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Relaxed Exponential Kernels for Unsupervised Learning
"... Abstract. Many unsupervised learning algorithms make use of kernels that rely on the Euclidean distance between two samples. However, the Euclidean distance is optimal for Gaussian distributed data. In this paper, we relax the global Gaussian assumption made by the Euclidean distance, and propose a ..."
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Abstract. Many unsupervised learning algorithms make use of kernels that rely on the Euclidean distance between two samples. However, the Euclidean distance is optimal for Gaussian distributed data. In this paper, we relax the global Gaussian assumption made by the Euclidean distance, and propose a
Geodesic Exponential Kernels: When Curvature and Linearity Conflict
, 2014
"... We consider kernel methods on general geodesic metric spaces and provide both negative and positive results. First we show that the common Gaussian kernel can only be generalized to a positive definite kernel on a geodesic metric space if the space is flat. As a result, for data on a Riemannian mani ..."
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Cited by 1 (1 self)
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We consider kernel methods on general geodesic metric spaces and provide both negative and positive results. First we show that the common Gaussian kernel can only be generalized to a positive definite kernel on a geodesic metric space if the space is flat. As a result, for data on a Riemannian
Integral transforms with exponential kernels and Laplace transform
 Journal of the AMS
, 1997
"... An integral transform associates to each section of some sheaf on a manifold X a section of another sheaf on a manifold Y,byaformulalike: (1.1) u → v = ..."
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Cited by 4 (1 self)
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An integral transform associates to each section of some sheaf on a manifold X a section of another sheaf on a manifold Y,byaformulalike: (1.1) u → v =
Heteroskedasticity and Autocorrelation Robust Tests with Exponentiated Kernels
, 2009
"... sample asymptotic properties of the ttest for di¤erent choices of power parameter (). We show that the nonstandard …xed limit distributions of the tstatistic provide more accurate approximations to the …nite sample distributions than the conventional large limit distribution. We prove that the s ..."
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Cited by 4 (2 self)
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sample asymptotic properties of the ttest for di¤erent choices of power parameter (). We show that the nonstandard …xed limit distributions of the tstatistic provide more accurate approximations to the …nite sample distributions than the conventional large limit distribution. We prove that the secondorder corrected critical value based on an asymptotic expansion of the nonstandard limit distribution is also secondorder correct under the large asymptotics. As a further contribution, we propose a new practical procedure for selecting the testoptimal power parameter that addresses the central concern of hypothesis testing: the selected power parameter is testoptimal in the sense that it minimizes the type II error while controlling for the type I error. A plugin procedure for implementing the testoptimal power parameter is suggested. Simulations indicate that the new test is as accurate in size as the nonstandard test of Kiefer and Vogelsang (2002a, 2002b; KV), and yet it does not incur the power loss that often hurts the performance of the latter test. The new test therefore combines the advantages of the KV test and the standard (MSE optimal) HAC test while avoiding their main disadvantages (power loss and size distortion, respectively). The
Closed Form Solution of an Exponential Kernel Integral Equation
"... In this note a Fredholm integral equation of the first kind with exponential expressions for the kernel and right hand side is considered. The task of finding a practically usable solution to such an equation may need more effort than following a standard procedure, even when such a procedure yields ..."
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In this note a Fredholm integral equation of the first kind with exponential expressions for the kernel and right hand side is considered. The task of finding a practically usable solution to such an equation may need more effort than following a standard procedure, even when such a procedure
CONTROL IN HETEROSKEDASTICITY AND AUTOCORRELATION ROBUST TESTS WITH EXPONENTIATED KERNELS
, 2011
"... Using the power kernels of Phillips, Sun, and Jin (2006, 2007), we examine the large sample asymptotic properties of the ttest for different choices of power parameter (ρ). We show that the nonstandard fixedρ limit distributions of the tstatistic provide more accurate approximations to the finite ..."
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Using the power kernels of Phillips, Sun, and Jin (2006, 2007), we examine the large sample asymptotic properties of the ttest for different choices of power parameter (ρ). We show that the nonstandard fixedρ limit distributions of the tstatistic provide more accurate approximations
Text Classification using String Kernels
"... We propose a novel approach for categorizing text documents based on the use of a special kernel. The kernel is an inner product in the feature space generated by all subsequences of length k. A subsequence is any ordered sequence of k characters occurring in the text though not necessarily contiguo ..."
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Cited by 495 (7 self)
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the dimension of the feature space grows exponentially with k. The paper describes how despite this fact the inner product can be e ciently evaluated by a dynamic programming technique. Experimental comparisons of the performance of the kernel compared with a standard word feature space kernel Joachims (1998
Generating Operator of XXX or Gaudin Transfer Matrices Has QuasiExponential Kernel
, 2007
"... Let M be the tensor product of finitedimensional polynomial evaluation Y (glN) modules. Consider the universal difference operator D = N∑ (−1) kTk(u)e−k∂u whose coefficients Tk(u) : M → M are the XXX transfer matrices associated with M. We show that the difference equation Df = 0 for an Mvalued ..."
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Cited by 12 (2 self)
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valued function f has a basis of solutions consisting of quasiexponentials. We prove the same for the universal differential operator D = N∑ (−1) kSk(u) ∂ N−k whose coefficients Sk(u) : M → M are the Gaudin transfer k=0 u matrices associated with the tensor product M of finitedimensional polynomial evaluation
Graph diffusion distance: A difference measure for weighted graphs based on the graph laplacian exponential kernel
 IN: GLOBAL CONFERENCE ON SIGNAL AND INFORMATION PROCESSING (GLOBALSIP), 2013 IEEE
, 2013
"... We propose a novel difference metric, called the graph diffusion distance (GDD), for quantifying the difference between two weighted graphs with the same number of vertices. Our approach is based on measuring the average similarity of heat diffusion on each graph. We compute the graph Laplacian expo ..."
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Cited by 2 (2 self)
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exponential kernel matrices, corresponding to repeatedly solving the heat diffusion problem with initial conditions localized to single vertices. The GDD is then given by the Frobenius norm of the difference of the kernels, at the diffusion time yielding the maximum difference. We study properties
Modelling of Creep and Stress Relaxation Test of a Polypropylene Microfibre by Using FractionExponential Kernel
"... A tensile test until breakage and a creep and relaxation test on a polypropylene fibre are carried out and the resulting creep and stress relaxation curves are fit by a model adopting a fractionexponential kernel in the viscoelastic operator. The models using fractionexponential functions are simp ..."
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A tensile test until breakage and a creep and relaxation test on a polypropylene fibre are carried out and the resulting creep and stress relaxation curves are fit by a model adopting a fractionexponential kernel in the viscoelastic operator. The models using fractionexponential functions
Results 1  10
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879