August 2019 Archives

Racing Up The Hierarchy

In the previous post we saw how to identify subsets of a set of data that are in some sense similar to each other, known as clusters, by constructing sequences of clusterings starting with each datum in its own cluster and ending with all of the data in the same cluster, subject to the constraint that if a pair of data are in the same cluster in one clustering then they must also be in the same cluster in the next, which are known as hierarchical clusterings.
We did this by selecting the closest pairs of clusters in one clustering and merging them to create the next, using one of three different measures of the distance between a pair of clusters; the average distance between their members, the distance between their nearest members and the distance between their farthest members, known as average linkage, single linkage and complete linkage respectively.
Unfortunately our implementation came in at a rather costly O(n3) operations and so in this post we shall look at how we can improve its performance.

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