Hierarchical clustering

As explained in Advanced Algorithms and Data Structures

Hierarchical clustering is a clustering technique that forms nested groups by successively merging or dividing clusters.

Hierarchical clustering organizes an unlabeled dataset into nested groups rather than producing only one flat partition. The result can be viewed at different resolutions by selecting a snapshot of the hierarchy. section 5.7.3 section 12.1.2

Agglomerative hierarchical clustering develops the hierarchy incrementally:

• Start with every point in its own cluster. section 5.7.3
• Repeatedly merge two points and their clusters until everything belongs to one cluster. section 5.7.3
• Keep the merge history so different stages can be selected as useful partitions. section 5.7.3

A dendrogram records this process as a tree. Earlier joins represent stronger inferred relationships: if A and B join before C joins them, A and B are treated as more closely related than either is to C. section 5.7.3

Hierarchical clustering produces a multi-layer partitioning, while partitioning or flat clustering produces groups that do not contain one another. A hierarchy can therefore be sliced at a chosen level, with the result controlled by algorithm parameters. section 12.1.2 section 12.4.4

Customer segmentation

Given customer attributes such as purchasing habits, financial situation, demographics, age, education, and location, clustering can infer groups without preassigned labels. A hierarchy lets analysts inspect broad groups and finer subgroups rather than committing to one partition immediately. section 12.0 section 5.7.3

Figure 5.15 An example of hierarchical clustering. On the left, the dataset (a collection of 2-D points) is shown with progressive grouping shown as ellipses. From the figure, it can be inferred that, for instance, A and B are grouped together before C is added to the two of them to form a larger cluster. Hence, the relationship between A and B is inferred to be stronger than the one between A and C or B and C. On the right, the same process is shown using a dendrogram.¹⁷ Note that both figures could be the result either of agglomerative or divisive clustering: the former produces the dendrogram starting from the bottom, the latter starting from the top.

Compare progressive grouping in a two-dimensional dataset with its dendrogram representation, including agglomerative and divisive construction directions. section 5.7.3

How Advanced Algorithms and Data Structures covers it

How deep it goes

Explains agglomerative construction, dendrograms, slicing, and parameter effects, but leaves the broader clustering taxonomy beyond the treatment.

Examples

Uses two-dimensional point datasets, progressive A–B–C grouping, dendrograms, reachability plots, and customer segmentation.

What it assumes

Assumes familiarity with datasets and points while framing unsupervised learning and clustering distinctions explicitly.

What you can do after

Evaluate or understand nested clusters, choose hierarchy snapshots, and relate implementation needs to disjoint-set data structures.

How it connects

Connects hierarchical clustering to unsupervised learning, partitioning clustering, density-based clustering, OPTICS, dendrograms, and disjoint sets.

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Related concepts

• K-means clusteringcontrasts with · K-means clustering partitions data into a specified number of groups by assigning observations to representative centers and iteratively updating those centers to reduce within-group distances.
• OPTICSincludes · OPTICS is a density-based clustering algorithm that orders points and computes reachability distances to reveal cluster structure across varying density thresholds.
• unsupervised learningkind of · Unsupervised learning is a machine-learning approach that discovers patterns, structure, or representations in data without labeled target outputs.
• clusteringkind of · Clustering is the technique of grouping data items according to similarity or shared characteristics.
• agglomerative clusteringincludes · Agglomerative clustering is a bottom-up hierarchical clustering method that starts with individual items as separate clusters and repeatedly merges clusters according to a linkage criterion.

This explainer was generated by Manning's knowledge graph from the text of Advanced Algorithms and Data Structures. The section links point to the parts of the book it draws on.