K-Means Algorithm
Jupyter Demos
▶️ Demo | K-means Algorithm - split Iris flowers into clusters based on petal_length and petal_width
Definition
K-means clustering aims to partition n observations into K clusters in which each observation belongs to the cluster with the nearest mean, serving as a prototype of the cluster.
The result of a cluster analysis shown below as the coloring of the squares into three clusters.
Clustering
Description
Given a training set of observations:
Training set
x-i
Where each observation is a d-dimensional real vector, k-means clustering aims to partition the m observations into K (≤ m) clusters:
Clusters
… so as to minimize the within-cluster sum of squares (i.e. variance).
Below you may find an example of 4 random cluster centroids initialization and further clusters convergence:
Clustering
Another illustration of k-means convergence:
Clustering
Cost Function (Distortion)
- index of cluster (1, 2, …, K) to which example x(i) is currently assigned.
- cluster centroid k (
) and 
.
- cluster centroid of a cluster to which the example x(i) has been assigned.
For example:
Cluster example
In this case optimization objective will look like the following:
Cost Function
Clustering
The Algorithm
Randomly initialize K cluster centroids (randomly pick K training examples and set K cluster centroids to that examples).
Centroids
k-means-algorithm