LH]

Thanks. It works well. I think the problem was the absence of the matrix initialisation in the beginning.