In Sections 7.14 and 7.15 we saw a clustering of a dataset with very differently scaled numeric variables. Yet, on first observation the resulting plot for the non-normalised dataset, from Section 7.14 and reproduced on the left below, pleasingly separates the clusters on the first principle component. After normalising the data in Section 7.15 the plot on the right below results, with more dispersion of the clusters.
Exercise: Explain why the clustering of the non-normalised dataset appears well separated with respect to the first principle component, and yet for what is claimed should be a better clustering after the data is normalised the separation is not at all pronounced.
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