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Kernel Expansions With Unlabeled Examples
 In Advances in Neural Information Processing Systems 13
, 2001
"... Modern classification applications necessitate supplementing the few available labeled examples with unlabeled examples to improve classification performance. We present a new tractable algorithm for exploiting unlabeled examples in discriminative classification. This is achieved essentially by expa ..."
Abstract

Cited by 24 (5 self)
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by expanding the input vectors into longer feature vectors via both labeled and unlabeled examples. The resulting classification method can be interpreted as a discriminative kernel density estimate and is readily trained via the EM algorithm, which in this case is both discriminative and achieves the optimal
HEAT KERNEL EXPANSIONS ON THE INTEGERS
, 2002
"... In the case of the heat equation ut = uxx + V u on the real line there are some remarkable potentials V for which the asymptotic expansion of the fundamental solution becomes a finite sum and gives an exact formula. We show that a similar phenomenon holds when one replaces the real line by the inte ..."
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Cited by 6 (1 self)
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In the case of the heat equation ut = uxx + V u on the real line there are some remarkable potentials V for which the asymptotic expansion of the fundamental solution becomes a finite sum and gives an exact formula. We show that a similar phenomenon holds when one replaces the real line
Kernel Expansions With Unlabeled Examples
 In Advances in Neural Information Processing Systems 13
"... Modern classification applications necessitate supplementing the few available labeled examples with unlabeled examples to improve classification performance. We present a new tractable algorithm for exploiting unlabeled examples in discriminative classification. This is achieved essentially by ..."
Abstract
 Add to MetaCart
by expanding the input vectors into longer feature vectors via both labeled and unlabeled examples. The resulting classification method can be interpreted as a discriminative kernel density estimate and is readily trained via the EM algorithm, which in this case is both discriminative and achieves
Heat kernel expansion for semitransparent boundaries
 J. Phys. A
"... We study the heat kernel for an operator of Laplace type with a δfunction potential concentrated on a closed surface. We derive the general form of the small t asymptotics and calculate explicitly several first heat kernel coefficients. 1 ..."
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Cited by 17 (6 self)
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We study the heat kernel for an operator of Laplace type with a δfunction potential concentrated on a closed surface. We derive the general form of the small t asymptotics and calculate explicitly several first heat kernel coefficients. 1
Approximation in Sobolev spaces by kernel expansions
, 2000
"... Governmental purposes notwithstanding any copyright notation thereon. The views conclusions contained herein are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of the Air Force Office of Scientific Re ..."
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Cited by 8 (2 self)
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Research or the U.S. Government. 1 2 For interpolation of smooth functions by smooth kernels having an expansion into eigenfunctions (e.g. on the circle, the sphere, and the torus), good results including error bounds are known, provided that the smoothness of the function is closely related
Learning Kernel Expansions for Image Classification
"... Kernel machines (e.g. SVM, KLDA) have shown stateoftheart performance in several visual classification tasks. The classification performance of kernel machines greatly depends on the choice of kernels and its parameters. In this paper, we propose a method to search over a space of parameterized ke ..."
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Cited by 4 (0 self)
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Kernel machines (e.g. SVM, KLDA) have shown stateoftheart performance in several visual classification tasks. The classification performance of kernel machines greatly depends on the choice of kernels and its parameters. In this paper, we propose a method to search over a space of parameterized
FINITE HEAT KERNEL EXPANSIONS ON THE REAL
, 2005
"... Abstract. Let L = d 2 /dx 2 +u(x) be the onedimensional Schrödinger operator and H(x,y,t) be the corresponding heat kernel. We prove that the nth Hadamard’s coefficient Hn(x,y) is equal to 0 if and only if there exists a differential operator M of order 2n − 1 such that L 2n−1 = M 2. Thus, the heat ..."
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Abstract. Let L = d 2 /dx 2 +u(x) be the onedimensional Schrödinger operator and H(x,y,t) be the corresponding heat kernel. We prove that the nth Hadamard’s coefficient Hn(x,y) is equal to 0 if and only if there exists a differential operator M of order 2n − 1 such that L 2n−1 = M 2. Thus
Results 1  10
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1,046