The pre-image problem in kernel methods

By James T. Kwok, Ivor Wai-Hung Tsang. 2003

504 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

Kernel Mean Embedding of Distributions: A Review and Beyonds (2016, methodology): “Many classical learning algorithms—such as the perceptron (Rosenblatt 1958), support vector machine (SVM) (Cortes and Vapnik 1995), and principal component analysis (PCA) (Pearson 1901, Hotelling 1933)—employ data instances, e.g., x,x′ ∈ X , only through an inner product 〈x,x′〉, which basically is a”
A Novel Algorithm for the Automatic Detection of Sleep Apnea From Single-Lead ECG (2015, methodology): “After that, the EDR is computed in the feature space and then mapped back to the input space by means of pre-image [20].”
Computer Vision - ECCV 2004 (2004, methodology): “when the 3-D points lie on a plane [16].”
Optimizing the Latent Space of Generative Networks (2017, background): “All of these inverting efforts are instances of the pre-image problem , [Kwok and Tsang, 2004].”
Kernel Methods in Computer Vision (2009, methodology): “It is noteworthy that [Kwok and Tsang, 2004] later introduced a different optimization technique to solve the preimage problem of kernelPCA for certain kernel types, achieving improved denoising results and higher numerical stability.”
A Review of Feature Reduction Techniques in Neuroimaging (2013, background): “linear SVM), continuing efforts in solving the ‘pre-image problem’ (Kwok and Tsang 2004) have recently allowed extraction of feature/voxel weights in non-linear feature spaces (e.”
Iterative kernel principal component analysis for image modeling (2005, methodology): “For the minimization, we use gradient descent [6] with starting points obtained from the method of [28].”
A Nonrigid Kernel-Based Framework for 2D-3D Pose Estimation and 2D Image Segmentation (2011, unknown): “This is referred to in the literature as the preimage problem [25].”