IJ IJ Let d'single, daverage be the dissimilarities between a generic pair of clusters I, J. As the names indicate, these dissimilarities are built using single linkage and average linkage, respectively. Briefly ellaborate whether the following inequality holds or not: IJ d single average IJ 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 6.85 6.69 6.12 6.34 6.2 6.53 6.57 6 6.44 6.38 With these data, perform agglomerative clustering using the manhattan metric and single 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 = 0.14, how many clusters are formed at that value h and which sizes do they have?

IJ IJ Let d'single, daverage be the dissimilarities between a generic pair of clusters I, J. As the names indicate, these dissimilarities are built using single linkage and average linkage, respectively. Briefly ellaborate whether the following inequality holds or not: IJ d single average IJ 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 6.85 6.69 6.12 6.34 6.2 6.53 6.57 6 6.44 6.38 With these data, perform agglomerative clustering using the manhattan metric and single 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 = 0.14, how many clusters are formed at that value h and which sizes do they have?