Kernel Principal Component Analysis

By Bernhard Schölkopf, Alex Smola, K. Müller. 1997

Subfields: Representation & Self-Supervised Learning, Statistical Learning Theory

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Citations in the corpus

Relational autoencoder for feature extraction (2017, background): “Subsequent studies [12–16] overcome this issue by employing non-linear kernel functions.”
Hypothesis testing using pairwise distances and associated kernels (2012, background): “The latter requires empirical computation of the spectrum of kernel integral operators, a problem studied extensively in the context of kernel PCA (Schölkopf et al., 1997).”
Generative and Latent Mean Map Kernels (2010, methodology): “By using kernels that incorporate statistical dependence information, we can leverage a rich set of existing methods such as kernel support vector machines (SVMs) and kernel principal components analysis (kPCA) [19] to learn from this data.”
Taming VAEs (2018, background): “In the literature of spectral clustering and kernel PCA it is known that reconstructions based on a Gaussian Gram matrix may suffer phase-transitions (sudden change in eigen-values or reconstruction ﬁxed-points) as a function of the scale parameter [51, 52, 53, 54, 55].”
Deep UQ: Learning deep neural network surrogate models for high dimensional uncertainty quantification (2018, methodology): “One can alleviate the linearity constraint by using the kernel PCA (KPCA) [29, 30], which uses the kernel trick to discover nonlinear manifolds.”
Fast Robust PCA on Graphs (2015, methodology): “Fast Robust PCA on Graphs Nauman Shahid ∗ , Nathanael Perraudin, Vassilis Kalofolias, Gilles Puy † , Pierre Vandergheynst Email: { nauman.shahid, Signal Processing nathanael.perraudin, vassilis.kalofolias, pierre.vandergheynst @epﬂ.ch, † gilles.puy@inria.fr Switzerland Laboratory 2”
A Generalized Kernel Approach to Dissimilarity-based Classification (2002, methodology): “…to treat kernels as generalized distance measures and also strengthened the link to algorithms based on positive definite kernels, such as the support vector classifier (SVC) (Vapnik, 1995, Schölkopf, 1997) or the kernel principal component analysis (Schölkopf et al., 1999, Schölkopf, 1997).”
Toward a Quantitative Survey of Dimension Reduction Techniques (2019, methodology): “Kernel PCA ( K-PCA ) [79] and Gaussian Process Latent Variable Model ( GPLVM ) [80] are nonlinear extensions of PCA that use kernel methods and probabilistic models, respectively.”
A DEEP LEARNING APPROACH FOR CANCER DETECTION AND RELEVANT GENE IDENTIFICATION (2017, methodology): “25 Similarly, researchers have applied PCA to a set of combined genes of 13 data sets to obtain the linear representation of the gene expression and then apply a autoencoder to capture nonlinear relationships.”
Kernel Methods in Finance (2008, methodology): “The kernel trick was also employed to kernelise other methods such as PCA (Schölkopf et al., 1996, 1997; Schölkopf, 1997).”
Training highly multiclass classifiers (2014, methodology): “We then perform kernel PCA (Schoelkopf et al., 1999) on the combined feature representation using the intersection kernel (Barla et al., 2003) to produce a 1024-dimensional or 479-dimensional input vector per image (see Tab.”
Automated Machine Learning: Methods, Systems, Challenges (2019, unknown): “22) In [44], the authors generalize this type of data generative process to image data.”
The MITLL NIST LRE 2007 language recognition system (2008, methodology): “The loading matrix was calculated with direct Eigen decomposition [9] with a latent variable dimension (corank) of 40.”