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Visualizing Data using t-SNE - Journal of Machine Learning ...

JournalofMachineLearningResearch9 ,5000 LETilburg, King s College Road,M5S3G4 Toronto,ON,CanadaEditor:YoshuaBengioAbst ractWe presenta newtechniquecalled t-SNE thatvisualizeshigh-dimensionaldatabygivi ngeachdatapointa locationina two a variationofStochasticNeighborEmbedding(H intonandRoweis,2002)thatismucheasiertoop timize,andproducessignificantlybettervis ualizationsbyreducingthetendency betterthanexistingtechniquesat creatinga singlemapthatrevealsstructureat many particularlyimportantforhigh-dimensional datathatlieonseveraldifferent,butrelated ,low-dimensionalmanifolds, ,weshow howt-SNEcanuserandomwalksonneighborhoodg raphstoallowtheimplicitstructureofalloft hedatato influencethewayin whicha subsetofthedatais illustratetheperformanceoft-SNEona widevarietyofdatasetsandcompareit withmany othernon-parametricvisualizationtechniqu es,includingSammonmapping,Isomap, :visualization,dimensionalityreduction,m anifoldlearning,embeddingalgorithms, differentdomains,anddealswithdataofwidel yvaryingdimensionality.

Leibler divergence (which is in this case equal to the cross-entropy up to an additive constant). SNE minimizes the sum of Kullback-Leibler divergences over all datapoints using a gradient descent method. The cost function C is given by C =∑ i KL(PijjQi)=∑ i ∑ j pjji log p ji qjji; (2)

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