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.
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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.
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Citations
A Spectral Series Approach to High-Dimensional Nonparametric Regression
Ann B. Lee,Rafael Izbicki +1 more
TL;DR: This work presents an orthogonal series estimator for predictors that are complex aggregate objects, such as natural images, galaxy spectra, trajectories, and movies, and ties together ideas from kernel machine learning, and Fourier methods.
Noisy multi-label semi-supervised dimensionality reduction
TL;DR: The proposed Noisy multi-label semi-supervised dimensionality reduction (NMLSDR) method, the noisy multi-labels are denoised and unlabeled data are labeled simultaneously via a specially designed label propagation algorithm and outperforms state-of-the-art multi- label feature extraction algorithms.
A comparison of PCA, KPCA and LDA for feature extraction to recognize affect in gait kinematics
Michelle Karg,Robert Jenke,Wolfgang Seiberl,Kolja Kuuhnlenz,Ansgar Schwirtz,Martin Buss +5 more
- 08 Dec 2009
TL;DR: Principal component analysis, kernel PCA, Kernel PCA and linear discriminant analysis are applied to kinematic parameters and compared for feature extraction and LDA in combination with naive Bayes leads to an accuracy of 91% for person-dependent recognition of four discrete affective states based on observation of barely a single stride.
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G-hash: towards fast kernel-based similarity search in large graph databases
Xiaohong Wang,Aaron Smalter,Jun Huan,Gerald H. Lushington +3 more
- 24 Mar 2009
TL;DR: In this article, a graph kernel function is defined to capture the intrinsic similarity of graphs and for fast similarity query processing, and a hash table is utilized to support efficient storage and fast search of the extracted local features.
Shared Gaussian Process Latent Variables Models
Carl Henrik Ek
- 01 Jan 2009
TL;DR: This thesis presents a Gaussian Process Latent Variable Model (GP-LVM) for shared dimensionality reduction without making assumptions about therelationship between the observations and suggests an extension to Canonical Correlation Analysis (CCA) called Non Consolidating Component Analysis (NCCA).
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