Spectral Methods for Dimensionality Reduction

By Lawrence K. Saul, Kilian Q. Weinberger, Fei Sha, Jihun Ham, Daniel D. Lee. Semi-Supervised Learning, 2006

296 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Biomedical Engineering, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/47c0d8742e9c9868918e34a81bbe845e65ab1bcc

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In Atomic and Molecular Physics, and Optics

In Biomedical Engineering

In Computational Theory and Mathematics

Citations in the corpus

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”
A Survey of Modern Questions and Challenges in Feature Extraction (2015, methodology): “An overview of these and other related methods is provided in (Saul et al., 2006; Venna et al., 2007).”
Introduction to Semi-Supervised Learning (2009, unknown): “Related papers: [148]”
On Similarity Preserving Feature Selection (2013, unknown): “Many frameworks have been proposed to unify the aforementioned feature extraction methods in various ways [5], [33], [37], [43], [45].”
Dimensionality Reduction: A Comparative Review (2008, background): “Therefore, in the last decade, a large number of nonlinear techniques for dimensionality reduction have been proposed (see for an overview, e.g., [23] [95] [113]).”
Semi-supervised clinical text classification with Laplacian SVMs: an application to cancer case management (2013, methodology): “The resulting graph is a discretized approximation to the underlying manifold [8], and is used to formalize the ‘smoothness’ of a function on the manifold.”
Universal Local Parametrizations via Heat Kernels and Eigenfunctions of the Laplacian (2007, background): “A variety of algorithms for manifold learning have been proposed [41, 3, 4, 31, 13, 9, 10, 28, 59, 20, 55, 59, 56, 54, 43, 42].”
Semi-Supervised Dimensionality Reduction (2007, background): “5 is similar as that of the Laplacian spectral embedding methods [3, 10, 13], actually they are completely different.”
Label Propagation through Linear Neighborhoods (2006, unknown): “In general, these methods can be categorized into two classes: transductive learning ( e.g. (Joachims, 1999)) and inductive learning ( e.g. (Belkin et al , 2005)).”
Learning in high-dimensional multimedia data: the state of the art (2015, methodology): “Some other non-linear feature transformation methods include kernel PCA [76], Hessian LLE [14], Laplacian Eigenmaps [2], LTSA [102] and so on.”
Accelerating t-SNE using tree-based algorithms (2014, background): “Mekelweg 4, 2628 CD Delft, The Netherlands Editor: Aaron Courville”
Kernel Methods in Finance (2008, methodology): “This shows that kernels which are successful for large margin classification are not necessarily suitable for dimensionality reduction and vice versa ( Saul et al. 2006 ).”
Trace optimization and eigenproblems in dimension reduction methods (2011, background): “This in turn leads to eigenvalue problems [38].”
An Introduction to Nonlinear Dimensionality Reduction by Maximum Variance Unfolding (2006, methodology): “In essence, this is the goal of statistical methods for dimensionality reduction (Burges 2005; Saul et al. 2006).”