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Hierarchical Clustering
Unsupervised learning method that organizes data into a hierarchy of nested clusters, generally represented by a binary tree called a dendrogram.
Dendrogram
Tree-like graphical representation of the cluster hierarchy, where each node represents a cluster merge and the height indicates the distance at which this merge occurred.
Single Linkage
Merging criterion where the distance between two clusters is defined as the minimum distance between all pairs of points from the two clusters, favoring chain-like clusters.
Complete Linkage
Agglomeration method using the maximum distance between points of two different clusters, tending to create compact and spherical clusters.
Average Linkage
Linkage criterion calculating the average distance between all pairs of objects belonging to two distinct clusters, offering a compromise between single and complete linkage.
Ward's Linkage
Agglomeration method that minimizes the increase in within-cluster variance at each merge, typically producing clusters of relatively equal size and spherical shape.
Linkage Matrix
Upper triangular data structure storing the distances between clusters at each step of the hierarchical algorithm, essential for computational optimization.
Cophenetic Correlation Coefficient
Metric measuring the correlation between the original distances between pairs of objects and their cophenetic distances in the dendrogram, evaluating the quality of the clustering.
Cophenetic Distance
Distance between two objects defined as the height of the first node in the dendrogram where these objects are grouped in the same cluster.
Agglomerative Clustering
Bottom-up approach of hierarchical clustering where each observation starts as an individual cluster and progressively merges until forming a single cluster containing all data.
Divisive Clustering
Top-down strategy starting with a single cluster containing all observations and recursively dividing clusters until each observation forms its own cluster.
Stopping Criterion
Set of conditions defining when the hierarchical clustering process should stop, generally based on a predefined number of clusters or a distance threshold.
Agglomerative Clustering
Variant of hierarchical clustering using a bottom-up approach where the closest clusters are iteratively merged according to a specified distance criterion.
Monotonicity
Property of hierarchical linkage methods ensuring that fusion distances are non-decreasing, essential to avoid inversions in the dendrogram.
Linkage Space
Metric space induced by a specific linkage method, defining how distances between clusters are calculated and influencing the final clustering structure.