T-distributed stochastic neighbor embedding: Difference between revisions

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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=2579-26052579–2605|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.

== t-Distributed Stochastic Neighbor Embedding ==

'''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.

The t-SNE algorithms comprises two main stages. First, t-SNE constructs a [[probability distribution]] over pairs of high-dimensional objects in such a way that similar objects have a high probability of being picked, whilst dissimilar points have an [[infinitessimal]] probability of being picked. Second, t-SNE defines a similar probability distribution over the points in the low-dimensional map, and it minimizes the [Kullback-Leibler divergence]] between the two distributions with respect to the locations of the points in the map.

t-SNE has been used in a wide range of applications, including [[computer security]] research<ref>{{cite journal|last=Gashi|first=I.|coauthors=Stankovic, V., Leita, C., Thonnard, O.|title=An Experimental Study of Diversity with Off-the-shelf AntiVirus Engines|journal=Proceedings of the IEEE International Symposium on Network Computing and Applications|year=2009|pages=4-114–11}}</ref>, [[music analysis]]<ref>{{cite journal|last=Hamel|first=P.|coauthors=Eck, D.|title=Learning Features from Music Audio with Deep Belief Networks|journal=Proceedings of the International Society for Music Information Retrieval Conference|year=2010|pages=339-344339–344}}</ref>, [[cancer research]]<ref>{{cite journal|last=Jamieson|first=A.R.|coauthors=Giger, M.L., Drukker, K., Lui, H., Yuan, Y., Bhooshan, N.|title=Exploring Nonlinear Feature Space Dimension Reduction and Data Representation in Breast CADx with Laplacian Eigenmaps and t-SNE|journal=Medical Physics 37(1)|year=2010|pages=339-351339–351|doi=10.1118/1.3267037|volume=37}}</ref>, and [[bio-informatics]]<ref>{{cite journal|last=Wallach|first=I.|coauthors=Liliean, R.|title=The Protein-Small-Molecule Database, A Non-Redundant Structural Resource for the Analysis of Protein-Ligand Binding|journal=Bioinformatics 25(5)|year=2009|pages=615-620615–620|doi=10.1093/bioinformatics/btp035|volume=25|issue=5}}</ref>.

== 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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== References ==

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