Kernel PCA and De-Noising in Feature Spaces

By Sebastian Mika, Bernhard Schölkopf, Alex Smola, K. Müller, Matthias Scholz, Gunnar Rätsch. 1998

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Citations in the corpus

Characteristic Kernels and Infinitely Divisible Distributions (2014, methodology): “• Preimage algorithms (Mika et al., 1999; Fukumizu et al., 2013) and kernel herding algorithms (Chen et al.”
Kernel Bayes' Rule (2010, methodology): “In the case of the Gaussian kernel, a fixed point method can be used to sequentially optim izex [13].”
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].”
The Multiscale Laplacian Graph Kernel (2016, methodology): “We introduce a further layer of approximation by restricting ˜ W G to be the space spanned by the ﬁrst ˜ P P basis vectors (ordered by descending eigenvalue), effectively doing kernel PCA on { φ (˜ v ) } ˜ v ˜ V , equivalently, a low rank approximation of ˜ K .”
Time series filtering, smoothing and learning using the kernel Kalman filter (2005, background): “Although this might seem to be very strong an assumption, the efficiency of Kernel PCA (Mika et al., 1999) for denoising shows that such a noise model can cover a wide range of noise distributions in the input space.”
Diffusion kernels on graphs and other discrete structures (2002, background): “Kernel-based algorithms, such as Gaussian processes (Mackay, 1997), support vector machines (Burges, 1998), and kernel PCA (Mika et al., 1998), are enjoying great popularity in the statistical learning community.”
SWIRL: A sequential windowed inverse reinforcement learning algorithm for robot tasks with delayed rewards (2018, methodology): “The basic idea is to apply Kernelized PCA to the features before hierarchy learning, an-oft used technique in computer vision [20].”
Kernel PCA for novelty detection (2007, methodology): “The reconstruction error in F is similar to but diﬀers from the squared error in the denoising application of kernel PCA [26].”
Two view learning: SVM-2K, Theory and Practice (2005, methodology): “Methods of performing this include principle components analysis (PCA) [7], partial least squares [8], kernel independent component analysis (KICA) [1] and kernel canonical correlation analysis (KCCA) [5].”
Diffusion Kernels on Graphs and Other Discrete Input Spaces (2002, background): “Kernel-based algorithms, such as Gaussian processes (Mackay, 1997), support vector machines (Burges, 1998), and kernel PCA (Mika et al., 1998), are enjoying great popularity in the statistical learning community.”
ClusterGAN : Latent Space Clustering in Generative Adversarial Networks (2018, background): “This differentiates GANs from traditional dimensionality reduction techniques (Mika et al. 1999) (Maaten and Hinton 2008) which lack interpretability.”
Static prediction games for adversarial learning problems (2012, methodology): “To find such a solution, the data generator may solve a non-convex optimization problem as proposed by Mika et al. (1999), or may apply a non-iterative method (Kwok and Tsang, 2003) based on multidimensional scaling.”