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clustering2-1

# clustering2-1 - Clustering Algorithms Hierarchical...

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1 Clustering Algorithms Hierarchical Clustering k  -Means Algorithms CURE Algorithm

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2 Methods of Clustering Hierarchical (Agglomerative) : Initially, each point in cluster by itself. Repeatedly combine the two “nearest”  clusters into one. Point Assignment : Maintain a set of clusters. Place points into their “nearest” cluster.
3 Hierarchical Clustering Two important questions: 1. How do you determine the “nearness” of  clusters? 2. How do you represent a cluster of more  than one point?

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4 Hierarchical Clustering – (2) Key problem : as you build clusters, how  do you represent the location of each  cluster, to tell which pair of clusters is  closest? Euclidean case : each cluster has a  centroid   = average of its points. Measure intercluster distances by  distances of centroids.
5 Example    (5,3) o (1,2) o o (2,1) o (4,1) o (0,0) o (5,0) x (1.5,1.5) x (4.5,0.5) x (1,1) x (4.7,1.3)

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6 And in the Non-Euclidean Case? The only “locations” we can talk about  are the points themselves. I.e., there is no “average” of two points. Approach 1 clustroid   = point “closest”  to other points. Treat clustroid as if it were centroid, when  computing intercluster distances.
7 “Closest” Point? Possible meanings: 1. Smallest maximum distance to the other  points. 2. Smallest average distance to other  points. 3. Smallest sum of squares of distances to  other points. 4. Etc., etc.

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8 Example 1 2 3 4 5 6 intercluster distance clustroid clustroid
9 Other Approaches to Defining  “Nearness” of Clusters Approach 2 : intercluster distance =  minimum of the distances between any  two points, one from each cluster. Approach 3 : Pick a notion of “cohesion”  of clusters, e.g., maximum distance from  the clustroid. Merge clusters whose  union   is most  cohesive.

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10 Cohesion Approach 1 : Use the  diameter   of the  merged cluster = maximum distance  between points in the cluster. Approach 2 : Use the average distance  between points in the cluster.
11 Cohesion – (2) Approach 3 : Use a density-based  approach:  take the diameter or average  distance, e.g., and divide by the number  of points in the cluster.

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clustering2-1 - Clustering Algorithms Hierarchical...

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