250 research outputs found
Variable selection for the multicategory SVM via adaptive sup-norm regularization
The Support Vector Machine (SVM) is a popular classification paradigm in
machine learning and has achieved great success in real applications. However,
the standard SVM can not select variables automatically and therefore its
solution typically utilizes all the input variables without discrimination.
This makes it difficult to identify important predictor variables, which is
often one of the primary goals in data analysis. In this paper, we propose two
novel types of regularization in the context of the multicategory SVM (MSVM)
for simultaneous classification and variable selection. The MSVM generally
requires estimation of multiple discriminating functions and applies the argmax
rule for prediction. For each individual variable, we propose to characterize
its importance by the supnorm of its coefficient vector associated with
different functions, and then minimize the MSVM hinge loss function subject to
a penalty on the sum of supnorms. To further improve the supnorm penalty, we
propose the adaptive regularization, which allows different weights imposed on
different variables according to their relative importance. Both types of
regularization automate variable selection in the process of building
classifiers, and lead to sparse multi-classifiers with enhanced
interpretability and improved accuracy, especially for high dimensional low
sample size data. One big advantage of the supnorm penalty is its easy
implementation via standard linear programming. Several simulated examples and
one real gene data analysis demonstrate the outstanding performance of the
adaptive supnorm penalty in various data settings.Comment: Published in at http://dx.doi.org/10.1214/08-EJS122 the Electronic
Journal of Statistics (http://www.i-journals.org/ejs/) by the Institute of
Mathematical Statistics (http://www.imstat.org
The Role of Grain Boundaries under Long-Time Radiation
Materials containing a high proportion of grain boundaries offer significant
potential for the development of radiation-resistent structural materials.
However, a proper understanding of the connection between the radiation-induced
microstructural behaviour of grain boundary and its impact at long natural time
scales is still missing. In this letter, point defect absorption at interfaces
is summarised by a jump Robin-type condition at a coarse-grained level, wherein
the role of interface microstructure is effectively taken into account. Then a
concise formula linking the sink strength of a polycrystalline aggregate with
its grain size is introduced, and is well compared with experimental
observation. Based on the derived model, a coarse-grained formulation
incorporating the coupled evolution of grain boundaries and point defects is
proposed, so as to underpin the study of long-time morphological evolution of
grains induced by irradiation. Our simulation results suggest that the presence
of point defect sources within a grain further accelerates its shrinking
process, and radiation tends to trigger the extension of twin boundary
sections
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