Summary  
This chapter explains linkage methods for hierarchical clustering, detailing how to choose reference points between clusters—such as the closest (single linkage), farthest (complete linkage), centroids, or all point pairs (average linkage)—to compute inter-cluster distances and shape the resulting clusters.

General domain of usage  
Unsupervised machine learning (hierarchical clustering)

**Linkage methods** decide how to measure distance between clusters when building clusters step-by-step. Different linkages create **different cluster shapes**.

- Uses the **shortest distance** between points in two clusters;
- Links clusters when **any points get close**;
- Creates long, chaining clusters;
- Good for irregular shapes;
- Sensitive to noise.

Single Linkage

- Uses the **longest distance** between points in two clusters;
- Links clusters only when **all points are relatively close**;
- Creates compact, spherical clusters;
- Less chaining;
- More robust to noise.

Complete Linkage

- Uses the **average distance** between all pairs of points from two clusters;
- A compromise between single and complete linkage;
- Often a good balance.

Average Linkage

- Uses the **distance between the centroids** of two clusters;
- Centroid is the mean position of all points in the cluster;
- Can sometimes cause inversions (clusters getting closer as they grow);
- Good for geometrically meaningful clustering.

Centroid Linkage

Minimum distance between points in clusters

Maximum distance between points in clusters

Average distance between points in clusters

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Which linkage method is known for creating long, chaining clusters and is most sensitive to noise?

Gain a solid understanding of cluster analysis, a key unsupervised learning technique for uncovering patterns in unlabeled data. Explore the essentials of K-Means, Hierarchical Clustering, DBSCAN, and GMMs, and get hands-on experience with real datasets to build confidence in applying clustering to real-world problems.

Dive into the fundamentals of clustering and discover how it differs from classification. Explore essential algorithms, tools, and libraries that power this unsupervised learning technique to uncover hidden patterns in data.

Gain a solid understanding of key preprocessing techniques that ensure effective clustering. Learn how to handle missing values, encode categorical features, normalize data, and choose appropriate distance measures and linkages to boost clustering accuracy.

Master the skills needed to apply K-Means clustering effectively. Learn how the algorithm works, determine the optimal number of clusters, and gain hands-on experience by implementing K-Means on both synthetic and real-world datasets.

Explore the essentials of hierarchical clustering and learn how to group data into meaningful clusters using dendrograms. Build confidence in identifying the optimal number of clusters and implementing the technique on both synthetic and real-world datasets.

Discover how DBSCAN excels at detecting clusters of varying shapes and handling noise in data. Learn the mechanics behind this density-based algorithm, how to assign points to clusters, and apply it to both synthetic and real datasets with confidence.

Gain a solid understanding of Gaussian Mixture Models and how they use probability to model complex cluster shapes. Learn the principles of Gaussian distribution, explore how GMMs work, and build confidence by applying them to both dummy and real-world data.

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