Differential Equations Solutions 54

Differential Equations Solutions 54 - 64 Chapter 11....

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Unformatted text preview: 64 Chapter 11. Solutions: Case Study: Classified Information Original Data 2 clusters 1 1 0.5 0.5 0 0 −0.5 −0.5 −1 −1 −1 −0.5 0 0.5 1 −1 −0.5 3 clusters 0 0.5 1 0.5 1 4 clusters 1 1 0.5 0.5 0 0 −0.5 −0.5 −1 −1 −1 −0.5 0 0.5 1 −1 −0.5 0 Figure 11.5. Clustering the data for Challenge 5 using the first initialization of centers. CHALLENGE 11.5. The website contains a sample program, and Figures 11.5 and 11.6 display the results. Each datapoint is displayed with a color and symbol that represent its cluster. An intuitive clustering of this data is to make two vertical clusters, as determined by the algorithm with the first initialization and k = 2. Note, however, that the distance between the top and bottom data points in each cluster is the same as the distance between the clusters (measured by the minimum distance between points in different clusters)! The two clusters determined by the second initialization have somewhat greater radii, but are not much worse. What is worse about them, though, is that there is less distance between clusters. If we choose to make too many clusters (k > 2), we add artificial distinctions between data points. CHALLENGE 11.6. The website contains a sample program, and Figures 11.7 ...
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This note was uploaded on 01/21/2012 for the course MAP 3302 taught by Professor Dr.robin during the Fall '11 term at University of Florida.

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