# What are the elements in Hierarchical clustering?

A hierarchical clustering approach operates by merging data objects into a tree of clusters. Hierarchical clustering algorithms are top-down or bottom-up. The feature of accurate hierarchical clustering techniques degenerates from its lack to perform adjustment because a merge or split decision is completed.

There are various elements of hierarchical clustering which are as follows −

Lack of a Global Objective Function

Agglomerative hierarchical clustering methods use several elements to decide locally, at each step, which clusters must be merged (or split for divisive approaches).

This method yields clustering algorithms that prevent the difficulty of undertaking to solve a complex combinatorial optimization problem.

Ability to Handle Different Cluster Sizes

The element of agglomerative hierarchical clustering that how to consider the associative sizes of the group of clusters that are combined. It uses only to cluster proximity schemes that contain sums, such as centroid, Ward's, and group average.

There are two methods such as weighted, which considers all clusters equally, and unweighted, which creates the number of points in each cluster into account. The terminology of weighted or unweighted defines the data points, not the clusters. In other terms, considering clusters of unequal size equally provides multiple weights to the points in different clusters, while creating the cluster size into account provides points in different clusters the similar weight.

Merging Decisions are Final

Agglomerative hierarchical clustering algorithms influence to creation of good local decisions about combining two clusters because they can need data about the pairwise similarity of all points. Because a decision is made to merge two clusters, it cannot be undone the next time. This method avoids a local optimization element from becoming a global optimization criterion.

For instance, although the "minimize squared error" criterion from K-means is used in determining which clusters to merge in Ward's method, the clusters at each level do not define local minima concerning the total SSE. Indeed, the clusters are not dynamic, in the sense that a point in one cluster can be nearer to the centroid of a different cluster than it is to the centroid of its recent cluster.

Some methods that try to overcome the limitation that merges are final. One method tries to furnish the hierarchical clustering by modifying branches of the tree around to enhance a worldwide objective function. Another method needs a partitional clustering technique including Kmeans to produce some small clusters and then implement hierarchical clustering using these small clusters as the beginning point.

Updated on: 14-Feb-2022

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