kmeans.md

K-means

K-means is a classical method for clustering or vector quantization. It produces a fixed number of clusters, each associated with a center (also known as a prototype), and each data point is assigned to a cluster with the nearest center.

From a mathematical standpoint, K-means is a coordinate descent algorithm that solves the following optimization problem:

$$\text{minimize} \ \sum_{i=1}^n \| \mathbf{x}_i - \boldsymbol{\mu}_{z_i} \|^2 \ \text{w.r.t.} \ (\boldsymbol{\mu}, z)$$

Here, \boldsymbol{\mu}_k is the center of the k-th cluster, and z_i is an index of the cluster for i-th point \mathbf{x}_i.

kmeans
KmeansResult

If you already have a set of initial center vectors, kmeans! could be used:

kmeans!

Examples

using Clustering

# make a random dataset with 1000 random 5-dimensional points
X = rand(5, 1000)

# cluster X into 20 clusters using K-means
R = kmeans(X, 20; maxiter=200, display=:iter)

@assert nclusters(R) == 20 # verify the number of clusters

a = assignments(R) # get the assignments of points to clusters
c = counts(R) # get the cluster sizes
M = R.centers # get the cluster centers

Scatter plot of the K-means clustering results:

using RDatasets, Clustering, Plots
iris = dataset("datasets", "iris"); # load the data

features = collect(Matrix(iris[:, 1:4])'); # features to use for clustering
result = kmeans(features, 3); # run K-means for the 3 clusters

# plot with the point color mapped to the assigned cluster index
scatter(iris.PetalLength, iris.PetalWidth, marker_z=result.assignments,
        color=:lightrainbow, legend=false)