T-distributed stochastic neighbor embedding: Difference between revisions

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'''t-distributed stochastic neighbor embedding''' ('''t-SNE''') is a [[statistical]] method for visualizing high-dimensional data by giving each datapoint a ___location in a two or three-dimensional map. It is based on Stochastic Neighbor Embedding originally developed by Sam Roweis and [[Geoffrey Hinton]], and Sam Roweis<ref name=SNE>{{cite conference|author1-last=RoweisHinton|author1-first=SamGeoffrey| author2-last=HintonRoweis|author2-first=GeoffreySam|conference=[[Neural Information Processing Systems]]|title=Stochastic neighbor embedding|date= January 2002 |url=https://cs.nyu.edu/~roweis/papers/sne_final.pdf}}</ref>, where Laurens van der Maaten proposed the [[Student's t-distribution|''t''-distributed]] variant.<ref name=MaatenHinton>{{cite journal|last=van der Maaten|first=L.J.P.|author2=Hinton, G.E. |title=Visualizing Data Using t-SNE|journal=Journal of Machine Learning Research |volume=9|date=Nov 2008|pages=2579–2605|url=http://jmlr.org/papers/volume9/vandermaaten08a/vandermaaten08a.pdf}}</ref> It is a [[nonlinear dimensionality reduction]] technique for embedding high-dimensional data for visualization in a low-dimensional space of two or three dimensions. Specifically, it models each high-dimensional object by a two- or three-dimensional point in such a way that similar objects are modeled by nearby points and dissimilar objects are modeled by distant points with high probability.

The t-SNE algorithm comprises two main stages. First, t-SNE constructs a [[probability distribution]] over pairs of high-dimensional objects in such a way that similar objects are assigned a higher probability while dissimilar points are assigned a lower probability. Second, t-SNE defines a similar probability distribution over the points in the low-dimensional map, and it minimizes the [[Kullback–Leibler divergence]] (KL divergence) between the two distributions with respect to the locations of the points in the map. While the original algorithm uses the [[Euclidean distance]] between objects as the base of its similarity metric, this can be changed as appropriate. A Riemannian variant is [[Uniform manifold approximation and projection|UMAP]].