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
OS-ELM-FPGA: An FPGA-Based Online Sequential Unsupervised Anomaly Detector
Mineto Tsukada,Masaaki Kondo,Hiroki Matsutani +2 more
- 27 Aug 2018
TL;DR: An FPGA-based unsupervised anomaly detector that combines Autoencoder and an online sequential learning algorithm OS-ELM is proposed that achieves favorable anomaly detection accuracy compared to CPU and GPU implementations of BP-NNs.
11
Dictionary learning enhancement framework: Learning a non-linear mapping model to enhance discriminative dictionary learning methods
TL;DR: In the proposed framework, a non-linear mapping model is introduced to learn a feature space in a way that any standard discriminative dictionary learning algorithms could achieve higher classification accuracies.
11
Web document ranking via active learning and kernel principal component analysis
Fei Cai,Honghui Chen,Shu Zhen +2 more
TL;DR: This work is the first to perform the document ranking via dimension reductions in two dimensions, namely, the number of documents and features simultaneously, and is particularly suitable for document ranking on the noisy dataset in practice.
11
•Posted Content
Intrinsic Isometric Manifold Learning with Application to Localization
Ariel Schwartz,Ronen Talmon +1 more
TL;DR: This work builds a new metric and proposes a method for its robust estimation by assuming mild statistical priors and by using artificial neural networks as a mechanism for metric regularization and parametrization, and shows successful application to unsupervised indoor localization in ad-hoc sensor networks.
11
•Proceedings Article
Solving Interpretable Kernel Dimensionality Reduction
Chieh Wu,Jared Miller,Yale Chang,Mario Sznaier,Jennifer G. Dy +4 more
- 01 Jan 2019
TL;DR: The theoretical guarantees of ISM are extended to an entire family of kernels, thereby empowering ISM to solve any kernel method of the same objective and it is proved that each kernel within the family has a surrogate $\Phi$ matrix and the optimal projection is formed by its most dominant eigenvectors.
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