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# Scalable Optimization of Neighbor Embedding for Visualization

*Proceedings of the 30th International Conference on Machine Learning*, PMLR 28(2):127-135, 2013.

#### Abstract

Neighbor embedding (NE) methods have found their use in data visualization but are limited in big data analysis tasks due to their O(n^2) complexity for n data samples. We demonstrate that the obvious approach of subsampling produces inferior results and propose a generic approximated optimization technique that reduces the NE optimization cost to O(n log n). The technique is based on realizing that in visualization the embedding space is necessarily very low-dimensional (2D or 3D), and hence efficient approximations developed for n-body force calculations can be applied. In gradient-based NE algorithms the gradient for an individual point decomposes into “forces” exerted by the other points. The contributions of close-by points need to be computed individually but far-away points can be approximated by their “center of mass”, rapidly computable by applying a recursive decomposition of the visualization space into quadrants. The new algorithm brings a significant speed-up for medium-size data, and brings “big data” within reach of visualization.