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I Let dr single dcomplete IJ be the dissimilarities between a generic pair of clusters I, J. As the names indicate, these dissimilarities are built using single linkage and complete linkage, respectively. Briefly ellaborate whether the following inequality holds or not: single d IJ

I Let dr single dcomplete IJ be the dissimilarities between a generic pair of clusters I, J. As the names indicate, these dissimilarities are built using single linkage and complete linkage, respectively. Briefly ellaborate whether the following inequality holds or not: single d IJ

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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I Let dr single dcomplete IJ be the dissimilarities between a generic pair of clusters I, J. As the names indicate, these dissimilarities are built using single linkage and complete linkage, respectively. Briefly ellaborate whether the following inequality holds or not: single d IJ <dcomplete II The following data are acidity measurements (in pH scale) of n = 5 soil samples. The variables measured are results obtained with litmus paper (x1) and with electric probe (x2), and the samples (individuals) are labelled as usual 1 to 5 from top to bottom. X1 X2 6.22 6.65 6.49 6.5 6.58 6.35 6.41 6.57 6.14 6.7 With these data, perform agglomerative clustering using the manhattan metric and complete linkage. In particular, a) Compute and write the distance matrix between individuals, then b) report the steps of agglomerative clustering. At each stage of clustering, state the dissimilarity matrix and the new cluster formed. c) Sketch the dendrogram for this analysis. d) If the tree is cut at a height (distance) h = 0.51, how many clusters are formed at that value h and which sizes do they have? Write your replies to all items of this question in a single side of A4. Do NOT write on the textbox, instead upload a scan of your handwork.
Transcribed Image Text:I Let dr single dcomplete IJ be the dissimilarities between a generic pair of clusters I, J. As the names indicate, these dissimilarities are built using single linkage and complete linkage, respectively. Briefly ellaborate whether the following inequality holds or not: single d IJ <dcomplete II The following data are acidity measurements (in pH scale) of n = 5 soil samples. The variables measured are results obtained with litmus paper (x1) and with electric probe (x2), and the samples (individuals) are labelled as usual 1 to 5 from top to bottom. X1 X2 6.22 6.65 6.49 6.5 6.58 6.35 6.41 6.57 6.14 6.7 With these data, perform agglomerative clustering using the manhattan metric and complete linkage. In particular, a) Compute and write the distance matrix between individuals, then b) report the steps of agglomerative clustering. At each stage of clustering, state the dissimilarity matrix and the new cluster formed. c) Sketch the dendrogram for this analysis. d) If the tree is cut at a height (distance) h = 0.51, how many clusters are formed at that value h and which sizes do they have? Write your replies to all items of this question in a single side of A4. Do NOT write on the textbox, instead upload a scan of your handwork.
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