🧪 t-SNE Interactive Visualization

t-Distributed Stochastic Neighbor Embedding (t-SNE) is the standard technique for turning a high-dimensional dataset into a 2D picture a human can actually read. This simulation generates a synthetic dataset of points sampled from several separated Gaussian blobs in a 4–20 dimensional space, then runs the real t-SNE optimization: it computes Gaussian-kernel conditional probabilities between every pair of points in the original space (with per-point bandwidth chosen by binary search to hit a target perplexity), turns those into symmetric joint probabilities, initializes a random 2D layout, and repeatedly follows the exact gradient of the Kullback–Leibler divergence between the high-dimensional probabilities and a Student-t-distributed low-dimensional approximation. Watch the scattered initial layout resolve into distinct, separated clusters as the KL divergence readout falls, and use the perplexity slider to see how the size of the neighbourhood t-SNE considers "local" changes the shape of the resulting map.