Linear basis-function t-SNE for fast nonlinear dimensionality reduction

t-distributed stochastic neighbor embedding (t-SNE) constitutes a nonlinear dimensionality reduction technique which is particularly suited to visualize high dimensional data sets with intrinsic nonlinear structures. A major drawback, however, consists in its squared complexity which makes the technique infeasible for large data sets or online application in an interactive framework. In addition, since the technique is non parametric, it possesses no direct method to extend the technique to novel data points. In this contribution, we propose an extension of t-SNE to an explicit mapping. In the limit, it reduces to standard non-parametric t-SNE, while offering a feasible nonlinear embedding function for other parameter choices. We evaluate the performance of the technique when trained on a small subpart of the given data only. It turns out that its generalization ability is good when evaluated with the standard quality curve. Further, in many cases, it obtains a quality which approximates the quality of t-SNE when trained on the full data set, albeit only 10% of the data are used for training. This opens the way towards efficient nonlinear dimensionality reduction techniques as required in interactive settings.