For a classification task with C classes, what is the MAXIMUM number of non-zero linear discriminants (components) that LDA can extract?
Between-class scatter matrix $S_{B}$ has rank at most C - 1, restricting LDA to at most C - 1 discriminant dimensions.
How does Singular Value Decomposition (SVD) of a matrix X (size N x d) relate to Principal Component Analysis?
For centered X, $X^{T}$ $X = V \Sigma^2 V^{T}$. The right singular vectors V are the principal component directions, and singular values sigma_i = sqrt((N-1) * lambda_i).
In a Gaussian Mixture Model (GMM) with K components, what algorithm is used to estimate the parameters (means, covariances, mixing coefficients)?
GMM parameters are estimated via EM: E-step calculates posterior responsibilities gamma_{ik}; M-step updates component parameters.
What problem does t-SNE (t-Distributed Stochastic Neighbor Embedding) solve in low-dimensional visualizations compared to standard SNE?
t-SNE uses a 1-degree-of-freedom Student-t distribution for low-dimensional distances, allowing moderate distances in high-dim space to map to larger distances in 2D/3D.
The Silhouette Coefficient s(i) for a sample i is bounded in which range?
s(i) = (b(i) - a(i)) / max(a(i), b(i)) lies in [-1, +1]. Values near +1 indicate excellent clustering, near 0 overlapping, negative misclassified.