compute_tightness {mappeR} | R Documentation |
Compute dispersion of a single cluster
Description
Compute dispersion of a single cluster
Usage
compute_tightness(dists, cluster)
Arguments
dists |
A distance matrix for points in the cluster. |
cluster |
A list containing named vectors, whose names are data point names and whose values are cluster labels |
Details
This method computes a measure of cluster dispersion. It finds the medoid of the input data set and returns the sum of distances from the medoid divided by the largest distance from the medoid. Formally, we say the tightness \tau
of a cluster C
is given by
\tau(C) = \dfrac{\displaystyle\sum_{i}\text{dist}(x_i, x_j)}{\left(\displaystyle\max_{x_i\in C, i\neq j}{\text{dist}(x_i, x_j)}\right)\left(|C| - 1\right)}
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.
Value
A real number in [0,1]
representing a measure of dispersion of a cluster.