K-Means Clustering

Global Algorithm - One-Dimensional Algorithm

K-Means Clustering algorithm is a simple unsupervised learning algorithm used to solve clustering problems. By assuming $k$ clusters, it minimizes the sum of distances (points to cluster centroids) through iteration.

For details refer to the online tutorial http://www-2.cs.cmu.edu/~awm/tutorials/kmeans.html.

Input Parameters

Parameter	Type	Constraint	Description	Remarks
$Y$	$Y \in \mathbb R^{N}$	$N \in \mathbb{N}$	Input data of size $N$
$k$	$k \in \mathbb{N}$	$k \lt N$	Specified number of clusters

Output Parameters

Parameter	Type	Constraint	Description	Remarks
$\hat{Y}$	$\hat{Y} \in \mathbb R^{k}$		A vector of $k$ cluster centroid locations

Tool Support

• Matlab

  For details refer to the online documentation of the function ‘kmeans’.

Single Steps using the Algorithm

• Data Discretization with K-Means Clustering
• Data Reduction with K-Means Clustering
• Outlier Detection with K-Means Clustering

References

• J.B. MacQueen, Some Methods for classification and Analysis of Multivariate Observations, Proceedings of 5th Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, University of California Press, vol. 1, pp. 281-297, 1967.