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
Improving Word Embeddings Using Kernel PCA
Vishwani Gupta,Sven Giesselbach,Stefan Rüping,Christian Bauckhage +3 more
- 01 Aug 2019
TL;DR: This paper uses word embeddings generated using both word2vec and fastText models and enrich them with morphological information of words, derived from kernel principal component analysis (KPCA) of word similarity matrices, in order to reduce training time and enhance their performance.
Cognitive Insights into Sentic Spaces Using Principal Paths
Edoardo Ragusa,Paolo Gastaldo,Rodolfo Zunino,Marco Jacopo Ferrarotti,Walter Rocchia,Sergio Decherchi +5 more
TL;DR: A protocol for evaluating the coherence between an embedding space and a given cognitive model is developed, using the recently introduced notion of principal path, which can support the exploration of a high-dimensional space.
10
•Posted Content
Robust Generative Restricted Kernel Machines using Weighted Conjugate Feature Duality
TL;DR: Experiments show that the weighted RKM is capable of generating clean images when contamination is present in the training data, and that the robust method also preserves uncorrelated feature learning through qualitative and quantitative experiments on standard datasets.
Robust nuclear signal reconstruction by a novel ensemble model aggregation procedure
TL;DR: In this work, three different methods for aggregating the model outcomes are investigated and a novel procedure is proposed for obtaining robust ensemble-aggregated outputs.
Kernel optimisation for KPCA based on Gaussianity estimation
TL;DR: A kernel parameter optimisation method by using principle component subspace-based Gaussianity estimation, based on the idea that optimal kernel parameters lead the mapped feature space close to Gaussian distribution, is proposed.
10
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