Generalized Discriminant Analysis Using a Kernel Approach

By B. G, A. F. Neural Computation, 2000

1,823 citations recorded by the source corpus.

Subfields: Analytical Chemistry, Artificial Intelligence, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/994e91efb53a4a6b04a562ec10751cd0bbcdeac5

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Citations in the corpus

Scenario Reduction Applied to Geostatistical Simulations (2013, background): “require the scalar product to be computed (Baudat and Anouar 2000, 2003). Scheidt and Caers (2009a) chose to use the Gaussian kernel k(x, y) = exp−‖x − y‖2/2σ 2.”
Adaptive computation and machine learning (1998, methodology): “In the first section of this chapter we introduced the Bayesian inference principle whose basis is given by Bayes’ theorem (see equation (3.1)). Excellent monographs introducing this principle in more detail are by Bernardo and Smith (1994) and by Robert (1994); for a more applied treatment of ideas”
Comments on "Globally Maximizing, Locally Minimizing: Unsupervised Discriminant Projection with Application to Face and Palm Biometrics" (2007, methodology): “The representative techniques are kernel principal component analysis (KPCA) [15] and kernel Fisher discriminant(KFD)[16],[ 17 ].Bothhaveproventobeeffective in many real-world applications [18], [19], [20].”
Locality Preserving Projections (2003, methodology): “Kernel method have recently been used to generalize PCA and LDA to nonlinear maps [64],[8].”
Covariance discriminative learning: A natural and efficient approach to image set classification (2012, methodology): “The kernel variant of LDA (KLDA) [4] is formulated using the kernel trick as follows.”
Dimensionality Reduction: A Comparative Review (2008, background): “Linear Discriminant Analysis [46], Generalized Discriminant Analysis [9], and Neighborhood Components Analysis [53, 106], and recently proposed metric learners [32, 8, 51, 137] are not included in the review, because of their supervised nature.”
Gabor-Based Region Covariance Matrices for Face Recognition (2008, methodology): “In KPCA and KDA, a radial basis function is used as a kernel function with the parameter (variance) chosen by cross-validation strategy, which has been widely employed in kernel-based learning algorithms [16].”
AdaBoost with SVM-based component classifiers (2008, background): “Input: a set of training samples with labels fðx1; y1Þ; . . . ; ðxN ; yN Þg, a ComponentLearn algorithm, the number of cycles T. 2.”
Optimizing the kernel in the empirical feature space (2005, methodology): “Given a training data set , ( ), the different algorithms, such as the support vector machine (SVM) [6], [10], [16], [22], kernel Fisher discriminant (KFD) [4], [15], [20], and kernel principal component analysis (KPCA) [23], perform only in a subspace of the feature space spanned by the images of…”
Benchmarking Least Squares Support Vector Machine Classifiers (2004, methodology): “This least squares regression problem (Bishop, 1995; Duda & Hart, 1973) yields the same linear discriminant wF as is obtained from a generalized eigenvalue problem in Baudat and Anouar (2000) and Mika et al.”
Dimensionality Reduction of Multimodal Labeled Data by Local Fisher Discriminant Analysis (2007, background): “FDA, LPP, and MCML can also be kernelized similarly (Baudat and Anouar, 2000; Mika et al., 2003; Belkin and Niyogi, 2003; He and Niyogi, 2004; Globerson and Roweis, 2006).”
Information, Divergence and Risk for Binary Experiments (2009, methodology): “…classifier (where αi = 1/m for all i ∈ I) (Devroye et al., 1996, Chapter 10) to the Generalised Portrait (Aizerman et al., 1964), the Generalised Discriminant (Baudat and Anouar, 2000) and the panoply of techniques inspired by Support Vector Machines (Schölkopf and Smola, 2002; Herbrich, 2002).”
Recent advances in visual and infrared face recognition - a review (2005, methodology): “Kernel PCA [88,89] and generalized discriminant analysis using a kernel approach [90] have been successful in pattern regression and classification tasks.”
Overview and comparative study of dimensionality reduction techniques for high dimensional data (2020, positive): “To accomplish better classiﬁcation, Baudat and Anouar [153] introduced a Generalized Discriminant Analysis (GDA) using the kernel functionality.”
Kernel Methods and Machine Learning (2014, background): “Learning models of this type have been explored by numerous researchers [10, 63, 76, 147, 178, 179, 180, 181, 189, 226, 241].”
Linear discriminant analysis: A detailed tutorial (2017, positive): “In other words, the φ function is used to map the original features into Z space by creating a non-linear combination of the original samples using a dot-products of it [3].”
Bayesian Framework for Least-Squares Support Vector Machine Classifiers, Gaussian Processes, and Kernel Fisher Discriminant Analysis (2002, methodology): “Also the SVM formulation has been related to Fisher Discriminant Analysis (Shashua, 1999).”