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ML | Types of Linkages in Clustering

  • Last Updated : 25 Oct, 2021

Prerequisites: Hierarchical Clustering

The process of Hierarchical Clustering involves either clustering sub-clusters(data points in the first iteration) into larger clusters in a bottom-up manner or dividing a larger cluster into smaller sub-clusters in a top-down manner. During both the types of hierarchical clustering, the distance between two sub-clusters needs to be computed. The different types of linkages describe the different approaches to measure the distance between two sub-clusters of data points. The different types of linkages are:-

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1. Single Linkage: For two clusters R and S, the single linkage returns the minimum distance between two points i and j such that i belongs to R and j belongs to S.



L(R, S) = min(D(i, j)), i\epsilon R, j\epsilon S

2. Complete Linkage: For two clusters R and S, the complete linkage returns the maximum distance between two points i and j such that i belongs to R and j belongs to S.

L(R, S) = max(D(i, j)), i\epsilon R, j\epsilon S

3. Average Linkage: For two clusters R and S, first for the distance between any data-point i in R and any data-point j in S and then the arithmetic mean of these distances are calculated. Average Linkage returns this value of the arithmetic mean.

L(R, S) = \frac{1}{n_{R}+n_{S}}\sum _{i=1}^{n_{R}}\sum _{j=1}^{n_{S}} D(i, j), i\epsilon R, j\epsilon S

where

n_{R} – Number of data-points in R

n_{S} – Number of data-points in S

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