Compute dispersion of a single cluster
compute_tightness(dists, cluster)A real number in \([0,1]\) representing a measure of dispersion of a cluster.
A distance matrix for points in the cluster.
A list containing named vectors, whose names are data point names and whose values are cluster labels
This method computes a measure of cluster dispersion. It finds the medoid of the input data set and returns the average distance to the medoid. Formally, we say the tightness \(\tau\) of a cluster \(C\) is given by $$\tau(C) = \dfrac{1}{\left(|C|-1\right)}\displaystyle\sum_{i}\text{dist}(x_i, x_j)$$ where $$x_j = \text{arg}\,\min\limits_{x_j\in C}\, \sum_{x_i \in C, i\neq j}\text{dist}(x_i, x_j)$$ A smaller value indicates a tighter cluster based on this metric.