A kernel view of the dimensionality reduction of manifolds

By Jihun Ham, Daniel D. Lee, Sebastian Mika, Bernhard Schölkopf. International Conference on Machine Learning, 2004

632 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Computational Theory and Mathematics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/94f7f1ccd7e25c4d5f997d66365b00231478e987

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Citations in the corpus

Dimensionality reduction on Anchorgraph with an efficient Locality Preserving Projection (2016, background): “[24] stated the kernel view of some manifold based dimensionality reduction methods.”
Geometric diffusions as a tool for harmonic analysis and structure definition of data: diffusion maps. (2005, neutral): “Among the different techniques developed, particular attention has been paid to kernel methods (3).”
Two Manifold Problems with Applications to Nonlinear System Identification (2012, methodology): “We begin by examining PCA, a linear special case of manifold learning, and studying why it produces biased embeddings in the presence of noise.”
Kernel methods in machine learning (2007, neutral): “ation (Section 5.3). Kernel PCA can be shown to contain several popular dimensionality reduction algorithms as special cases, including LLE, Laplacian Eigenmaps and (approximately) Isomap (Ham et al. [60]). 5.2. Canonical correlation and measures of independence. Given two samples X,Y, canonical cor”
Dimensionality Reduction: A Comparative Review (2008, methodology): “Third, the spectral techniques Kernel PCA, Isomap, LLE, and Laplacian Eigenmaps can all be viewed upon as special cases of the more general problem of learning eigenfunctions [14, 57].”
Graph Embedding and Extensions: A General Framework for Dimensionality Reduction (2007, methodology): “1 Kernel Interpretation [13] and Out-of-Sample”
Diffusion maps, spectral clustering and reaction coordinates of dynamical systems (2005, methodology): “Similar constructions, falling under the general term of kernel methods have been used in the machine learning community for classification and regression [24].”
Type 1 and 2 mixtures of Kullback-Leibler divergences as cost functions in dimensionality reduction based on similarity preservation (2013, background): “Previous work has shown that this immunity stems partly from a property of shift invariance that allows appropriately normalized softmax similarities to mitigate the phenomenon of norm concentration.”
Dimensionality Reduction of Multimodal Labeled Data by Local Fisher Discriminant Analysis (2007, background): “However, it is sometimes dropped for the sake of simplicity (Ham et al., 2004).”
Local Kernels and the Geometric Structure of Data (2014, neutral): “There has been a movement to reinterpret kernel PCA methods geometrically, as a form of manifold learning, for a particular class of kernels.”
Learning a kernel matrix for nonlinear dimensionality reduction (2004, background): “…learning has recently at-tracted a great deal of attention (Tenenbaum et al., 2000; Roweis & Saul, 2000; Belkin & Niyogi, 2003; Saul & Roweis, 2003), and a number of authors (Ben-gio et al., 2004; Ham et al., 2004) have developed connections between manifold learning algorithms and kernel PCA.”
Learning with Kernels: support vector machines, regularization, optimization, and beyond (2001, neutral): “, via alignment [17] – kernels for dimensionality reduction [27]”
Learning Eigenfunctions Links Spectral Embedding and Kernel PCA (2004, background): “where the expectations are taken on the training set D. An extension of metric MDS to new points has already been proposed in Gower (1968) , in which”