In the version of this article initially published, the Acknowledgements section was incomplete and has now been amended to include the following: “NIH BRAIN Initiative awards U01 MH121282 to J.R.E and M.M.B, U19 MH114831 to J.R.E. and E.M.C., U19 MH114830 to H.Z., U01 MH114819 to G.F., 1U01MH114828 to K.Z. and J.C., RF1MH123220 to M.H. and R.H.S., and U19 MH114821. NIH awards R01DC019370 to R.H., R24MH114815 to R.H. and O.R.W., and R24 MH114788 to O.R.W. Nancy and Buster Alvord Endowment to C.D.K.” The changes have been made to the HTML and PDF versions of the article.

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In recent years the t-distributed Stochastic Neighbor Embedding (t-SNE) algorithm has become one of the most used and insightful techniques for exploratory data analysis of high-dimensional data. It reveals clusters of high-dimensional data points at different scales while only requiring minimal tuning of its parameters. However, the computational complexity of the algorithm limits its application to relatively small datasets. To address this problem, several evolutions of t-SNE have been developed in recent years, mainly focusing on the scalability of the similarity computations between data points. However, these contributions are insufficient to achieve interactive rates when visualizing the evolution of the t-SNE embedding for large datasets. In this work, we present a novel approach to the minimization of the t-SNE objective function that heavily relies on graphics hardware and has linear computational complexity. Our technique decreases the computational cost of running t-SNE on datasets by orders of magnitude and retains or improves on the accuracy of past approximated techniques. We propose to approximate the repulsive forces between data points by splatting kernel textures for each data point. This approximation allows us to reformulate the t-SNE minimization problem as a series of tensor operations that can be efficiently executed on the graphics card. An efficient implementation of our technique is integrated and available for use in the widely used Google TensorFlow.js, and an open-source C++ library.@en

Spatial and temporal brain transcriptomics has recently emerged as an invaluable data source for molecular neuroscience. The complexity of such data poses considerable challenges for analysis and visualization. We present BrainScope: A web portal for fast, interactive visual exploration of the Allen Atlases of the adult and developing human brain transcriptome. Through a novel methodology to explore high-dimensional data (dual t-SNE), BrainScope enables the linked, all-in-one visualization of genes and samples across the whole brain and genome, and across developmental stages. We show that densities in t-SNE scatter plots of the spatial samples coincide with anatomical regions, and that densities in t-SNE scatter plots of the genes represent gene co-expression modules that are significantly enriched for biological functions. We also show that the topography of the gene t-SNE maps reflect brain region-specific gene functions, enabling hypothesis and data driven research. We demonstrate the discovery potential of BrainScope through three examples: (i) analysis of cell type specific gene sets, (ii) analysis of a set of stable gene co-expression modules across the adult human donors and (iii) analysis of the evolution of co-expression of oligodendrocyte specific genes over developmental stages. Brain- Scope is publicly accessible at www.brainscope.nl.@en