Kernel Fisher’s linear discriminant analysis (KFLDA) has been proposed for nonlinear binary classification (Mika, Rätsch, Weston, Schölkopf and Müller, 1999, Baudat and Anouar, 2000). It is a hybrid method of the classical Fisher’s linear discriminant analysis and a kernel machine. Experimental results (e.g., Schölkopf and Smola, 2002) have shown that the KFLDA performs slightly better in terms...

Quadratic forms q(x1, . . . , xn) over a field k are the classical examples of nonlinear scalar-valued functions on a vector space V = k, and they lie at the foundation of nineteenth-century analytic geometry. Motivated by problems such as finding the axes of a conic, geometers studied quadratic forms under symmetries of V . Given two quadratic forms q, q′ on V , how may we tell if q and q′ are...

Nonlinear Support Vector Machines (SVMs) are investigated for visual sex classification with low resolution "thumbnail" faces (21by-12 pixels) processed from 1,755 images from the FE RET face database. The performance of SVMs is shown to be superior to traditional pattern classifiers (Linear, Quadratic, Fisher Linear Discriminant, Nearest-Neighbor) as well as more modern techniques such as Radi...

An algorithm is introduced to assess spectral quality for peptide CID spectra acquired by a quadrupole ion trap mass spectrometer. The method employs a quadratic discriminant function calibrated with manually classified 'bad' and 'good' quality spectra, producing a single 'spectral quality' score. Many spectra examined that do not have significant matches are assessed to have good spectral qual...

Let K be a totally imaginary quadratic extension of a totally real number field F , and assume that F has narrow ideal class number 1. Let χ be a character of the ideal class group CL(K) of K, and let LK(χ, s) be its associated L–function. In this paper we prove that for all > 0, #{χ ∈ CL(K)∧ : LK(χ, 1 2 ) 6= 0} ,F d 1 100− K as the absolute discriminant dK →∞.

We investigated several aspects of using neural networks as a diagnostic tool: the design of an optimal network, the amount of patients' data needed to train the network, the question of training the network optimally while avoiding overfitting, and the influence of redundant variables. The specific clinical problem chosen for illustration was the diagnosis of acute myocardial infarction, given...

In this study, four statistical classifiers, namely linear discriminant classifier, quadratic discriminant classifier, k-Nearest Neighborhood classifier, and parzen classifier are considered for recognition of 2D-shapes. The octagonal shape features are identified from 2D-shapes with the morphological shape decomposition technique. These features are reduced using principle component analysis. ...