SOA ATPAAdvanced Topics in Predictive Analytics

Before running k-means on variables with very different scales (e.g., premium in dollars and age in years), the analyst should:

In a scree plot of PCA eigenvalues, the recommended number of components to retain by the 'elbow' rule is the point where:

A clustered point has average within-cluster distance $a_i=2$ and average distance to the nearest other cluster $b_i=5$. Calculate its silhouette coefficient.

A categorical rating variable (vehicle make/model) has over 500 levels. Explain the risk of using simple target-mean encoding for this variable and propose a safer alternative.