categorize points by distance

I have 51 points(x,y) that represent locations, four of them are the main locations(stores) to which the rest of the locations must be divided by distance (for example locations 4,6,18,33 etc are closer to store 1, locations 5,19,22, etc closer to store 2 and 48,46.7 etc to store 3) . I already made a matrix 51x51 that represents the distances among all points (using the euclidean distance) if it's better to work like that , but how can i do it?

Answer 1

[Image Analyst]

How did you create the 51x51 matrix? Using pdist2()?

Why not just use the 4 if that's what you want?

distances = pdist2(xy51Points, xy4Points);

I'm not really sure what you want as the output? Do you want to somehow categorize the distances into classes (ranges), like class #1 is 0-10 km away, class #2 is 10-20 km, etc.

[Nikoleta]

I used ecxel to make the 51x51 array and then inport it in matlab. The output i want is to find for the 47 locations , the closest store they belong (so that i end up with four new arrays of each store)

[Walter Roberson]

Index the 51 x 51 matrix by the 4 rows corresponding to the stores. Use the two-output form of min() to find the index of the closest store for each of the columns.

[Nikoleta]

how can i use it? i have made an array that consists of the distances from every store to the rest of the locations , each row belongs to each store. so i have to find the min of each column (which is simple) but how can i get the store it belongs to and not the distance as a return?

[Walter Roberson]

Use the two-output form of min() to find the index of the closest store for each of the columns.

https://www.mathworks.com/help/matlab/ref/min.html#d117e915376

[Nikoleta]

thank you!

[Image Analyst]

Is this what you want?

% Define our 4 reference points.
xy4 = rand(4, 2);
% Define our 47 other points.
xy47 = rand(47, 2);
% Plot them
plot(xy4(:, 1), xy4(:, 2), 'r.', 'MarkerSize', 15);
grid on;
hold on;
plot(xy47(:, 1), xy47(:, 2), 'b.', 'MarkerSize', 15);

% Find the distance from every one of the 4 reference points
% to every one of the 47 other points.
distances = pdist2(xy4, xy47)
% Find the index and distance of the closest of the other 47 to each reference point.
for k = 1 : size(xy4, 1)
	[closestDistance(k), closestIndex(k)] = min(distances(k,:));
	fprintf('The closest point to reference point #%d is #%d with a distance of %f.\n', ...
		k, closestIndex(k), closestDistance(k));
	% Draw a line connecting them
	line([xy4(k, 1), xy47(closestIndex(k), 1)], [xy4(k, 2), xy47(closestIndex(k), 2)], ...
		'LineWidth', 2, 'Color', 'm');
end
xlabel('X', 'FontSize', 20);
ylabel('Y', 'FontSize', 20);
fprintf('Done!\n');

Answer 2

[Walter Roberson]

Use pdist2() between the locations of the stores and the rest of the locations. Ue the two-output form of min() to find the index of the closest store for each of the 47 points.

[Nikoleta]

thank you very much!