T-distributed stochastic neighbor embedding: Difference between revisions

Revision as of 19:48, 18 April 2014

Revision as of 19:50, 18 April 2014

Line 13:

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

The bandwidth of the [[Gaussian kernelskernel]]s <math>\sigma_i</math>, is set in such a way that the [[perplexity]] of the conditional distribution equals a predefined perplexity using a [[binary search]]. As a result, the bandwidth is adapted to the [[density]] of the data: smaller values of <math>\sigma_i</math> are used in denser parts of the data space.

t-SNE aims to learn a <math>d</math>-dimensional map <math>\mathbf{y}_1, \dots, \mathbf{y}_N</math> (with <math>\mathbf{y}_i \in \mathbb{R}^d</math>) that reflects the similarities <math>p_{ij}</math> as well as possible. To this end, it measures similarities <math>q_{ij}</math> between two points in the map <math>\mathbf{y}_i</math> and <math>\mathbf{y}_j</math>, using a very similar approach. Specifically, <math>q_{ij}</math> is defined as: