2,846 research outputs found
Sparsifying the Fisher Linear Discriminant by Rotation
Many high dimensional classification techniques have been proposed in the
literature based on sparse linear discriminant analysis (LDA). To efficiently
use them, sparsity of linear classifiers is a prerequisite. However, this might
not be readily available in many applications, and rotations of data are
required to create the needed sparsity. In this paper, we propose a family of
rotations to create the required sparsity. The basic idea is to use the
principal components of the sample covariance matrix of the pooled samples and
its variants to rotate the data first and to then apply an existing high
dimensional classifier. This rotate-and-solve procedure can be combined with
any existing classifiers, and is robust against the sparsity level of the true
model. We show that these rotations do create the sparsity needed for high
dimensional classifications and provide theoretical understanding why such a
rotation works empirically. The effectiveness of the proposed method is
demonstrated by a number of simulated and real data examples, and the
improvements of our method over some popular high dimensional classification
rules are clearly shown.Comment: 30 pages and 9 figures. This paper has been accepted by Journal of
the Royal Statistical Society: Series B (Statistical Methodology). The first
two versions of this paper were uploaded to Bin Dong's web site under the
title "A Rotate-and-Solve Procedure for Classification" in 2013 May and 2014
January. This version may be slightly different from the published versio
The extended BLMSSM with a 125 GeV Higgs boson and dark matter
To extend the BLMSSM, we not only add exotic Higgs superfields
to make the exotic lepton heavy, but also introduce
the superfields(,) having couplings with lepton and exotic lepton
at tree level. The obtained model is called as EBLMSSM, which has difference
from BLMSSM especially for the exotic slepton(lepton) and exotic
sneutrino(neutrino). We deduce the mass matrices and the needed couplings in
this model. To confine the parameter space, the Higgs boson mass and
the processes , are
studied in the EBLMSSM. With the assumed parameter space, we obtain reasonable
numerical results according to data on Higgs from ATLAS and CMS. As a cold dark
mater candidate, the relic density for the lightest mass eigenstate of and
mixing is also studied
Hinge solitons in three-dimensional second-order topological insulators
A second-order topological insulator in three dimensions refers to a
topological insulator with gapless states localized on the hinges, which is a
generalization of a traditional topological insulator with gapless states
localized on the surfaces. Here we theoretically demonstrate the existence of
stable solitons localized on the hinges of a second-order topological insulator
in three dimensions when nonlinearity is involved. By means of systematic
numerical study, we find that the soliton has strong localization in real space
and propagates along the hinge unidirectionally without changing its shape. We
further construct an electric network to simulate the second-order topological
insulator. When a nonlinear inductor is appropriately involved, we find that
the system can support a bright soliton for the voltage distribution
demonstrated by stable time evolution of a voltage pulse.Comment: 11 pages, 6 figure
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