# Efficient Algorithms for t-distributed Stochastic Neighborhood Embedding

arXiv: https://arxiv.org/abs/1712.09005 · HTML: https://mlsanity.com/paper/1712.09005/

## Key facts

- Cited by 75 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Dec 2017.

## Built on by (most cited first, 30 of 75)

- [Interpretable Machine Learning: Fundamental Principles and 10 Grand Challenges](https://mlsanity.com/paper/2103.11251/) (2021)
- [Theoretical Foundations of t-SNE for Visualizing High-Dimensional Clustered Data](https://mlsanity.com/paper/2105.07536/) (2021)
- [From t-SNE to UMAP with contrastive learning](https://mlsanity.com/paper/2206.01816/) (2022)
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- [Unsupervised visualization of image datasets using contrastive learning](https://mlsanity.com/paper/2210.09879/) (2022)
- [Hierarchical Nearest Neighbor Graph Embedding for Efficient Dimensionality Reduction](https://mlsanity.com/paper/2203.12997/) (2022)
- [A Probabilistic Graph Coupling View of Dimension Reduction](https://mlsanity.com/paper/2201.13053/) (2022)
- [Question-guided Knowledge Graph Re-scoring and Injection for Knowledge Graph Question Answering](https://mlsanity.com/paper/2410.01401/) (2024)
- [Uniform Manifold Approximation with Two-phase Optimization](https://mlsanity.com/paper/2205.00420/) (2022)
- [SNEkhorn: Dimension Reduction with Symmetric Entropic Affinities](https://mlsanity.com/paper/2305.13797/) (2023)
- [t-SNE, Forceful Colorings and Mean Field Limits](https://mlsanity.com/paper/2102.13009/) (2021)
- [Merging and Splitting Diffusion Paths for Semantically Coherent Panoramas](https://mlsanity.com/paper/2408.15660/) (2024)
- [SQuadMDS: a lean Stochastic Quartet MDS improving global structure preservation in neighbor embedding like t-SNE and UMAP](https://mlsanity.com/paper/2202.12087/) (2022)
- [Multi-modal Differentiable Unsupervised Feature Selection](https://mlsanity.com/paper/2303.09381/) (2023)
- [ActUp: Analyzing and Consolidating tSNE and UMAP](https://mlsanity.com/paper/2305.07320/) (2023)
- [Intensity Profile Projection: A Framework for Continuous-Time Representation Learning for Dynamic Networks](https://mlsanity.com/paper/2306.06155/) (2023)
- [Assessing and improving reliability of neighbor embedding methods: a map-continuity perspective](https://mlsanity.com/paper/2410.16608/) (2024)
- [IAN: Iterated Adaptive Neighborhoods for manifold learning and dimensionality estimation](https://mlsanity.com/paper/2208.09123/) (2022)
- [Convergence analysis of t-SNE as a gradient flow for point cloud on a manifold](https://mlsanity.com/paper/2401.17675/) (2024)
- [CLICv2: Image Complexity Representation via Content Invariance Contrastive Learning](https://mlsanity.com/paper/2503.06641/) (2025)
- [DREAMS: Preserving both Local and Global Structure in Dimensionality Reduction](https://mlsanity.com/paper/2508.13747/) (2025)
- [Laplacian-based Cluster-Contractive t-SNE for High Dimensional Data Visualization](https://mlsanity.com/paper/2207.12214/) (2022)
- [NeuroDAVIS: A neural network model for data visualization](https://mlsanity.com/paper/2304.01222/) (2023)
- [Accelerating hyperbolic t-SNE](https://mlsanity.com/paper/2401.13708/) (2024)
- [Review of Deep Representation Learning Techniques for Brain-Computer Interfaces and Recommendations](https://mlsanity.com/paper/2405.19345/) (2024)
- [Contrastive analysis for scatterplot-based representations of dimensionality reduction](https://mlsanity.com/paper/2101.12044/) (2021)
- [Deep Recursive Embedding for High-Dimensional Data](https://mlsanity.com/paper/2104.05171/) (2021)
- [Revised Conditional t-SNE: Looking Beyond the Nearest Neighbors](https://mlsanity.com/paper/2302.03493/) (2023)
- [Sailing in high-dimensional spaces: Low-dimensional embeddings through angle preservation](https://mlsanity.com/paper/2406.09876/) (2024)
- [Deep Learning in Single-Cell and Spatial Transcriptomics Data Analysis: Advances and Challenges from a Data Science Perspective](https://mlsanity.com/paper/2412.03614/) (2024)

## Abstract (arXiv)

t-distributed Stochastic Neighborhood Embedding (t-SNE) is a method for dimensionality reduction and visualization that has become widely popular in recent years. Efficient implementations of t-SNE are available, but they scale poorly to datasets with hundreds of thousands to millions of high dimensional data-points. We present Fast Fourier Transform-accelerated Interpolation-based t-SNE (FIt-SNE), which dramatically accelerates the computation of t-SNE. The most time-consuming step of t-SNE is a convolution that we accelerate by interpolating onto an equispaced grid and subsequently using the fast Fourier transform to perform the convolution. We also optimize the computation of input similarities in high dimensions using multi-threaded approximate nearest neighbors. We further present a modification to t-SNE called "late exaggeration," which allows for easier identification of clusters in t-SNE embeddings. Finally, for datasets that cannot be loaded into the memory, we present out-of-core randomized principal component analysis (oocPCA), so that the top principal components of a dataset can be computed without ever fully loading the matrix, hence allowing for t-SNE of large datasets to be computed on resource-limited machines.