k-means_1_1.jl

data_simple = [0.1, 0.2, 0.3, 0.7, 0.8, 0.9]'

k-means_1_2.jl

using StatsBase

function kmeans_simple(X, k, max_iter = 100, threshold = 0.001)

    # Let's pick k points from X without replacment
    centroids = X[:, sample(1:size(X,2), k, replace = false)]

    # create a copy. This is used to check if the centroids are moving or not.
    new_centroids = copy(centroids)

    # start an empty array for our cluster ids. This will hold the cluster assignment
    # for each point in X
    cluster_ids = Array{Int32}(size(X,2))

    for i in 1:max_iter # I use _ here as we're not using this variable inside the loop
        for col_idx in 1:size(X, 2) # iterate over each point

            # let's index the ponts one by one
            p = X[:, col_idx]

            # calculate the distance between the point and each centroid
            point_difference = mapslices(x -> x - p, centroids, 1)

            # we calculate the squared Euclidian distance
            distances = mapslices(sum, point_difference .^ 2, 1)

            # now find the index of the closest centroid
            cluster_ids[col_idx] = findmin(distances)[2]
            # this gives the index of the minimum

            # you can uncomment this line to see how the loop progresses
            # println("p: $p diff: $point_difference dist: $distances $cluster_ids")
        end

        # you can uncomment this line to see the internal workings of the funtion
        # println("old: $centroids new: $new_centroids")

        # Iterate over each centroid
        for cluster_id in 1:size(centroids, 2)

            # find the mean of the assigned points for that particluar cluster
            new_centroids[:, cluster_id] = mapslices(mean, X[:, cluster_id .== cluster_ids], 2)
        end

        # You can uncomment this line to see how the centers move after each update
        # println("old_centroids: $centroids new_centroids: $new_centroids point assignemnts: $cluster_ids")

        # now measure the total distance that the centroids moved
        center_change = sum(mapslices(x -> sum(x.^2), new_centroids .- centroids, 2))

        centroids = copy(new_centroids)

        # if the centroids move negligably, then we're done
        if center_change < threshold
            # println(i)
            break
        end
    end

    # we'll send back both the location of the centroids as well as the cluster ids for each point
    return centroids, cluster_ids
end

k-means_1_3.jl

kmeans_simple(data_simple, 2)

k-means_1_4.jl

data_complex = [0.1 0.1; 0.1 0.2; 0.2 0.1;  # our first designed cluster
                0.4 0.4; 0.5 0.3; 0.5 0.4; # second cluster
                0.9 1.0]' # third cluster

k-means_1_5.jl

complex_result = kmeans_simple(data_complex, 3)

k-means_1_6.jl

# let's visualise the points
using Plots
scatter(data_complex[1, :], data_complex[2, :])
# and add the cluster centroids - red points
scatter!(complex_result[1][1, :], complex_result[1][2, :])