Book Chapter10.1007/BFB0020217
Kernel Principal Component Analysis
Bernhard Schölkopf,Alexander J. Smola,Klaus-Robert Müller +2 more
- 08 Oct 1997
- pp 583-588
2.6K
TL;DR: A new method for performing a nonlinear form of Principal Component Analysis by the use of integral operator kernel functions is proposed and experimental results on polynomial feature extraction for pattern recognition are presented.
read more
Abstract: A new method for performing a nonlinear form of Principal Component Analysis is proposed. By the use of integral operator kernel functions, one can efficiently compute principal components in highdimensional feature spaces, related to input space by some nonlinear map; for instance the space of all possible d-pixel products in images. We give the derivation of the method and present experimental results on polynomial feature extraction for pattern recognition.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Modelling life cycle related and individual shapevariation in biological specimens
Yulia Hicks,Andrew David Marshall,Paul L. Rosin,Ralph R. Martin,Micha Bayer,David G. Mann +5 more
- 01 Jan 2002
TL;DR: A novel model based on principal curves representing the life cycle related shape variation of a number of diatom species has been developed and is suitable for reconstruction purposes, allowing it to produce drawings of a variety of diatoms shapes, thus providing a link between the photographs and drawings.
•Posted Content
Random Maxout Features
TL;DR: This paper derives generalization bounds for learning that assess the error in approximating locally linear functions by linear functions in the maxout feature space, and empirically evaluates the efficacy of the approach on the MNIST and TIMIT classification tasks.
8
Geodesic Forests
Meghana Madhyastha,Gongkai Li,Veronika Strnadová-Neeley,J.D. Browne,Joshua T. Vogelstein,Randal Burns,Carey E. Priebe +6 more
- 23 Aug 2020
TL;DR: In this paper, an unsupervised random forest approach called geodesic forests (GF) is proposed to estimate the distance between data points in linear and nonlinear manifolds with noise.
8
Translation Invariance in the Polynomial Kernel Space and Its Applications in kNN Classification
György Kovács,Andras Hajdu +1 more
TL;DR: The theoretical background of linear invariance in the polynomial kernel space is examined, the centered correlation and centered Euclidean dissimilarity in kernel space are introduced, formulas to compute it efficiently are deduced and the experimental results show that the presented techniques are highly competitive in similarity or Dissimilarity based classification methods.
8
Machine learning-assisted high-throughput exploration of interface energy space in multi-phase-field model with CALPHAD potential
Vahid Attari,Raymundo Arroyave +1 more
TL;DR: The study shows that the machine learning-reinforced phase-field method is a convenient approach to analyze microstructure design space in the framework of the ICME.
8
References
Support-Vector Networks
Corinna Cortes,Vladimir Vapnik +1 more
TL;DR: High generalization ability of support-vector networks utilizing polynomial input transformations is demonstrated and the performance of the support- vector network is compared to various classical learning algorithms that all took part in a benchmark study of Optical Character Recognition.
A training algorithm for optimal margin classifiers
Bernhard E. Boser,Isabelle Guyon,Vladimir Vapnik +2 more
- 01 Jul 1992
TL;DR: A training algorithm that maximizes the margin between the training patterns and the decision boundary is presented, applicable to a wide variety of the classification functions, including Perceptrons, polynomials, and Radial Basis Functions.
Nonlinear component analysis as a kernel eigenvalue problem
TL;DR: A new method for performing a nonlinear form of principal component analysis by the use of integral operator kernel functions is proposed and experimental results on polynomial feature extraction for pattern recognition are presented.
Application of the Karhunen-Loeve procedure for the characterization of human faces
Michael Kirby,Lawrence Sirovich +1 more
TL;DR: The use of natural symmetries (mirror images) in a well-defined family of patterns (human faces) is discussed within the framework of the Karhunen-Loeve expansion, which results in an extension of the data and imposes even and odd symmetry on the eigenfunctions of the covariance matrix.
2.8K
Simplified neuron model as a principal component analyzer
TL;DR: A simple linear neuron model with constrained Hebbian-type synaptic modification is analyzed and a new class of unconstrained learning rules is derived.
2.6K