T-distributed stochastic neighbor embedding: Difference between revisions

Revision as of 06:11, 17 March 2016

Revision as of 20:38, 31 March 2016

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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:

: <math>p_{j\mid i} = \frac{\exp(-\lVert\mathbf{x}_i - \mathbf{x}_j\rVert^2 / 2\sigma_i^2)}{\sum_{k \neq i\ell} \exp(-\lVert\mathbf{x}_i_\ell - \mathbf{x}_k\rVert^2 / 2\sigma_i^2)},</math>

: <math>p_{ij} = \frac{p_{j\mid i} + p_{i\mid j}}{2N}</math>