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Hierarchical cluster analysis is a method of cluster analysis which builds, by steps, a hierarchy of clusters, a dendrogram. Most popular is agglomerative hierarchical clustering (HAC) which starts from individual objects and collects them into bigger and bigger clusters.

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Geometric significance of the dimensional reduction part of spectral clustering?

Spectral embedding, the dimensional reduction part of spectral clustering, preserves topological features of the adjacency graph, not metric properties of the embedded data set. Your $W$ is an affinit …
Charles Pehlivanian's user avatar