Results 1  10
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11
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 known locations in the room are required for training and calibration. The proposed algorithm relies on a computation of a diffusion kernel with a speciallytailored distance measure. Experimental results in a real reverberant environment demonstrate accurate recovery of the source location. Index Terms — Source localization, acoustic localization, diffusion geometry, diffusion kernel, manifold learning
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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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 specific predefined model for a specific task or system, and enables a generic datadriven method to characterize a system based solely on its output observations. We claim that each system can be viewed as a black box controlled by several independent parameters. Moreover, we assume that the perceptual characterization of the system output is determined by these independent parameters. Consequently, by recovering the independent controlling parameters, we find in fact a generic modeling for the system. In this work, we propose a supervised algorithm to recover the controlling parameters of natural and artificial 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.
Filtering via a Reference Set
, 2011
"... Patchbased denoising algorithms and patch manifold smoothing have emerged as efficient denoising methods. This paper provides a new insight on these methods, such as the Non Local Means or the image graph denoising, by showing its use for filtering a selected pattern. ..."
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Cited by 4 (1 self)
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Patchbased denoising algorithms and patch manifold smoothing have emerged as efficient denoising methods. This paper provides a new insight on these methods, such as the Non Local Means or the image graph denoising, by showing its use for filtering a selected pattern.
Differential Stochastic Sensing: Intrinsic Modeling of Random Time Series with Applications to Nonlinear Tracking
, 2012
"... Many natural and artificial highdimensional time series are often controlled by a set of lowerdimensional independent factors. In this paper anisotropic diffusion is combined with local dynamical models to provide intrinsic global modeling that reveals these factors. The obtained model is shown to ..."
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Cited by 2 (2 self)
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Many natural and artificial highdimensional time series are often controlled by a set of lowerdimensional independent factors. In this paper anisotropic diffusion is combined with local dynamical models to provide intrinsic global modeling that reveals these factors. The obtained model is shown to be invariant to the measuring equipment and can be efficiently extended. These two properties are paramount for sequential processing and provide a foundation for probabilistic analysis. The widely applicable approach is demonstrated on nonlinear tracking problems based on both simulated and recorded data.
Contents lists available at ScienceDirect Artificial Intelligence
"... www.elsevier.com/locate/artint ..."
Analysis of Car Crash Simulation Data with Nonlinear Machine Learning Methods
"... Nowadays, product development in the car industry heavily relies on numerical simulations. For example, it is used to explore the influence of design parameters on the weight, costs or functional properties of new car models. Car engineers spend a considerable amount of their time analyzing these in ..."
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Nowadays, product development in the car industry heavily relies on numerical simulations. For example, it is used to explore the influence of design parameters on the weight, costs or functional properties of new car models. Car engineers spend a considerable amount of their time analyzing these influences by inspecting the arising simulations one at a time. Here, we propose using methods from machine learning to semiautomatically analyze the arising finite element data and thereby significantly assist in the overall engineering process. We combine clustering and nonlinear dimensionality reduction to show that the method is able to automatically detect parameter dependent structure instabilities or reveal bifurcations in the timedependent behavior of beams. In particular we study recent nonlinear and sparse grid approaches, respectively. Our examples demonstrate the strong potential of our approach for reducing the data analysis effort in the engineering process, and emphasize the need for nonlinear methods for such tasks.
Operator Based MultiScale Analysis of Simulation Bundles
, 2015
"... We propose a new mathematical data analysis approach, which is based on the mathematical principle of symmetry, for the postprocessing of bundles of finite element data from computeraided engineering. Since all those numerical simulation data stem from the numerical solution of the same partial d ..."
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We propose a new mathematical data analysis approach, which is based on the mathematical principle of symmetry, for the postprocessing of bundles of finite element data from computeraided engineering. Since all those numerical simulation data stem from the numerical solution of the same partial differential equation, there exists a set of transformations, albeit unknown, which map simulation to simulation. The transformations can be obtained indirectly by constructing a transformation invariant positive definitive operator valid for all simulations. The eigenbasis of such an operator turns out to be a convenient basis for the handled simulation set due to two reasons. First, the spectral coefficients decay very fast, depending on the smoothness of the function being represented, and therefore a reduced multiscale representation of all simulations can be obtained, which depends on the employed operator. Second, at each level of the eigendecomposition the eigenvectors can be seen to recover different independent variation modes like rotation, translation or local deformation. Furthermore, this representation enables the definition of a new distance measure between
Empirical Intrinsic Modeling of Signals and Information Geometry
, 2012
"... In many natural and realworld applications, the measured signals are controlled by underlying processes or drivers. As a result, these signals exhibit highly redundant representations and their temporal evolution can be compactly described by a dynamical process on a lowdimensional manifold. In thi ..."
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In many natural and realworld applications, the measured signals are controlled by underlying processes or drivers. As a result, these signals exhibit highly redundant representations and their temporal evolution can be compactly described by a dynamical process on a lowdimensional manifold. In this paper, we propose a graphbased method for revealing the lowdimensional manifold and inferring the underlying process. This method provides intrinsic modeling for signals using empirical information geometry. We construct an intrinsic representation of the underlying parametric manifold from noisy measurements based on local density estimates. This construction is shown to be equivalent to an inverse problem, which is formulated as a nonlinear differential equation and is solved empirically through eigenvectors of an appropriate Laplace operator. The learned intrinsic nonlinear model exhibits two important properties. We show that it is invariant under different observation and instrumental modalities and is noise resilient. In addition, the learned model can be efficiently extended to newly acquired measurements in a sequential manner. We examine our method on two nonlinear filtering applications: a nonlinear and nonGaussian tracking problem and a nonstationary hidden Markov chain scheme. The experimental results demonstrate the power of our theory by extracting the underlying processes, which were measured through different nonlinear instrumental conditions.
unknown title
, 2012
"... In many fields including economics, collection of time series such as stocks or energy prices are governed by a similar nonlinear dynamical process. These time series are often measured hourly, thus, each day can be viewed as a highdimensional data point. In this paper, we apply a spectral method, ..."
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In many fields including economics, collection of time series such as stocks or energy prices are governed by a similar nonlinear dynamical process. These time series are often measured hourly, thus, each day can be viewed as a highdimensional data point. In this paper, we apply a spectral method, which based on anisotropic diffusion kernels to the model high dimensional electricity price data. We demonstrate the proposed method on price data that was collected from several zones. We show that even though the observed output spaces differ by local spatial influences and noise, the common global parameters that drive the underlying process are extracted. Modeling zonal electricity prices by anisotropic diffusion embeddings