In the k-Means clustering algorithm, what objective function is minimized during iteration?
k-Means iteratively minimizes WCSS = \sum_{i=1}^{k} sum_{x in $C_i$} ||x - mu_i||^2.
How does the k-Means++ initialization technique improve standard k-Means clustering?
$k-Means++ selects initial centroids probabilistically based on squared distance D(x)^2 from nearest existing centroid, avoiding poor local minima.$
What is a known limitation of the standard k-Means clustering algorithm?
k-Means converges to local minima (sensitive to initial seeds), assumes spherical clusters, and is affected heavily by outliers.
In Hierarchical Agglomerative Clustering, which linkage criterion merges clusters based on the MINIMUM distance between any single pair of points?
Single linkage defines distance between clusters A and B as min { d(x, y) : x in A, y in B }. It is susceptible to chaining.
Which hierarchical clustering linkage criterion merges clusters based on the MAXIMUM distance between any pair of points in the two clusters?
Complete linkage uses max { d(x, y) : x in A, y in B }, producing compact, spherical clusters.