Why is hierarchical clustering algorithm so crucial?

Hierarchical clustering method is the hierarchical decomposition of a given set of data objects. According to the decomposition strategy used in the hierarchical decomposition, the hierarchical clustering method can be divided into aggregated and divisive hierarchical clustering.

Cohesive hierarchical clustering

It adopts a bottom-up strategy, first treating each object as a class, and then combining these classes into larger classes based on a certain measure (such as the distance between the center points of two current classes) until all objects are in the same class or meet a certain termination condition. The vast majority of hierarchical clustering algorithms belong to this class, and they only differ in the definition of inter class similarity.

Split hierarchical clustering

It adopts the opposite strategy of hierarchical clustering with aggregation - top-down. It first places all objects in one class, and then gradually subdivides them into smaller classes based on some measure, until each object forms its own class or reaches a certain termination condition (such as reaching the desired number of classes, or the distance between two close classes exceeds a certain threshold).

Although hierarchical clustering is relatively simple, it often encounters the problem of selecting merging or splitting points. This choice is crucial because once a set of objects is merged or split, the next step is to do it on the newly formed class, and the already done processing cannot be undone, and objects cannot be exchanged between classes. If the decision to merge or split is not appropriate, low-quality clustering results may be obtained. Moreover, hierarchical clustering algorithms do not have good scalability and require checking and estimating a large number of objects and classes before deciding to merge or split.

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