Kmeans sorts data based on averages. Dr Mike Pound explains how it works.

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Dr. Mike's Code:
% This script is the one mentioned during the Computerphile Image
% Segmentation video. I chose matlab because it's a popular tool for
% quickly prototyping things. Matlab licenses are pricey, if you don't have
% one (or, like me, work for an organisation that does) try Octave as a
% good free alternative. This code should work in Octave too.

% Load in an input image
im = imread('C:\Path\Of\Input\Image.jpg');

% In matlab, Kmeans operates on a 2D array, where each sample is one row,
% and the features are the columns. We can use the reshape function to turn
% the image into this format, where each pixel is one row, and R,G and B
% are the columns. We are turning a W,H,3 image into W*H,3

% We also cast to a double array, because Kmeans requires it in matlab
imflat = double(reshape(im, size(im,1) * size(im,2), 3));

% I specify that initialisation shuold sample points at
% random, rather than anything complex like kmeans++ initialisation.
% Kmeans++ takes a long time if you are using 256 classes.

% Perform kmeans. This function returns the class IDs assigned to each
% pixel, and in this case we also want the mean values for each class
% what colour is each class. This can take a long time if the value for K
% is large, I've used the sampling start strategy to speed things up.

% While KMeans is running, it will show you the iteration count, and the
% number of pixels that have changed class since last iteration. This
% number should get lower and lower, as the means settle on appropriate
% values. For large K, it's unlikely that we will ever reach zero movement
% (convergence) within 150 iterations.
K = 3
[kIDs, kC] = kmeans(imflat, K, 'Display', 'iter', 'MaxIter', 150, 'Start', 'sample');

% Matlab can output paletted images, that is, grayscale images where the
% colours are stored in a separate array. This array is kC, and kIDs are
% the grayscale indices.
colormap = kC / 256; % Scale 01, since this is what matlab wants

% Reshape kIDs back into the original image shape
imout = reshape(uint8(kIDs), size(im,1), size(im,2));

% Save file out, you need to subtract 1 from the image classes, since once
% stored in the file the values should go from 0255, not 1256 like matlab
% would do.
imwrite(imout 1, colormap, 'C:\Path\Of\Output\Image.png');


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This video was filmed and edited by Sean Riley.

Computer Science at the University of Nottingham: http://bit.ly/nottscomputer

Computerphile is a sister project to Brady Haran's Numberphile. More at http://www.bradyharan.com