2DkcTXceO

328 The present’s future12435698107FIGURE 29.1Ward’s method agglomerative tree based on histograms.Example 29.2 Figure 29.4 displays simulated individual classical observations(Y 1 ,Y 2 ) drawn from bivariate normal distributions N 2 (µ, Σ). Thereare five samples each with n = 100 observations. Sample S = 1 has meanµ = (5, 0), standard deviations σ 1 = σ 2 = .25 and correlation coefficientρ = 0; samples S=2,3 have µ =(1, 1), σ 1 = σ 2 = .25 and ρ = 0; and samplesS =4, 5haveµ =(1, 1), σ 1 = σ 2 =1andρ = .8. Each of the samples can beaggregated to produce a bivariate histogram observation Y s , s =1,...,5.When a divisive algorithm for histogram data is applied to these data, threeclusters emerge containing the observations C 1 = {Y 1 }, C 2 = {Y 2 ,Y 3 }, andC 3 = {Y 4 ,Y 5 }, respectively. In contrast, applying algorithms, e.g., a K-means12731049568FIGURE 29.2Ward’s method agglomerative tree based on means.