T-distributed stochastic neighbor embedding: Difference between revisions

Revision as of 14:22, 30 January 2014

Revision as of 20:41, 5 February 2014

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

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