If we cut the single linkage tree at the point shown below, we would say that there are two clusters. One of the problems with hierarchical clustering is that there is no objective way to say how many clusters there are.

It starts with cluster '35' but the distance between '35' and each item is now the minimum of d(x,3) and d(x,5). Different visualizations use different measures of cluster height.Д«elow is the single linkage dendrogram for the same distance matrix. On this plot, the y-axis shows the distance between the objects at the time they were clustered. This will be 2 and 4.Д¬ontinuing in this way, after 6 steps, everything is clustered. The items with the smallest distance get clustered next. Since we are using complete linkage clustering, the distance between '35' and every other item is the maximum of the distance between this item and 3 and this item and 5. To obtain the new distance matrix, we need to remove the 3 and 5 entries, and replace it by an entry '35'.

The smallest distance is between three and five and they get linked up or merged first into a the cluster '35'. Only the lower triangle is shown, because the upper triangle can be filled in by reflection. The table below is an example of a distance matrix. A distance matrix will be symmetric (because the distance between x and y is the same as the distance between y and x) and will have zeroes on the diagonal (because every item is distance zero from itself). Clustering starts by computing a distance between every pair of units that you want to cluster.

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