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Centroid, Radius and Diameter of a Cluster (for numerical data sets)

• Centroid: the “middle” of a cluster
  \[C_{m}=\frac{\sum_{i=1}^{N}(t_{ip})}{N}\]
• Radius: square root of average distance from any point of the cluster to its centroid
  \[R_{m}=\sqrt{\frac{\sum_{i=1}^{N}(t_{ip}-c_{m})^{2}}{N}}\]
• Diameter: square root of average mean squared distance between all pairs of points in the cluster
  \[D_{m}=\sqrt{\frac{\sum_{i=1}^{N} \sum_{i=1}^{N}(t_{ip}-t_{iq})^{2}}{N(N-1)}}\]