T-distributed stochastic neighbor embedding: Difference between revisions

Revision as of 20:26, 25 July 2014

Revision as of 21:27, 23 September 2014

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Herein a heavy-tailed [[Student-t distribution]] is used to measure similarities between low-dimensional points in order to allow dissimilar objects to be modeled far apart in the map CITATION.

The locations of the points <math>\mathbf{y}_i</math> in the map are determined by minimizing the (non-symmetric) [[Kullback–Leibler divergence]] betweenof the two distributionsdistribution <math>PQ</math> andfrom the distribution <math>QP</math>, that is:

<math>KL(P||Q) = \sum_{i \neq j} p_{ij} \, \log \frac{p_{ij}}{q_{ij}}</math>

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.