Book Chapter10.1007/BFB0020217
Kernel Principal Component Analysis
Bernhard Schölkopf,Alexander J. Smola,Klaus-Robert Müller +2 more
- 08 Oct 1997
- pp 583-588
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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
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TL;DR: A maximum entropy-based discriminative learning model that incorporates the minimal entropy (ME) set anomaly detection technique is proposed and the resulting probabilistic model can perform both nonparametric classification and anomaly detection simultaneously.
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•Dissertation
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Extracting information from a query image, for content based image retrieval
Nitin Gupta,Sukhendu Das,Sutanu Chakraborti +2 more
- 02 Mar 2015
TL;DR: A RADAR (Retrieval After Detection and Recognition) framework is proposed, to solve the problem of object-centric CBIR, which retrieves a set of samples from a database of identified categories, similar to the categories in a query image using a matching criteria based on features extracted from the localized region.
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Nonlinearly structured low-rank approximation
Ivan Markovsky,Konstantin Usevich +1 more
- 01 Dec 2014
TL;DR: This book proposes a computationally cheap and statistically consistent estimator based on a bias correction procedure, called Adjusted Least-Squares Estimation, which is successfully used for conic section fitting and was recently generalized to algebraic curve fitting.
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Kernel-Based Methods
Shigeo Abe
- 01 Jan 2010
TL;DR: Inspired by the success of support vector machines, to improve generalization and classification abilities, conventional pattern classification techniques have been extended to incorporate maximizing margins and mapping to a feature space.
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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