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.


[Package mappeR version 1.2.0 Index]