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Unformatted text preview: 1 CSE 572: Data Mining Lecture 16: Hierarchical Clustering 2 Hierarchical Clustering ● Produces a set of nested clusters organized as a hierarchical tree ● Can be visualized as a dendrogram – A tree like diagram that records the sequences of merges or splits 1 3 2 5 4 6 0.05 0.1 0.15 0.2 1 2 3 4 5 6 1 2 3 4 5 3 Strengths of Hierarchical Clustering ● Do not have to assume any particular number of clusters – Any desired number of clusters can be obtained by ‘cutting’ the dendrogram at the proper level ● They may correspond to meaningful taxonomies – Example in biological sciences (e.g., animal kingdom, phylogeny reconstruction, …) 4 Hierarchical Clustering ● Two main types of hierarchical clustering – Agglomerative: Start with the points as individual clusters At each step, merge the closest pair of clusters until only one cluster (or k clusters) left – Divisive: Start with one, allinclusive cluster At each step, split a cluster until each cluster contains a point (or there are k clusters) ● Traditional hierarchical algorithms use a similarity or distance matrix – Merge or split one cluster at a time 5 MST: Divisive Hierarchical Clustering ● Build MST (Minimum Spanning Tree) – Start with a tree that consists of any point – In successive steps, look for the closest pair of points (p, q) such that one point (p) is in the current tree but the other (q) is not – Add q to the tree and put an edge between p and q 6 MST: Divisive Hierarchical Clustering ● Use MST for constructing hierarchy of clusters 7 Agglomerative Clustering Algorithm ● More popular hierarchical clustering technique ● Basic algorithm is straightforward 1. Compute the proximity matrix 2. Let each data point be a cluster 3. Repeat 1. Merge the two closest clusters 2. Update the proximity matrix 1. Until only a single cluster remains ●...
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 Spring '02
 dawsonengler
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