07-clustering

Euclidean case each cluster has a centroid average of

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Unformatted text preview: erage of its points Measure cluster distances by distances of centroids 11/26/2010 Jure Leskovec, Stanford C246: Mining Massive Datasets 9 (5,3) o (1,2) o x (1.5,1.5) x (1,1) o (2,1) o (4,1) x (4.7,1.3) x (4.5,0.5) o (5,0) o (0,0) Data Dendrogram 11/26/2010 Jure Leskovec, Stanford C246: Mining Massive Datasets 10 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. 11/26/2010 Jure Leskovec, Stanford C246: Mining Massive Datasets 11 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. For distance d centroid c of cluster C is: min ∑ d ( x, c) c 11/26/2010 2 x∈C Jure Leskovec, Stanford C246: Mining Massive Datasets 12 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. 11/26/2010 Jure Leskovec, Stanford C246: Mining Massive Dataset...
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