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This paper investigates the theoretical foundations of the t-distributed stochastic neighbor embedding (t-SNE) algorithm, a popular nonlinear dimension reduction and data visualization method.
Multidimensional Scaling
Joseph B Kruskal · 1978
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Increased rates of convergence through learning rate adaptation
Robert A Jacobs · 1988
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Kernel principal component analysis
Bernhard Schölkopf, Alexander Smola, and Klaus-Robert Müller · 1997
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Stochastic neighbor embedding
Geoffrey Hinton and Sam T Roweis · 2002
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Laplacian eigenmaps for dimensionality reduction and data representation
Mikhail Belkin and Partha Niyogi · 2003
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Numerical methods for ordinary differential equations
John Charles Butcher · 2008
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Visualizing data using t-SNE
Laurens van der Maaten and Geoffrey Hinton · 2008
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Heavy-tailed symmetric stochastic neighbor embedding
Zhirong Yang, Irwin King, Zenglin Xu, and Erkki Oja · 2009
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The elastic embedding algorithm for dimensionality reduction
Miguel A Carreira-Perpinán · 2010
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Geršgorin and his circles , volume 36
Richard S Varga · 2010
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Noise thresholds for spectral clustering
Sivaraman Balakrishnan, Min Xu, Akshay Krishnamurthy, and Aarti Singh · 2011
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Shift-invariant similarities circumvent distance concentration in stochastic neighbor embedding and variants
John A Lee and Michel Verleysen · 2011
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m-SNE: Multiview stochastic neighbor embedding
Bo Xie, Yang Mu, Dacheng Tao, and Kaiqi Huang · 2011
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The singular values and vectors of low rank perturbations of large rectangular random matrices
Florent Benaych-Georges and Raj Rao Nadakuditi · 2012
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Eigenvalues of the laplacian and their relationship to the connectedness of a graph
Anne Marsden · 2013
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Visualization of snps with t-SNE
Alexander Platzer · 2013
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Hanson-wright inequality and sub-gaussian concentration
Mark Rudelson and Roman Vershynin · 2013
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Two key properties of dimensionality reduction methods
John A Lee and Michel Verleysen · 2014
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Accelerating t-SNE using tree-based algorithms
Laurens van der Maaten · 2014
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Silhouette analysis for human action recognition based on supervised temporal t-SNE and incremental learning
Jian Cheng, Haijun Liu, Feng Wang, Hongsheng Li, and Ce Zhu · 2015
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Parametric nonlinear dimensionality reduction using kernel t-SNE
Andrej Gisbrecht, Alexander Schulz, and Barbara Hammer · 2015
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Metgem software for the generation of molecular networks based on the t-SNE algorithm
Florent Olivon, Nicolas Elie, Gwendal Grelier, Fanny Roussi, Marc Litaudon, and David Touboul · 2018
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The art of using t-SNE for single-cell transcriptomics
Dmitry Kobak and Philipp Berens · 2019
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Clustering with t-SNE, provably
George C Linderman and Stefan Steinerberger · 2019
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Fast interpolation-based t-SNE for improved visualization of single-cell RNA-seq data
George C Linderman, Manas Rachh, Jeremy G Hoskins, Stefan Steinerberger, and Yuval Kluger · 2019
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t-viSNE: Interactive assessment and interpretation of t-SNE projections
Angelos Chatzimparmpas, Rafael M Martins, and Andreas Kerren · 2020
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Spectral clustering revisited: Information hidden in the fiedler vector
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Nicola Pezzotti, Boudewijn PF Lelieveldt, Laurens Van Der Maaten, Thomas Höllt, Elmar Eisemann, and Anna Vilanova · 2016
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50 years of data science
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Stochastic neighbor embedding separates well-separated clusters
Uri Shaham and Stefan Steinerberger · 2017
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The galah survey: classification and diagnostics with t-SNE reduction of spectral information
Gregor Traven, Gal Matijevič, Tomaz Zwitter, M Žerjal, Janez Kos, Martin Asplund, Joss Bland-Hawthorn, Andrew R Casey, Gayandhi De Silva, Kenneth Freeman, et al · 2017
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An analysis of the t-SNE algorithm for data visualization
Sanjeev Arora, Wei Hu, and Pravesh K Kothari · 2018
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Rate-optimal perturbation bounds for singular subspaces with applications to high-dimensional statistics
T Tony Cai and Anru Zhang · 2018
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Adela DePavia and Stefan Steinerberger · 2020
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Tree-sne: Hierarchical clustering and visualization using t-sne
Isaac Robinson and Emma Pierce-Hoffman · 2020
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Concentration of kernel matrices with application to kernel spectral clustering
Arash A Amini and Zahra S Razaee · 2021
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Singular vector and singular subspace distribution for the matrix denoising model
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The specious art of single-cell genomics
Tara Chari, Joeyta Banerjee, and Lior Pachter · 2021
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Initialization is critical for preserving global data structure in both t-SNE and UMAP
Dmitry Kobak and George C Linderman · 2021
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Understanding how dimension reduction tools work: An empirical approach to deciphering t-sne, umap, trimap, and pacmap for data visualization
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Xiucai Ding and Rong Ma · 2022
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