Clustering Feature

Part of a CF-Tree which is used in the BIRCH algorithm.

It is a 3D summarizing statistic about the current Clusters.

$CF=(n,LS,SS)$ where $n$ is the number of data points in the cluster, $LS$ is the linear sum of the points in the cluster and $SS$ is the square sum of the points in the cluster.

This statistic allows to derive some useful information about a cluster.

Centroid: $\frac{LS}{n}$ Radius: $\sqrt{\frac{nSS-2L{S}^2+n}{n^2}}$ Diameter: $\sqrt{\frac{2nSS-2L{S}^2}{n(n-1)}}$

A nice way of merging two clusters is to just add the two CFs of two clusters.

Example