MML-15-08: t-SNE Mathematics: High-Dimensional Affinities, Student-t Kernels & Gradient Flow – Practice Quiz

Deconstruct the complete mathematical machinery of Stochastic Neighbor Embedding (SNE) and t-Distributed Stochastic Neighbor Embedding (t-SNE): asymmetric Gaussian conditional probabilities $p_{j|i}$, Shannon entropy and Perplexity-driven binary search for local bandwidths $\sigma_i$, symmetrized joint affinities $p_{ij}$, the high-dimensional crowding problem, heavy-tailed Cauchy / Student-$t$ kernels $q_{ij}$, and the analytical KL divergence gradient flow. Aligns with Prerequisites: QS 15.7, Part 11; Cognitive Level: Tier 2–4.