The Elastic Embedding Algorithm for Dimensionality Reduction

By M. A. Carreira-Perpiñán. 2010

122 citations recorded by the source corpus.

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Citations in the corpus

Distributed optimization of deeply nested systems (2012, methodology): “In this experiment, instead of using random initial weights, we obtained initial values for the Z coordinates by running a nonlinear dimensionality reduction method, the elastic embedding (EE) (Carreira-Perpiñán, 2010); this gives significantly better embeddings than spectral methods; (Tenenbaum et ”
Barnes-Hut-SNE (2013, methodology): “A plethora of embedding techniques have been proposed over the last decade, e.g. , [5, 15, 20, 23, 25, 26].”
Hashing with binary autoencoders (2015, unknown): “Admittedly, there are objective functions that are more suited for information retrieval than the autoencoder, by explicitly encouraging distances in the original and Hamming space to match in order to preserve nearest neighbors [28, 3, 20, 17, 19, 18].”
Accelerating t-SNE using tree-based algorithms (2014, methodology): “Because the objective functions of most1 stochastic neighbor embedding techniques are non-convex, the minimization of the objective is typically performed using first-order or second-order gradient-descent techniques (Carreira-Perpiñán, 2010; Hinton and Roweis, 2003; Vladymyrov and Carreira-Perpiñán”
Interpretable dimensionality reduction of single cell transcriptome data with deep generative models (2017, background): “Equation (6) is a data-dependent term (depending on the high-dimensional data) that keeps nearby data points in the high-dimensional data nearby in the low-dimensional space 37 .”
Inductive Hashing on Manifolds (2013, methodology): “The results are consistent with the analysis in [4, 29].”
A Unifying Perspective on Neighbor Embeddings along the Attraction-Repulsion Spectrum (2020, background): “Carreira-Perpiñán (2010) and Linderman and Steinerberger (2019) noticed that the attractive term in the t-SNE loss function reduces to the loss function of Laplacian eigenmaps.”
Topological Data Analysis (2016, background): “Carreira-Perpinán (2010) provided an explanation of why t-SNE works.”