One of the challenges in data analysis is to distinguish between different sources of variability... more One of the challenges in data analysis is to distinguish between different sources of variability manifested in data. In this paper, we consider the case of multiple sensors measuring the same physical phenomenon, such that the properties of the physical phenomenon are manifested as a hidden common source of variability (which we would like to extract), while each sensor has its own sensor-specific effects. We present a method based on alternating products of diffusion operators, and show that it extracts the common source of variability. Moreover, we show that this method extracts the common source of variability in a multi-sensor experiment as if it were a standard manifold learning algorithm used to analyze a simple single-sensor experiment, in which the common source of variability is the only source of variability.
ABSTRACT In a broad range of natural and real-world dynamical systems, measured signals are contr... more ABSTRACT In a broad range of natural and real-world dynamical systems, measured signals are controlled by underlying processes or drivers. As a result, these signals exhibit highly redundant representations, while their temporal evolution can often be compactly described by dynamical processes on a low-dimensional manifold. In this paper, we propose a graph-based method for revealing the low-dimensional manifold and inferring the processes. This method provides intrinsic models for measured signals, which are noise resilient and invariant under different random measurements and instrumental modalities. Such intrinsic models may enable mathematical calibration of complex measurements and build an empirical geometry driven by the observations, which is especially suitable for applications without a priori knowledge of models and solutions. We exploit the temporal dynamics and natural small perturbations of the signals to explore the local tangent spaces of the low-dimensional manifold of empirical probability densities. This information is used to define an intrinsic Riemannian metric, which in turn gives rise to the construction of a graph that represents the desired low-dimensional manifold. Such a construction is equivalent to an inverse problem, which is formulated as a nonlinear differential equation and is solved empirically through eigenvectors of an appropriate Laplace operator. We examine our method on two nonlinear filtering applications: a nonlinear and non-Gaussian tracking problem as well as a non-stationary 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, in an entirely data-driven nonparametric way.
Convolutive Transfer Function Generalized Sidelobe Canceler
Ieee Transactions on Audio Speech and Language Processing, Sep 1, 2009
In this paper, we propose a convolutive transfer function generalized sidelobe canceler (CTF-GSC)... more In this paper, we propose a convolutive transfer function generalized sidelobe canceler (CTF-GSC), which is an adaptive beamformer designed for multichannel speech enhancement in reverberant environments. Using a complete system representation in the short-time Fourier transform (STFT) domain, we formulate a constrained minimization problem of total output noise power subject to the constraint that the signal component of the output
In this paper, two modern adaptive signal processing techniques, Empirical Intrinsic Geometry and... more In this paper, two modern adaptive signal processing techniques, Empirical Intrinsic Geometry and Synchrosqueezing transform, are applied to quantify different dynamical features of the respiratory and electroencephalographic signals. We show that the proposed features are theoretically rigorously supported, as well as capture the sleep information hidden inside the signals. The features are used as input to multiclass support vector machines with the radial basis function to automatically classify sleep stages. The effectiveness of the classification based on the proposed features is shown to be comparable to human expert classification -the proposed classification of awake, REM, N1, N2 and N3 sleeping stages based on the respiratory signal (resp. respiratory and EEG signals) has the overall accuracy 81.7% (resp. 89.3%) in the relatively normal subject group. In addition, by examining the combination of the respiratory signal with the electroencephalographic signal, we conclude that the respiratory signal consists of ample sleep information, which supplements to the information stored in the electroencephalographic signal.
Typical transient interferences, e.g. door knocks and keyboard tapping, are short in time, widely... more Typical transient interferences, e.g. door knocks and keyboard tapping, are short in time, widely spread across the frequency domain, and have an abrupt nature. Thus, traditional speech enhancement techniques that use temporal smoothing to estimate the power spectral density (PSD) of the interference are inadequate. In this paper, we present a speech enhancement algorithm that suppresses transient interferences and pseudo-stationary background noise. The algorithm comprises an estimation of the transient and the pseudostationary noise PSDs, and enhancement of speech. The proposed algorithm is capable of tracking rapid variations of the input signal spectra and enables to effectively estimate the PSD of the transients. Experimental results show that the proposed algorithm is robust, does not rely on transient periodicity or reoccurrence, and exhibits good performance for various transient interference types.
Clustering and suppression of transient noise in speech signals using diffusion maps
2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2011
Recently we have presented a novel approach for transient noise reduction that relies on non-loca... more Recently we have presented a novel approach for transient noise reduction that relies on non-local (NL) filtering. In this paper, we modify and extend our approach to support clustering and suppression of a few transient noise types simultaneously, by introducing two novel concepts. We observe that voiced speech spectral components are slowly varying compared to transient noise. Thus, by applying
Chemical and molecular systems are inherently high-dimensional: reactors can contain tens or hund... more Chemical and molecular systems are inherently high-dimensional: reactors can contain tens or hundreds of chemical species participating in a reaction network, while macromolecules can contain hundreds or thousands of atoms. The dynamics of such systems can often be well described in fewer dimensions, and obtaining accurate reduced models can significantly enhance computer-assisted analysis. We propose to validate reduced dynamic models using nonlinear independent component analysis (NLICA) to compare full, high-dimensional simulation data and reduced, lower-dimensional simulations. NLICA [1,2] is a nonlinear dimensionality reduction technique that embeds a high-dimensional data set in a low-dimensional, intrinsic space; data sets resulting from different observations of the same underlying (stochastic) process will thus be mapped to a space spanned by the same intrinsic variables. By comparing the intrinsic variable embeddings of data sets produced from the full as well as the reduc...
Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in r... more Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in recent years to the analysis of large and complex data sets. However, such algorithms still encounter challenges when faced with real data. One such challenge is the existence of "repeated eigendirections," which obscures the detection of the true dimensionality of the underlying manifold and arises when several embedding coordinates parametrize the same direction in the intrinsic geometry of the data set. We propose an algorithm, based on local linear regression, to automatically detect coordinates corresponding to repeated eigendirections. We construct a more parsimonious embedding using only the eigenvectors corresponding to unique eigendirections, and we show that this reduced diffusion maps embedding induces a metric which is equivalent to the standard diffusion distance. We first demonstrate the utility and flexibility of our approach on synthetic data sets. We then apply our algorithm to data collected from a stochastic model of cellular chemotaxis, where our approach for factoring out repeated eigendirections allows us to detect changes in dynamical behavior and the underlying intrinsic system dimensionality directly from data.
ABSTRACT We study the inference of latent intrinsic variables of dynamical systems from output si... more ABSTRACT We study the inference of latent intrinsic variables of dynamical systems from output signal measurements. The primary focus is the construction of an intrinsic distance between signal measurements, which is independent of the measurement device. This distance enables us to infer the latent intrinsic variables through the solution of an eigenvector problem with a Laplace operator based on a kernel. The signal geometry and its dynamics are represented with nonlinear observers. An analysis of the properties of the observers that allow for accurate recovery of the latent variables is given, and a way to test whether these properties are satisfied from the measurements is proposed. Scattering and window Fourier transform observers are compared. Applications are shown on simulated data, and on real intracranial Electroencephalography (EEG) signals of epileptic patients recorded prior to seizures.
One of the challenges in data analysis is to distinguish between different sources of variability... more One of the challenges in data analysis is to distinguish between different sources of variability manifested in data. In this paper, we consider the case of multiple sensors measuring the same physical phenomenon, such that the properties of the physical phenomenon are manifested as a hidden common source of variability (which we would like to extract), while each sensor has its own sensor-specific effects. We present a method based on alternating products of diffusion operators, and show that it extracts the common source of variability. Moreover, we show that this method extracts the common source of variability in a multi-sensor experiment as if it were a standard manifold learning algorithm used to analyze a simple single-sensor experiment, in which the common source of variability is the only source of variability.
ABSTRACT In a broad range of natural and real-world dynamical systems, measured signals are contr... more ABSTRACT In a broad range of natural and real-world dynamical systems, measured signals are controlled by underlying processes or drivers. As a result, these signals exhibit highly redundant representations, while their temporal evolution can often be compactly described by dynamical processes on a low-dimensional manifold. In this paper, we propose a graph-based method for revealing the low-dimensional manifold and inferring the processes. This method provides intrinsic models for measured signals, which are noise resilient and invariant under different random measurements and instrumental modalities. Such intrinsic models may enable mathematical calibration of complex measurements and build an empirical geometry driven by the observations, which is especially suitable for applications without a priori knowledge of models and solutions. We exploit the temporal dynamics and natural small perturbations of the signals to explore the local tangent spaces of the low-dimensional manifold of empirical probability densities. This information is used to define an intrinsic Riemannian metric, which in turn gives rise to the construction of a graph that represents the desired low-dimensional manifold. Such a construction is equivalent to an inverse problem, which is formulated as a nonlinear differential equation and is solved empirically through eigenvectors of an appropriate Laplace operator. We examine our method on two nonlinear filtering applications: a nonlinear and non-Gaussian tracking problem as well as a non-stationary 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, in an entirely data-driven nonparametric way.
Convolutive Transfer Function Generalized Sidelobe Canceler
Ieee Transactions on Audio Speech and Language Processing, Sep 1, 2009
In this paper, we propose a convolutive transfer function generalized sidelobe canceler (CTF-GSC)... more In this paper, we propose a convolutive transfer function generalized sidelobe canceler (CTF-GSC), which is an adaptive beamformer designed for multichannel speech enhancement in reverberant environments. Using a complete system representation in the short-time Fourier transform (STFT) domain, we formulate a constrained minimization problem of total output noise power subject to the constraint that the signal component of the output
In this paper, two modern adaptive signal processing techniques, Empirical Intrinsic Geometry and... more In this paper, two modern adaptive signal processing techniques, Empirical Intrinsic Geometry and Synchrosqueezing transform, are applied to quantify different dynamical features of the respiratory and electroencephalographic signals. We show that the proposed features are theoretically rigorously supported, as well as capture the sleep information hidden inside the signals. The features are used as input to multiclass support vector machines with the radial basis function to automatically classify sleep stages. The effectiveness of the classification based on the proposed features is shown to be comparable to human expert classification -the proposed classification of awake, REM, N1, N2 and N3 sleeping stages based on the respiratory signal (resp. respiratory and EEG signals) has the overall accuracy 81.7% (resp. 89.3%) in the relatively normal subject group. In addition, by examining the combination of the respiratory signal with the electroencephalographic signal, we conclude that the respiratory signal consists of ample sleep information, which supplements to the information stored in the electroencephalographic signal.
Typical transient interferences, e.g. door knocks and keyboard tapping, are short in time, widely... more Typical transient interferences, e.g. door knocks and keyboard tapping, are short in time, widely spread across the frequency domain, and have an abrupt nature. Thus, traditional speech enhancement techniques that use temporal smoothing to estimate the power spectral density (PSD) of the interference are inadequate. In this paper, we present a speech enhancement algorithm that suppresses transient interferences and pseudo-stationary background noise. The algorithm comprises an estimation of the transient and the pseudostationary noise PSDs, and enhancement of speech. The proposed algorithm is capable of tracking rapid variations of the input signal spectra and enables to effectively estimate the PSD of the transients. Experimental results show that the proposed algorithm is robust, does not rely on transient periodicity or reoccurrence, and exhibits good performance for various transient interference types.
Clustering and suppression of transient noise in speech signals using diffusion maps
2011 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2011
Recently we have presented a novel approach for transient noise reduction that relies on non-loca... more Recently we have presented a novel approach for transient noise reduction that relies on non-local (NL) filtering. In this paper, we modify and extend our approach to support clustering and suppression of a few transient noise types simultaneously, by introducing two novel concepts. We observe that voiced speech spectral components are slowly varying compared to transient noise. Thus, by applying
Chemical and molecular systems are inherently high-dimensional: reactors can contain tens or hund... more Chemical and molecular systems are inherently high-dimensional: reactors can contain tens or hundreds of chemical species participating in a reaction network, while macromolecules can contain hundreds or thousands of atoms. The dynamics of such systems can often be well described in fewer dimensions, and obtaining accurate reduced models can significantly enhance computer-assisted analysis. We propose to validate reduced dynamic models using nonlinear independent component analysis (NLICA) to compare full, high-dimensional simulation data and reduced, lower-dimensional simulations. NLICA [1,2] is a nonlinear dimensionality reduction technique that embeds a high-dimensional data set in a low-dimensional, intrinsic space; data sets resulting from different observations of the same underlying (stochastic) process will thus be mapped to a space spanned by the same intrinsic variables. By comparing the intrinsic variable embeddings of data sets produced from the full as well as the reduc...
Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in r... more Nonlinear manifold learning algorithms, such as diffusion maps, have been fruitfully applied in recent years to the analysis of large and complex data sets. However, such algorithms still encounter challenges when faced with real data. One such challenge is the existence of "repeated eigendirections," which obscures the detection of the true dimensionality of the underlying manifold and arises when several embedding coordinates parametrize the same direction in the intrinsic geometry of the data set. We propose an algorithm, based on local linear regression, to automatically detect coordinates corresponding to repeated eigendirections. We construct a more parsimonious embedding using only the eigenvectors corresponding to unique eigendirections, and we show that this reduced diffusion maps embedding induces a metric which is equivalent to the standard diffusion distance. We first demonstrate the utility and flexibility of our approach on synthetic data sets. We then apply our algorithm to data collected from a stochastic model of cellular chemotaxis, where our approach for factoring out repeated eigendirections allows us to detect changes in dynamical behavior and the underlying intrinsic system dimensionality directly from data.
ABSTRACT We study the inference of latent intrinsic variables of dynamical systems from output si... more ABSTRACT We study the inference of latent intrinsic variables of dynamical systems from output signal measurements. The primary focus is the construction of an intrinsic distance between signal measurements, which is independent of the measurement device. This distance enables us to infer the latent intrinsic variables through the solution of an eigenvector problem with a Laplace operator based on a kernel. The signal geometry and its dynamics are represented with nonlinear observers. An analysis of the properties of the observers that allow for accurate recovery of the latent variables is given, and a way to test whether these properties are satisfied from the measurements is proposed. Scattering and window Fourier transform observers are compared. Applications are shown on simulated data, and on real intracranial Electroencephalography (EEG) signals of epileptic patients recorded prior to seizures.
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Papers by Ronen Talmon