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Diffusion Kernels on Statistical Manifolds
, 2004
"... A family of kernels for statistical learning is introduced that exploits the geometric structure of statistical models. The kernels are based on the heat equation on the Riemannian manifold defined by the Fisher information metric associated with a statistical family, and generalize the Gaussian ker ..."
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Cited by 115 (9 self)
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A family of kernels for statistical learning is introduced that exploits the geometric structure of statistical models. The kernels are based on the heat equation on the Riemannian manifold defined by the Fisher information metric associated with a statistical family, and generalize the Gaussian
Diffusion kernels on graphs and other discrete input spaces
 in: Proceedings of the 19th International Conference on Machine Learning
, 2002
"... The application of kernelbased learning algorithms has, so far, largely been confined to realvalued data and a few special data types, such as strings. In this paper we propose a general method of constructing natural families of kernels over discrete structures, based on the matrix exponentiation ..."
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Cited by 223 (5 self)
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idea. In particular, we focus on generating kernels on graphs, for which we propose a special class of exponential kernels called diffusion kernels, which are based on the heat equation and can be regarded as the discretization of the familiar Gaussian kernel of Euclidean space.
Information diffusion kernels
 In Neural Information Processing Systems
, 2002
"... A new family of kernels for statistical learning is introduced that exploits the geometric structure of statistical models. Based on the heat equation on the Riemannian manifold defined by the Fisher information metric, information diffusion kernels generalize the Gaussian kernel of Euclidean spac ..."
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Cited by 27 (3 self)
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A new family of kernels for statistical learning is introduced that exploits the geometric structure of statistical models. Based on the heat equation on the Riemannian manifold defined by the Fisher information metric, information diffusion kernels generalize the Gaussian kernel of Euclidean
Diffusion kernels on graphs and other discrete structures
 In Proceedings of the ICML
, 2002
"... The application of kernelbased learning algorithms has, so far, largely been confined to realvalued data and a few special data types, such as strings. In this paper we propose a general method of constructing natural families of kernels over discrete structures, based on the matrix exponentiation ..."
Abstract

Cited by 176 (4 self)
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idea. In particular, we focus on generating kernels on graphs, for which we propose a special class of exponential kernels, based on the heat equation, called diffusion kernels, and show that these can be regarded as the discretisation of the familiar Gaussian kernel of Euclidean space.
Variable Bandwidth Diffusion Kernels
"... A practical limitation of operator estimation via kernels is the assumption of a compact manifold. In practice we are often interested in data sets whose sampling density may be arbitrarily small, which implies that the data lies on an open set and cannot be modeled as a compact manifold. In this pa ..."
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. In this paper, we show that this limitation can be overcome by varying the bandwidth of the kernel spatially. We present an asymptotic expansion of these variable bandwidth kernels for arbitrary bandwidth functions; generalizing the theory of Diffusion Maps and Laplacian Eigenmaps. Subsequently, we present
1 Diffusion Kernels
"... Graphs are some one of the simplest type of objects in Mathematics. In Chapter Chapter?? we saw how to construct kernels between graphs, that is, when the individual examples x ∈ X are graphs. In this chapter we consider the case when the input space X is itself a graph and the examples are vertices ..."
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Graphs are some one of the simplest type of objects in Mathematics. In Chapter Chapter?? we saw how to construct kernels between graphs, that is, when the individual examples x ∈ X are graphs. In this chapter we consider the case when the input space X is itself a graph and the examples
Supervised source localization using diffusion kernels
 In IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, 245 –248 (, New Paltz
, 2011
"... Recently, we introduced a method to recover the controlling parameters of linear systems using diffusion kernels. In this paper, we apply our approach to the problem of source localization in a reverberant room using measurements from a single microphone. Prior recordings of signals from various k ..."
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Cited by 9 (2 self)
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Recently, we introduced a method to recover the controlling parameters of linear systems using diffusion kernels. In this paper, we apply our approach to the problem of source localization in a reverberant room using measurements from a single microphone. Prior recordings of signals from various
Fiber tracking by simulating diffusion process with diffusion Kernels in . . .
, 2005
"... A novel approach for noninvasively tracing brain white matter fiber tracts is presented using diffusion tensor magnetic resonance imaging (DTMRI) data. This technique is based on performing anisotropic diffusion simulations over a series of overlapping three dimensional diffusion kernels that cover ..."
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Cited by 2 (1 self)
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A novel approach for noninvasively tracing brain white matter fiber tracts is presented using diffusion tensor magnetic resonance imaging (DTMRI) data. This technique is based on performing anisotropic diffusion simulations over a series of overlapping three dimensional diffusion kernels
Robust diffusion kernels for optical flow smoothing
 In Proc. IEEE Workshop on Machine Learning for Signal Processing
, 2006
"... This paper provides a comparison study among a set of novel algorithms that implement robust diffusion on optical flows. The proposed algorithms combine the anisotropic smoothing ability of the heat kernel and the outlier rejection mechanism of robust statistics algorithms. The diffusion kernel is c ..."
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Cited by 2 (2 self)
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This paper provides a comparison study among a set of novel algorithms that implement robust diffusion on optical flows. The proposed algorithms combine the anisotropic smoothing ability of the heat kernel and the outlier rejection mechanism of robust statistics algorithms. The diffusion kernel
Parametrization of Linear Systems Using Diffusion Kernels
, 2011
"... Modeling natural and artificial systems has a key role in various applications, and has long been a task that drew enormous efforts. In this work, instead of exploring predefined models, we aim at implicitly identifying the system degrees of freedom. This approach circumvents the dependency of a spe ..."
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Cited by 6 (3 self)
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linear systems. The proposed algorithm relies on nonlinear independent component analysis using diffusion kernels and spectral analysis. Employment of the proposed algorithm on both synthetic and real examples has shown accurate recovery of parameters.
Results 1  10
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771