Expectation-Maximization (EM) algorithm for Gaussian Mixture Models (GMM) alternates between which two steps?
$EM alternates: E-step calculates posterior responsibilities gamma_{ik}; M-step updates parameters (\mu, \Sigma, pi) by maximizing expected log-likelihood.$
GMMs perform soft clustering because they assign each data point:
$GMM provides soft (probabilistic) assignments via responsibilities P(cluster k | x_i).$
What happens to the k-Means objective function (WCSS) as the number of clusters k increases up to n (number of data points)?
As k increases, WCSS monotonically decreases. When k = n, every point is its own centroid, so WCSS = 0.
Which index compares the similarity of two clusterings by assessing agreements and disagreements on pairs of elements?
Rand Index RI = (a + b) / C_2^n measures pair-wise agreements between predicted and true clusterings.
Davies-Bouldin Index evaluates clustering quality by computing the average ratio of:
Davies-Bouldin Index measures similarity between each cluster and its most similar one (ratio of scatter to separation). Lower values indicate better clustering.