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 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.

Value

A real number in [0,1] representing a measure of dispersion of a cluster.

mappeR documentation built on April 3, 2025, 6:19 p.m.