Suppose that we have the following data (one variable). Use single linkage to identify the

Step 1: Identify the data points. List all the data points that you have for the variable in que

Suppose that we have the following data (one variable). Use...

Key Concepts

Single Linkage Clustering

Single linkage clustering is a specific method in hierarchical clustering where the distance between two clusters is determined by the smallest distance between any two points, one from each cluster. This method is particularly sensitive to noise and outliers, as it can lead to the chaining effect, where clusters may become elongated as single data points link clusters together.

Hierarchical Clustering

Hierarchical clustering is a method of cluster analysis that seeks to build a hierarchy of clusters. It involves either a bottom-up approach (agglomerative clustering), where each data point starts in its own cluster and pairs of clusters are merged as one moves up the hierarchy, or a top-down approach (divisive clustering), where all data points start in one cluster and are progressively split. The result is typically represented as a dendrogram.

Agglomerative Clustering

Agglomerative clustering is a type of hierarchical clustering that starts with each observation as its own cluster and then successively merges the closest pairs of clusters based on a chosen linkage criterion, until all points are grouped into one cluster. Single linkage is one of the possible criteria used in the merging process.

Distance Metric

A distance metric is a measure used to quantify the similarity or dissimilarity between two data points. In clustering, common metrics include Euclidean distance, Manhattan distance, or others, and the choice of metric can significantly affect the clustering outcome. In single linkage clustering, the minimum distance between points in different clusters is used to determine which clusters to merge next.

Dendrogram

A dendrogram is a tree-like diagram that records the sequences of merges or splits in hierarchical clustering. It visually represents the arrangement of the clusters produced by the clustering algorithm, showing at what distance levels clusters are combined. This representation helps in determining the optimal number of clusters by 'cutting' the dendrogram at a suitable level.

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