33,328 research outputs found
Regularized Regression Problem in hyper-RKHS for Learning Kernels
This paper generalizes the two-stage kernel learning framework, illustrates
its utility for kernel learning and out-of-sample extensions, and proves
{asymptotic} convergence results for the introduced kernel learning model.
Algorithmically, we extend target alignment by hyper-kernels in the two-stage
kernel learning framework. The associated kernel learning task is formulated as
a regression problem in a hyper-reproducing kernel Hilbert space (hyper-RKHS),
i.e., learning on the space of kernels itself. To solve this problem, we
present two regression models with bivariate forms in this space, including
kernel ridge regression (KRR) and support vector regression (SVR) in the
hyper-RKHS. By doing so, it provides significant model flexibility for kernel
learning with outstanding performance in real-world applications. Specifically,
our kernel learning framework is general, that is, the learned underlying
kernel can be positive definite or indefinite, which adapts to various
requirements in kernel learning. Theoretically, we study the convergence
behavior of these learning algorithms in the hyper-RKHS and derive the learning
rates. Different from the traditional approximation analysis in RKHS, our
analyses need to consider the non-trivial independence of pairwise samples and
the characterisation of hyper-RKHS. To the best of our knowledge, this is the
first work in learning theory to study the approximation performance of
regularized regression problem in hyper-RKHS.Comment: 25 pages, 3 figure
Fermions on Thick Branes in the Background of Sine-Gordon Kinks
A class of thick branes in the background of sine-Gordon kinks with a scalar
potential was constructed by R. Koley and S.
Kar [Classical Quantum Gravity \textbf{22}, 753 (2005)]. In this paper, in the
background of the warped geometry, we investigate the issue of localization of
spin half fermions on these branes in the presence of two types of
scalar-fermion couplings: and . By presenting the mass-independent potentials in the corresponding
Schr\"{o}dinger equations, we obtain the lowest Kaluza--Klein (KK) modes and a
continuous gapless spectrum of KK states with for both types of
couplings. For the Yukawa coupling , the effective
potential of the right chiral fermions for positive and is always
positive, hence only the effective potential of the left chiral fermions could
trap the corresponding zero mode. This is a well-known conclusion which had
been discussed extensively in the literature. However, for the coupling
, the effective potential of the right chiral
fermions for positive and is no longer always positive. Although the
value of the potential at the location of the brane is still positive, it has a
series of wells and barriers on each side, which ensures that the right chiral
fermion zero mode could be trapped. Thus we may draw the remarkable conclusion:
for positive and , the potentials of both the left and right chiral
fermions could trap the corresponding zero modes under certain restrictions.Comment: 22 pages, 21 figures, published version to appear in Phys. Rev.
Extending twin support vector machine classifier for multi-category classification problems
© 2013 – IOS Press and the authors. All rights reservedTwin support vector machine classifier (TWSVM) was proposed by Jayadeva et al., which was used for binary classification
problems. TWSVM not only overcomes the difficulties in handling the problem of exemplar unbalance in binary classification problems, but also it is four times faster in training a classifier than classical support vector machines. This paper proposes one-versus-all twin support vector machine classifiers (OVA-TWSVM) for multi-category classification problems by utilizing the strengths of TWSVM. OVA-TWSVM extends TWSVM to solve k-category classification problems by developing k TWSVM where in the ith TWSVM, we only solve the Quadratic Programming Problems (QPPs) for the ith class, and get the ith nonparallel hyperplane corresponding to the ith class data. OVA-TWSVM uses the well known one-versus-all (OVA) approach to construct a corresponding twin support vector machine classifier. We analyze the efficiency of the OVA-TWSVM theoretically, and perform experiments to test its efficiency on both synthetic data sets and several benchmark data sets from the UCI machine learning repository. Both the theoretical analysis and experimental results demonstrate that OVA-TWSVM can outperform the traditional OVA-SVMs classifier. Further experimental comparisons with other multiclass classifiers demonstrated that comparable performance could be achieved.This work is supported in part by the grant
of the Fundamental Research Funds for the Central Universities of GK201102007 in PR China, and is also supported by Natural Science Basis Research Plan in Shaanxi Province of China (Program No.2010JM3004), and is at the same time supported by Chinese Academy of Sciences under the Innovative
Group Overseas Partnership Grant as well as Natural Science Foundation of China Major International Joint Research Project (NO.71110107026)
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