T-distributed stochastic neighbor embedding: Difference between revisions

Revision as of 20:38, 23 June 2013

Revision as of 20:38, 23 June 2013

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== t-Distributed Stochastic Neighbor Embedding ==

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'''t-Distributed Stochastic Neighbor Embedding (t-SNE)''' is a [[machine learning]] algorithm for [[dimensionality reduction]] developed by Laurens van der Maaten and [[Geoffrey Hinton]]<ref>{{cite journal|last=van der Maaten|first=L.J.P.|coauthors=Hinton, G.E.|title=Visualizing High-Dimensional Data Using t-SNE|journal=Journal of Machine Learning Research 9|year=2008|month=Nov|pages=2579-2605|url=http://jmlr.org/papers/volume9/vandermaaten08a/vandermaaten08a.pdf}}</ref>. It is a [[nonlinear dimensionality reduction]] technique that is particularly well suited for embedding high-dimensional data into a space of two or three dimensions, which can then be visualized in a scatter plot. 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.

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== Details ==

Given a set of <math>N</math> high-dimensional objects <math>\mathbf{x}_1, \dots, \mathbf{x}_N</math>, t-SNE first computes probabilities <math>p_{ij}</math> that are proportional to the similarity of objects <math>\mathbf{x}_i</math> and <math>\mathbf{x}_j</math>, as follows:

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The minimization of the Kullback-Leibler divergence with respect to the points <math>\mathbf{y}_i</math> is performed using [[gradient descent]]. The result of this optimization is a map that reflects the similarities between the high-dimensional inputs well.

== References ==

{{reflist}}

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