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DIFFERENTIABLE POSITIVE DEFINITE KERNELS ON SPHERES
, 2007
"... Abstract. We analyze termbyterm differentiability of uniformly convergent series of the form k=0 ρkYk(x)Yk(y), x, y ∈ Sm−1, where Sm−1 is the unit sphere in Rm, ρk ≥ 0, k = 0, 1,..., k=0 ρk> 0, and {Yk} is a sequence of spherical harmonics or even more general functions. Since this class of ke ..."
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of kernels includes the continuous positive definite kernels on Sm−1, the results in this paper will show that, under certain conditions, the action of convenient differential operators on positive definite (strictly positive definite) kernels on Sm−1 generate positive definite kernels. 1.
Approximation by Positive Definite Kernels
, 2002
"... This contribution extends earlier work [16] on interpolation/approximation by positive definite basis functions in several aspects. First, it works out the relations between various types of kernels in more detail and more generality. Second, it uses the new generality to exhibit the first example o ..."
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Cited by 2 (1 self)
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This contribution extends earlier work [16] on interpolation/approximation by positive definite basis functions in several aspects. First, it works out the relations between various types of kernels in more detail and more generality. Second, it uses the new generality to exhibit the first example
POSITIVE DEFINITE KERNELS AND LATTICE PATHS
, 2005
"... Abstract. We discuss the structure of positive definite kernels in terms of operator models. In particular, we introduce two models, one of Hessenberg type and another one that we call near tridiagonal. These models produce parametrizations of the kernels and we describe the combinatorial nature of ..."
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Abstract. We discuss the structure of positive definite kernels in terms of operator models. In particular, we introduce two models, one of Hessenberg type and another one that we call near tridiagonal. These models produce parametrizations of the kernels and we describe the combinatorial nature
Positive Definite Kernels in Machine Learning
, 2009
"... This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as reproducing kernel Hibert spaces, the natural extension of the set ..."
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This survey is an introduction to positive definite kernels and the set of methods they have inspired in the machine learning literature, namely kernel methods. We first discuss some properties of positive definite kernels as well as reproducing kernel Hibert spaces, the natural extension
Conditionally Positive Definite Kernels and Pontryagin Spaces
"... Abstract. Conditionally positive definite kernels provide a powerful tool for scattered data approximation. Many nice properties of such methods follow from an underlying reproducing kernel structure. While the connection between positive definite kernels and reproducing kernel Hilbert spaces is wel ..."
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Abstract. Conditionally positive definite kernels provide a powerful tool for scattered data approximation. Many nice properties of such methods follow from an underlying reproducing kernel structure. While the connection between positive definite kernels and reproducing kernel Hilbert spaces
Positive Definite Kernels: Past, Present and Future
"... Positive definite kernels play an increasingly prominent role in many applications such as scattered data fitting, numerical solution of PDEs, computer experiments, machine learning, rapid prototyping and computer graphics. We discuss some of the historical and current developments of the theory and ..."
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Cited by 8 (1 self)
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Positive definite kernels play an increasingly prominent role in many applications such as scattered data fitting, numerical solution of PDEs, computer experiments, machine learning, rapid prototyping and computer graphics. We discuss some of the historical and current developments of the theory
Hilbertian Metrics and Positive Definite Kernels on Probability Measures
 PROCEEDINGS OF AISTATS 2005
, 2005
"... We investigate the problem of defining Hilbertian metrics resp. positive definite kernels on probability measures, continuing the work in [5]. This type of kernels has shown very good results in text classification and has a wide range of possible applications. In this paper we extend the two ..."
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Cited by 91 (0 self)
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We investigate the problem of defining Hilbertian metrics resp. positive definite kernels on probability measures, continuing the work in [5]. This type of kernels has shown very good results in text classification and has a wide range of possible applications. In this paper we extend the two
Permanents, Transportation Polytopes and Positive Definite Kernels on Histograms
, 2007
"... For two integral histograms r =(r1,...,rd) and c = (c1,...,cd) of equal sum N, the MongeKantorovich distance dMK(r, c) between r and c parameterized by a d × d distance matrix T is the minimum of all costs <F,T>taken over matrices F of the transportation polytope U(r, c). Recent results sugge ..."
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Cited by 4 (0 self)
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suggest that this distance is not negative definite, and hence, through Schoenberg’s wellknown result, exp( − 1 t dMK) may not be a positive definite kernel for all t> 0. Rather than using directly dMK to define a similarity between r and c,wepropose in this paper to investigate kernels on r and c
Conditionally positive definite kernels for svm based image recognition
 Proc. of IEEE ICME’05
, 2005
"... Kernel based methods such as Support Vector Machine (SVM) have provided successful tools for solving many recognition problems. One of the reason of this success is the use of kernels. Positive definiteness has to be checked for kernels to be suitable for most of these methods. For instance for SVM, ..."
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Cited by 16 (0 self)
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Kernel based methods such as Support Vector Machine (SVM) have provided successful tools for solving many recognition problems. One of the reason of this success is the use of kernels. Positive definiteness has to be checked for kernels to be suitable for most of these methods. For instance for SVM
Operator monotone functions, positive definite kernels and majorization
 Proc. Amer. Math. Soc
"... Abstract. Let f(t) be a real continuous function on an interval, and consider the operator function f(X) defined for Hermitian operators X. We will show that if f(X) is increasing w.r.t. the operator order, then for F (t) = f(t)dt the operator function F (X) is convex. Let h(t) and g(t) be C1 functi ..."
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Cited by 4 (0 self)
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functions defined on an interval I. Suppose h(t) is nondecreasing and g(t) is increasing. Then we will define the continuous kernel function Kh, g by Kh, g(t, s) = (h(t) − h(s))/(g(t) − g(s)), which is a generalization of the Löwner kernel function. We will see that it is positive definite if and only
Results 1  10
of
2,612,997