tSNE

tSNE, short for t-Distributed Stochastic Neighbor Embedding, is a nonlinear dimensionality reduction technique used primarily for data visualization. Developed by Laurens van der Maaten and Geoffrey Hinton in 2008, it aims to preserve local structure by modeling pairwise similarities between points in high-dimensional space and in a low-dimensional embedding.

In the high-dimensional space, the algorithm converts the distances between data points into conditional probabilities that reflect neighborhood relationships, using a Gaussian distribution with a per-point bandwidth tuned by a parameter called perplexity. The low-dimensional embedding uses a Student t-distribution to compute similar pairwise similarities, which helps to alleviate the crowding problem by allowing moderate–to–large distances to be represented more effectively. The two sets of similarities are compared via a cost function based on the Kullback–Leibler divergence, and the embedding is found by gradient descent with momentum and optional early exaggeration to form tight clusters early in optimization.

tSNE is commonly preceded by dimensionality reduction (often PCA) to reduce noise and improve speed. The method is computationally intensive for large datasets, but scalable variants such as Barnes–Hut tSNE reduce complexity substantially. Other extensions include parametric tSNE, which learns a neural network to map new data into the embedding space, and faster implementations such as FIt-SNE.

Applications of tSNE span diverse domains, including visualization of image feature vectors, word or document representations, and single-cell RNA sequencing data. Limitations include sensitivity to hyperparameters (notably perplexity and initialization), non-deterministic results, difficulty in interpreting global structure, and the need to re-compute embeddings for new data in non-parametric variants.