The Out-of-sample Extensions of t-SNE: From Gradient Descent to Fixed-point Iteration Algorithms

Paul Honeine

Abstract: This paper addresses the out-of-sample extension of the t-distributed stochastic neighbor embedding (t-SNE), namely extending the embedding to other data that were not considered in the training of the t-SNE. We demonstrate the ease of deriving the out-of-sample extension of t-SNE, thanks to the proper nature of t-SNE, namely without any auxiliary model. Several resolution strategies are devised, from gradient descent to fixed-point iteration algorithms. Moreover, we establish several theoretical findings that allow to understand the underlying optimization mechanism of the fixed-point iteration, by providing several appealing properties, including connections with the mean shift algorithm and the resolution of the pre-image problem in Machine Learning. Experimental results on three well-known real data sets show the relevance and efficiency of the proposed out-of-sample methods, with the repulsion-free fixed-point iteration outperforming the other methods.

Submission Type: Long submission (more than 12 pages of main content)

Assigned Action Editor: ~Dan_Garber1

Submission Number: 6887