Which cluster validation metric measures the ratio of total within-cluster scatter to between-cluster separation (where LOWER values indicate better clustering)?
$Davies-Bouldin index DB = (1/k) \sum_{i=1}^{k} max_{j != i} (S_{i} + S_{j}) / M_{ij}. Lower values indicate tighter, well-separated clusters.$
Which manifold learning technique preserves GEODESIC shortest-path distances between data points along a low-dimensional manifold?
ISOMAP constructs a k-nearest neighbor graph, computes all-pairs shortest paths (geodesic distances), and applies Classical MDS to preserve these distances.
What is the main advantage of DBSCAN over k-Means clustering?
DBSCAN discovers arbitrarily shaped clusters based on density and isolates noise points without requiring pre-specification of cluster count k.
In Kernel PCA, how is non-linear dimensionality reduction achieved?
Kernel PCA performs linear PCA on non-linearly mapped feature vectors $\phi(x)$ by operating entirely on the centered N x N Kernel matrix K.
Which dimensionality reduction technique is SUPERVISED (uses class labels)?
LDA is a supervised technique that utilizes class labels to maximize between-class variance relative to within-class variance.