In order to group points into clusters, we need to know about their distance between each other.
An illustraction of intercluster and intracluster distance.
<aside> ☝ Best clustering → min intracluster & max intercluster.
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Intracluster -- Measuring distance between points in a cluster.
🔅 Complete Diameter Distance: the farthest distance between two points in a cluster.
$$ \delta (S) = \max_{x, y\in S} d(x,y) $$
🔅 Average Diameter Distance: the average distance between ALL points in a clusters.
$$ \delta (S) = \dfrac{1}{\vert S\vert (\vert S\vert-1)} \sum_{x, y\in S, x\ne y} d(x,y) $$
where $\vert S\vert$ is the number of points in $S$.
🔅 Centroid Diameter Distance: the double of average distance between points and the center of a cluster.
$$ \delta (S) = 2 \left( \dfrac{\sum_{x\in S}d(x, c_S)}{\vert S\vert} \right) $$
where $c_S$ (can be calculated as $\frac{\Sigma_{x\in S}x}{\vert S\vert}), \vert S\vert$ are the center and the number of points in $S$.
Intercluster -- Measuring distance between 2 clusters. They can be used in Agglomerative clustering.
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🔅 Single Linkage Distance: the closest distance between two objects in 2 clusters.
$$ \delta (S, T) = \min_{x\in S, y\in T} d(x,y) $$
