Think Globally, Fit Locally: Unsupervised Learning of Low Dimensional Manifold

By Lawrence K. Saul, Sam T. Roweis. Journal of machine learning research, 2003

1,587 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/8db95dbd08e4ee64fb258e5380e78cfa507ed94d

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Citations in the corpus

Face recognition using Laplacianfaces (2005, unknown): “Some nonlinear techniques have been proposed to discover the nonlinear structure of the manifold, e.g., Isomap [27], LLE [18], [20], and Laplacian Eigenmap [3].”
Nonlinear Dimensionality Reduction with Local Spline Embedding (2009, background): “Such a straightforward extension for out of samples can also be obtained in LLE [ 41 ] and LTSA [61].”
A survey of dimensionality reduction techniques (2014, methodology): “Locally linear embedding (LLE) [Roweis2000, Saul2003] is another technique used to learn manifolds close to the data and project them onto it.”
Structured Time Series Analysis for Human Action Segmentation and Recognition (2014, background): “Note that our goal is different from most latent variable models, which aim to identify τ [12], [13] and sometimes f (·) [17]–[19].”
Sparse multidimensional scaling using land-mark points (2004, unknown): “also derive Nyström-based out-of-sample extensions to other dimensionality reduction algorithms, including Locally Linear Embedding [10,23] and Laplacian Eigenmaps [24] (where the initial eigenvalue problem is not as acutely expensive as it is for Isomap).”
Learning Eigenfunctions Links Spectral Embedding and Kernel PCA (2004, methodology): “1 , the embedding obtained for a new point x converges to the extension of LLE proposed in (Saul and Roweis, 2002), as shown in (Bengio et al., 2004) (this is the kernel we actually used in the experiments reported here).”
A Physics-Constrained Data-Driven Approach Based on Locally Convex Reconstruction for Noisy Database (2019, methodology): “mental data points that are closest to the physical manifold, the locally linear reconstruction remains suitable for this scenario. In this sense, it is similar to the out-of-sample extension problem [63,67,68] where it is 16 desirable to add new projected data points (new samples) to a previously l”
Learning High Dimensional Correspondences from Low Dimensional Manifolds (2003, methodology): “There is no reason to assume that the high dimensional examples would lie on a purely low dimensional linear subspace as assumed by PCA and FA. In order to model the nonlinear low dimensional structure of this data, we generalize a recently-developed algorithm known as locally linear embedding (LLE)”
Nonlocal Estimation of Manifold Structure (2006, unknown): “This weight is obtained by the following equation (Saul & Roweis, 2002), KLLE(x, xi ) = ∑k j=1 G −1 i j∑k l=1 ∑k m=1 G −1 lm (2.2) D ow nloaded from http://direct.m it.edu/neco/article-pdf/18/10/2509/816637/neco.2006.18.10.2509.pdf by guest on 15 June 2021 tangent directions tangent plane Data on a…”
Discriminative analysis of resting-state functional connectivity patterns of schizophrenia using low dimensional embedding of fMRI (2010, methodology): “Some improved algorithms such as linear generalization (LG) approach (Saul and Roweis, 2003) and incremental LLE (ILLE) algorithm (Kouropteva et al., 2005) have also been proposed to solve this problem.”
Visual SLAM and Structure from Motion in Dynamic Environments (2018, methodology): “The method, known as Locally Linear Manifold Clustering (LLMC), is developed based on the Locally Linear Embedding (LLE) [135] algo-rithm.”
Super-resolution through neighbor embedding (2004, methodology): “These include isometric feature mapping (Isomap) [20] [21], locally linear embedding (LLE) [15] [16], and Laplacian eigenmap [3] [4].”