GPGPU linear complexity t-SNE optimization

Nicola Pezzotti, Julian Thijssen, Alexander Mordvintsev, Thomas Hollt, Baldur van Lew, Boudewijn P.F. Lelieveldt, Elmar Eisemann, Anna Vilanova

Research output: Contribution to journalArticleAcademic

Abstract

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.
LanguageEnglish
JournalIEEE Transactions on Visualization and Computer Graphics
DOIs
StateE-pub ahead of print - 2020

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Computational complexity
Tensors
Scalability
Tuning
Textures
Hardware
Costs

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Pezzotti, N., Thijssen, J., Mordvintsev, A., Hollt, T., Lew, B. V., Lelieveldt, B. P. F., ... Vilanova, A. (2020). GPGPU linear complexity t-SNE optimization. IEEE Transactions on Visualization and Computer Graphics. DOI: 10.1109/TVCG.2019.2934307
Pezzotti, Nicola ; Thijssen, Julian ; Mordvintsev, Alexander ; Hollt, Thomas ; Lew, Baldur van ; Lelieveldt, Boudewijn P.F. ; Eisemann, Elmar ; Vilanova, Anna. / GPGPU linear complexity t-SNE optimization. In: IEEE Transactions on Visualization and Computer Graphics. 2020
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abstract = "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.",
author = "Nicola Pezzotti and Julian Thijssen and Alexander Mordvintsev and Thomas Hollt and Lew, {Baldur van} and Lelieveldt, {Boudewijn P.F.} and Elmar Eisemann and Anna Vilanova",
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Pezzotti, N, Thijssen, J, Mordvintsev, A, Hollt, T, Lew, BV, Lelieveldt, BPF, Eisemann, E & Vilanova, A 2020, 'GPGPU linear complexity t-SNE optimization' IEEE Transactions on Visualization and Computer Graphics. DOI: 10.1109/TVCG.2019.2934307

GPGPU linear complexity t-SNE optimization. / Pezzotti, Nicola; Thijssen, Julian; Mordvintsev, Alexander; Hollt, Thomas; Lew, Baldur van; Lelieveldt, Boudewijn P.F.; Eisemann, Elmar; Vilanova, Anna.

In: IEEE Transactions on Visualization and Computer Graphics, 2020.

Research output: Contribution to journalArticleAcademic

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AU - Pezzotti,Nicola

AU - Thijssen,Julian

AU - Mordvintsev,Alexander

AU - Hollt,Thomas

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AU - Eisemann,Elmar

AU - Vilanova,Anna

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Pezzotti N, Thijssen J, Mordvintsev A, Hollt T, Lew BV, Lelieveldt BPF et al. GPGPU linear complexity t-SNE optimization. IEEE Transactions on Visualization and Computer Graphics. 2020. Available from, DOI: 10.1109/TVCG.2019.2934307