An Introduction to Nonlinear Dimensionality Reduction by Maximum Variance Unfolding

By Kilian Q. Weinberger, Lawrence K. Saul. AAAI Conference on Artificial Intelligence, 2006

302 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/29b72183b618c6a87b583fa0d03f3279900fbf25

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Citations in the corpus

GPU accelerated t-distributed stochastic neighbor embedding (2019, methodology): “A significant number of techniques have been proposed to do such dimensionality reduction with classical methods such as principal component analysis [13], [14], multi-dimensional scaling [15], and more modern methods such as Sammon mapping [16], curvilinear component analysis [17], stochastic neigh”
Dimension Reduction: A Guided Tour (2010, background): “Maximum Variance Unfolding (MVU) [96, 86, 77] preserves distances ‖xi − xj‖ = ‖yi − yj‖, as does Isomap, but it differs from Isomap in that it does so only locally: only distances between neighboring points are so constrained, as opposed to Isomap’s striving to preserve geodesic distances between po”
Large-scale manifold learning (2008, methodology): “Several manifold learning techniques have been proposed, e.g., Semidefinite Embedding (SDE) (Weinberger & Saul, 2006), Isomap (Tenenbaum et al., 2000), Laplacian Eigenmaps (Belkin & Niyogi, 2001) and Local Linear Embedding (LLE) (Roweis & Saul, 2000).”
Learning the 2-D Topology of Images (2007, methodology): “Nonparametric techniques such as Isomap [13], Local Linear Embedding (LLE) [12], or Semidefinite Embedding (SDE, also known as MVU for Maximum Variance Unfolding) [17] have computation time that scale polynomially in the number of examples n.”
Learning via Hilbert Space Embedding of Distributions (2007, methodology): “Clustering Teapots in a Ring We used the 400 consecutive teapot images (of size 76× 101 with RGB color) from [149].”
Kernelized Sorting (2008, background): “While there are a large number of algorithms for lowdimensional object layout (Maximum Variance Unfolding (MVU) [26], Local-Linear Embedding (LLE) [27], .”
Sparse Local Embeddings for Extreme Multi-label Classification (2015, background): “Note that the above problem formulation is somewhat similar to a few existing methods for nonlinear dimensionality reduction that also seek to preserve distances to a few near neighbors [18, 19].”
Universal Local Parametrizations via Heat Kernels and Eigenfunctions of the Laplacian (2007, background): “A variety of algorithms for manifold learning have been proposed [39, 3, 4, 29, 10, 12, 13, 52, 57, 19, 53, 54, 41, 40].”
SSE: Semantically Smooth Embedding for Knowledge Graphs (2017, background): “The first type performs the embedding task by modeling triple probability as distance (or similarity) between latent representations of entities and relations [11], [13], [15], [21], [22], [23].”
A dependence maximization view of clustering (2007, methodology): “Clustering Teapots in a Ring We used the 400 consecutive teapot images (of size 76◊101 with RGB color) from Weinberger & Saul (2006) .”
Dimensionality reduction on Anchorgraph with an efficient Locality Preserving Projection (2016, background): “[17] suggested the formulation which maximizes the Euclidean distances between the data points while retaining the distances in the neighborhood graph.”
Trace optimization and eigenproblems in dimension reduction methods (2011, background): “Maximum Variance Unfolding (MVU) is one such example; see [52, 53].”