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 logn). The technique is based on realizing that in visualization the embedding space is necessarily very lowdimensional (2D or 3D), and hence ecient approximations developed for n-body force calculations can be applied. In gradientbased 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 signicant speed-up for medium-size data, and brings \big data" within reach of visualization.
['Zhirong Yang', 'Jaakko Peltonen', 'Samuel Kaski']
Scalable Optimization of Neighbor Embedding for Visualization