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Hierarchical Clustering

Hierarchical Clustering
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Dr.JakeFinlay,Germany,Teacher
Published Date:22-07-2017
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Hierarchical Clustering www.ThesisScientist.comHierarchical 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 5 6 0.2 4 3 4 2 0.15 5 2 0.1 1 0.05 1 3 0 1 3 2 5 4 6 www.ThesisScientist.comStrengths of Hierarchical Clustering Do not have to assume any particular number of clusters  Any desired number of clusters can be obtained by „cutting‟ the dendogram at the proper level They may correspond to meaningful taxonomies  Example in biological sciences (e.g., animal kingdom, phylogeny reconstruction, …) www.ThesisScientist.comHierarchical 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, all-inclusive 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 www.ThesisScientist.comAgglomerative 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 4. Merge the two closest clusters 5. Update the proximity matrix 6. Until only a single cluster remains  Key operation is the computation of the proximity of two clusters  Different approaches to defining the distance between clusters distinguish the different algorithms www.ThesisScientist.comStarting Situation Start with clusters of individual points and p1 p2 p3 p4 p5 . . . a proximity matrix p1 p2 p3 p4 p5 . . . Proximity Matrix ... p1 p2 p3 p4 p9 p10 p11 p12 www.ThesisScientist.comIntermediate Situation C1 C2 C3 C4 C5  After some merging steps, we have some clusters C1 C2 C3 C3 C4 C4 C5 Proximity Matrix C1 C5 C2 ... p1 p2 p3 p4 p9 p10 p11 p12 www.ThesisScientist.comIntermediate Situation C1 C2 C3 C4 C5  We want to merge the two closest clusters (C2 and C1 C5) and update the proximity matrix. C2 C3 C3 C4 C4 C5 Proximity Matrix C1 C5 C2 ... p1 p2 p3 p4 p9 p10 p11 p12 www.ThesisScientist.comAfter Merging C2  The question is “How do we update the proximity U C1 C5 C3 C4 matrix?” C1 ? ? ? ? ? C2 U C5 C3 C3 ? C4 ? C4 Proximity Matrix C1 C2 U C5 ... p1 p2 p3 p4 p9 p10 p11 p12 www.ThesisScientist.comHow to Define Inter-Cluster Similarity p1 p2 p3 p4 p5 . . . p1 Similarity? p2 p3 p4 p5  MIN .  MAX .  Group Average . Proximity Matrix  Distance Between Centroids  Other methods driven by an objective function  Ward‟s Method uses squared error www.ThesisScientist.comHow to Define Inter-Cluster Similarity p1 p2 p3 p4 p5 . . . p1 p2 p3 p4 p5  MIN .  MAX .  Group Average . Proximity Matrix  Distance Between Centroids  Other methods driven by an objective function  Ward‟s Method uses squared error www.ThesisScientist.comHow to Define Inter-Cluster Similarity p1 p2 p3 p4 p5 . . . p1 p2 p3 p4 p5  MIN .  MAX .  Group Average . Proximity Matrix  Distance Between Centroids  Other methods driven by an objective function  Ward‟s Method uses squared error www.ThesisScientist.comHow to Define Inter-Cluster Similarity p1 p2 p3 p4 p5 . . . p1 p2 p3 p4 p5  MIN .  MAX .  Group Average . Proximity Matrix  Distance Between Centroids  Other methods driven by an objective function  Ward‟s Method uses squared error www.ThesisScientist.comHow to Define Inter-Cluster Similarity p1 p2 p3 p4 p5 . . . p1  p2 p3 p4 p5  MIN .  MAX .  Group Average . Proximity Matrix  Distance Between Centroids  Other methods driven by an objective function  Ward‟s Method uses squared error www.ThesisScientist.comCluster Similarity: MIN or Single Link Similarity of two clusters is based on the two most similar (closest) points in the different clusters  Determined by one pair of points, i.e., by one link in the proximity graph. I1 I2 I3 I4 I5 I1 1.00 0.90 0.10 0.65 0.20 I2 0.90 1.00 0.70 0.60 0.50 I3 0.10 0.70 1.00 0.40 0.30 I4 0.65 0.60 0.40 1.00 0.80 I5 0.20 0.50 0.30 0.80 1.00 1 2 3 4 5 www.ThesisScientist.comHierarchical Clustering: MIN 5 1 3 0.2 5 2 1 0.15 2 3 6 0.1 0.05 4 0 4 3 6 2 5 4 1 Nested Clusters Dendrogram www.ThesisScientist.comStrength of MIN Original Points Two Clusters • Can handle non-elliptical shapes www.ThesisScientist.comLimitations of MIN Original Points Two Clusters • Sensitive to noise and outliers www.ThesisScientist.comCluster Similarity: MAX or Complete Linkage Similarity of two clusters is based on the two least similar (most distant) points in the different clusters  Determined by all pairs of points in the two clusters I1 I2 I3 I4 I5 I1 1.00 0.90 0.10 0.65 0.20 I2 0.90 1.00 0.70 0.60 0.50 I3 0.10 0.70 1.00 0.40 0.30 I4 0.65 0.60 0.40 1.00 0.80 I5 0.20 0.50 0.30 0.80 1.00 1 2 3 4 5 www.ThesisScientist.comHierarchical Clustering: MAX 4 1 0.4 2 5 0.35 5 0.3 2 0.25 0.2 3 6 0.15 3 1 0.1 0.05 4 0 3 6 4 1 2 5 Nested Clusters Dendrogram www.ThesisScientist.com