19,976 research outputs found
Associated kernel discriminant analysis for multivariate mixed data
Associated kernels have been introduced to improve the classical (symmetric) continuous kernels for smoothing any functional on several kinds of supports such as bounded continuous and discrete sets. In this paper, an associated kernel for discriminant analysis with multivariate mixed variables is proposed. These variables are of three types: continuous, categorical andcount. The method consists of using a product of adapted univariate associated kernels and an estimate of the misclassication rate. A new prole version cross-validation procedure of bandwidth matrices selection is introduced for multivariate mixed data, while a classical cross-validation is used for homogeneous data sets having the same reference measures. Simulations and validation results show the relevance of the proposed method. The method has been validated on real coronary heart disease data in comparison to the classical kernel discriminant analysis
Neural Class-Specific Regression for face verification
Face verification is a problem approached in the literature mainly using
nonlinear class-specific subspace learning techniques. While it has been shown
that kernel-based Class-Specific Discriminant Analysis is able to provide
excellent performance in small- and medium-scale face verification problems,
its application in today's large-scale problems is difficult due to its
training space and computational requirements. In this paper, generalizing our
previous work on kernel-based class-specific discriminant analysis, we show
that class-specific subspace learning can be cast as a regression problem. This
allows us to derive linear, (reduced) kernel and neural network-based
class-specific discriminant analysis methods using efficient batch and/or
iterative training schemes, suited for large-scale learning problems. We test
the performance of these methods in two datasets describing medium- and
large-scale face verification problems.Comment: 9 pages, 4 figure
Stable rationality of quadric and cubic surface bundle fourfolds
We study the stable rationality problem for quadric and cubic surface bundles
over surfaces from the point of view of the degeneration method for the Chow
group of 0-cycles. Our main result is that a very general hypersurface X of
bidegree (2,3) in P^2 x P^3 is not stably rational. Via projections onto the
two factors, X is a cubic surface bundle over P^2 and a conic bundle over P^3,
and we analyze the stable rationality problem from both these points of view.
This provides another example of a smooth family of rationally connected
fourfolds with rational and nonrational fibers. Finally, we introduce new
quadric surface bundle fourfolds over P^2 with discriminant curve of any even
degree at least 8, having nontrivial unramified Brauer group and admitting a
universally CH_0-trivial resolution.Comment: 27 pages, comments welcome
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