compute_tightness: Compute dispersion of a single cluster

In mappeR: Construct and Visualize TDA Mapper Graphs

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 finds the medoid of the input data set and returns the average distance to the medoid, i.e.,

\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.

Value

A real number in [0,1] representing the mean distance to the medoid of the cluster.

mappeR documentation built on June 9, 2025, 5:08 p.m.