Global Versus Local Methods in Nonlinear Dimensionality Reduction

By Vin de Silva, Josh Tenenbaum. 2002

975 citations recorded by the source corpus.

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Citations in the corpus

TriMap: Large-scale Dimensionality Reduction Using Triplets (2019, methodology): “As a result, PCA has been shown to be effective in preserving the global structure of the data (Silva & Tenenbaum, 2003).”
Spectral Methods for Dimensionality Reduction (2006, unknown): “Other algorithms closely related to the ones covered here include hessian related work LLE [Donoho and Grimes, 2003], c-Isomap [de Silva and Tenenbaum, 2003], local tangent space alignment [Zhang and Zha, 2004], geodesic nullspace analysis [Brand, 2004], and conformal eigenmaps [Sha and Saul, 2005].”
Large-scale manifold learning (2008, methodology): “Similarly, the matrix C was obtained from squared geodesic distances between the landmark nodes and all other nodes using single-centering as described in [6].”
A new embedding quality assessment method for manifold learning (2011, methodology): “Representative methods include Locally Linear Embedding (LLE) [5], [6], ISOMAP [7], [8], Laplacian Eigenmap (LE) [9], [10], Hessian LLE (HLLE) [11], Diffusion Maps (DM) [12], [13], Local Tangent Space Alignment (LTSA) [14], Maximum Variance Unfolding (MVU) [15], and Riemannian Manifold Learning (RML”
A review of predictive nonlinear theories for multiscale modeling of heterogeneous materials (2017, methodology): “On the other hand, a global technique like the complete isometric feature mapping (Isomap) approximately preserves relevant geometrical scales [303,304,307].”
A kernel view of the dimensionality reduction of manifolds (2004, background): “It then weights each of the edges in this graph by the Euclidean distance between neighboring points (a variant called C-Isomap also normalizes these weights [5]).”
Overview and comparative study of dimensionality reduction techniques for high dimensional data (2020, unknown): “Moreover, graph based approaches and manifold learning [184] NLDRTs have also been discussed.”
Geodesic entropic graphs for dimension and entropy estimation in manifold learning (2004, methodology): “Global approaches include isometric feature mapping (ISOMAP) [1] and coformal ISOMAP (C-ISOMAP) [15].”
Low-dimensional, free-energy landscapes of protein-folding reactions by nonlinear dimensionality reduction (2006, background): “As stated in the paper, the use of landmark points has been recently proposed [43, 44] to significantly improve the efficiency of the Isomap algorithm when dealing with extremely large data sets.”
Riemannian Manifold Learning (2008, unknown): “A large number of nonlinear manifold learning methods have been proposed recently, including isometric feature mapping (ISOMAP) [13], [ 14 ], [15], locally linear embedding (LLE) [16], [17], Laplacian eigenmaps [18], [19], Hessian eigenmaps [20], semidefinite embedding (SDE) [21], manifold charting ”
Hierarchical Stochastic Neighbor Embedding (2016, methodology): “Non-linear landmark techniques embed them using metrics that estimate geodesic distances between points [ST02,vdMH08].”
Learning Eigenfunctions Links Spectral Embedding and Kernel PCA (2004, methodology): “A formula has been proposed ( de Silva and Tenenbaum, 2003 ) to approximate Isomap”
Local and Global Regressive Mapping for Manifold Learning with Out-of-Sample Extrapolation (2010, methodology): “The framework proposed in (Bengio et al. 2003) generalizes Landmark ISOMap (Silva & Tenenbaum 2003).”