Random Field Model

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Robert Blinc - One of the best experts on this subject based on the ideXlab platform.

  • NMR and the spherical Random bond-Random Field Model of relaxor ferroelectrics
    Journal of Physics and Chemistry of Solids, 2000
    Co-Authors: Robert Blinc, Janez Dolinšek, Alan Gregorovič, Boštjan Zalar, Cene Filipič, Zdravko Kutnjak, Adrijan Levstik, R Pirc
    Abstract:

    To determine the nature of the relaxor state and, in particular, to discriminate between a ferroelectric state broken up into nanodomains under the constraint of quenched Random Fields and a glassy state we have measured the temperature dependences of the nonlinear dielectric susceptibility in zero Field as well as the temperature dependence of the local polarization distribution function and the Edwards–Anderson order parameter in PMN single crystal via 93Nb NMR. The experimental results can be quantitatively described by the newly proposed Spherical Random Bond–Random Field Model of relaxor ferroelectrics.

  • spherical Random bond Random Field Model of relaxor ferroelectrics
    Physical Review B, 1999
    Co-Authors: R Pirc, Robert Blinc
    Abstract:

    A Model of relaxor ferroelectrics based on the interacting polar clusters picture has been formulated. The electric dipole moment of a nanosized polar domain is allowed a large number of discrete orientations and its length is assumed to fluctuate in a broad interval. Introducing a set of quasicontinuous order parameter Fields and imposing a global spherical constraint, the spherical Random-bond–Random-Field ~SRBRF! Model is written down and its static properties are investigated. It is found that for weak Random Fields the scaled third-order nonlinear susceptibility a35x3 /x1 4 shows a nearly divergent behavior in the spherical glass phase, but there is no such anomaly in a Random-Field frustrated ferroelectric state. The probability distribution of local cluster polarization is calculated and its relation to the quadrupole perturbed NMR line shape of Nb in PMN is discussed. The fact that the observed line shape is Gaussian at all temperatures provides strong support to the SRBRF Model. @S0163-1829~99!06943-X#

R Pirc - One of the best experts on this subject based on the ideXlab platform.

  • NMR and the spherical Random bond-Random Field Model of relaxor ferroelectrics
    Journal of Physics and Chemistry of Solids, 2000
    Co-Authors: Robert Blinc, Janez Dolinšek, Alan Gregorovič, Boštjan Zalar, Cene Filipič, Zdravko Kutnjak, Adrijan Levstik, R Pirc
    Abstract:

    To determine the nature of the relaxor state and, in particular, to discriminate between a ferroelectric state broken up into nanodomains under the constraint of quenched Random Fields and a glassy state we have measured the temperature dependences of the nonlinear dielectric susceptibility in zero Field as well as the temperature dependence of the local polarization distribution function and the Edwards–Anderson order parameter in PMN single crystal via 93Nb NMR. The experimental results can be quantitatively described by the newly proposed Spherical Random Bond–Random Field Model of relaxor ferroelectrics.

  • spherical Random bond Random Field Model of relaxor ferroelectrics
    Physical Review B, 1999
    Co-Authors: R Pirc, Robert Blinc
    Abstract:

    A Model of relaxor ferroelectrics based on the interacting polar clusters picture has been formulated. The electric dipole moment of a nanosized polar domain is allowed a large number of discrete orientations and its length is assumed to fluctuate in a broad interval. Introducing a set of quasicontinuous order parameter Fields and imposing a global spherical constraint, the spherical Random-bond–Random-Field ~SRBRF! Model is written down and its static properties are investigated. It is found that for weak Random Fields the scaled third-order nonlinear susceptibility a35x3 /x1 4 shows a nearly divergent behavior in the spherical glass phase, but there is no such anomaly in a Random-Field frustrated ferroelectric state. The probability distribution of local cluster polarization is calculated and its relation to the quadrupole perturbed NMR line shape of Nb in PMN is discussed. The fact that the observed line shape is Gaussian at all temperatures provides strong support to the SRBRF Model. @S0163-1829~99!06943-X#

Sotirios P. Chatzis - One of the best experts on this subject based on the ideXlab platform.

  • The Infinite-Order Conditional Random Field Model for Sequential Data Modeling
    IEEE Transactions on Pattern Analysis and Machine Intelligence, 2013
    Co-Authors: Sotirios P. Chatzis, Yiannis Demiris
    Abstract:

    Sequential data labeling is a fundamental task in machine learning applications, with speech and natural language processing, activity recognition in video sequences, and biomedical data analysis being characteristic examples, to name just a few. The conditional Random Field (CRF), a log-linear Model representing the conditional distribution of the observation labels, is one of the most successful approaches for sequential data labeling and classification, and has lately received significant attention in machine learning as it achieves superb prediction performance in a variety of scenarios. Nevertheless, existing CRF formulations can capture only one- or few-timestep interactions and neglect higher order dependences, which are potentially useful in many real-life sequential data Modeling applications. To resolve these issues, in this paper we introduce a novel CRF formulation, based on the postulation of an energy function which entails infinitely long time-dependences between the Modeled data. Building blocks of our novel approach are: 1) the sequence memoizer (SM), a recently proposed nonparametric Bayesian approach for Modeling label sequences with infinitely long time dependences, and 2) a mean-Field-like approximation of the Model marginal likelihood, which allows for the derivation of computationally efficient inference algorithms for our Model. The efficacy of the so-obtained infinite-order CRF ($({\rm CRF}^{\infty })$) Model is experimentally demonstrated.

  • The echo state conditional Random Field Model for sequential data Modeling
    Expert Systems With Applications, 2012
    Co-Authors: Sotirios P. Chatzis, Yiannis Demiris
    Abstract:

    Sequential data labeling is a fundamental task in machine learning applications, with speech and natural language processing, activity recognition in video sequences, and biomedical data analysis being characteristic such examples, to name just a few. The conditional Random Field (CRF), a log-linear Model representing the conditional distribution of the observation labels, is one of the most successful approaches for sequential data labeling and classification, and has lately received significant attention in machine learning, as it achieves superb prediction performance in a variety of scenarios. Nevertheless, existing CRF formulations do not account for temporal dependencies between the observed variables - they only postulate Markovian interdependencies between the predicted label variables. To resolve these issues, in this paper we propose a non-linear hierarchical CRF formulation that combines the power of echo state networks to extract high level temporal features with the graphical framework of CRF Models, yielding a powerful and scalable probabilistic Model that we apply to signal labeling tasks.

  • the infinite hidden markov Random Field Model
    IEEE Transactions on Neural Networks, 2010
    Co-Authors: Sotirios P. Chatzis, Gabriel Tsechpenakis
    Abstract:

    Hidden Markov Random Field (HMRF) Models are widely used for image segmentation, as they appear naturally in problems where a spatially constrained clustering scheme is asked for. A major limitation of HMRF Models concerns the automatic selection of the proper number of their states, i.e., the number of region clusters derived by the image segmentation procedure. Existing methods, including likelihood- or entropy-based criteria, and reversible Markov chain Monte Carlo methods, usually tend to yield noisy Model size estimates while imposing heavy computational requirements. Recently, Dirichlet process (DP, infinite) mixture Models have emerged in the cornerstone of nonparametric Bayesian statistics as promising candidates for clustering applications where the number of clusters is unknown a priori; infinite mixture Models based on the original DP or spatially constrained variants of it have been applied in unsupervised image segmentation applications showing promising results. Under this motivation, to resolve the aforementioned issues of HMRF Models, in this paper, we introduce a nonparametric Bayesian formulation for the HMRF Model, the infinite HMRF Model, formulated on the basis of a joint Dirichlet process mixture (DPM) and Markov Random Field (MRF) construction. We derive an efficient variational Bayesian inference algorithm for the proposed Model, and we experimentally demonstrate its advantages over competing methodologies.

  • the infinite hidden markov Random Field Model
    International Conference on Computer Vision, 2009
    Co-Authors: Sotirios P. Chatzis, Gabriel Tsechpenakis
    Abstract:

    Dirichlet process (DP) mixture Models have recently emerged in the cornerstone of nonparametric Bayesian statistics as promising candidates for clustering applications where the number of clusters is unknown a priori. Hidden Markov Random Field (HMRF) Models are parametric statistical Models widely used for image segmentation, as they appear naturally in problems where a spatially-constrained clustering scheme is asked for. A major limitation of HMRF Models concerns the automatic selection of the proper number of their states, i.e. the number of segments derived by the image segmentation procedure. Typically, for this purpose, various likelihood based criteria are employed. Nevertheless, such methods often fail to yield satisfactory results, exhibiting significant overfitting proneness. Recently, higher order conditional Random Field Models using potentials defined on superpixels have been considered as alternatives tackling these issues. Still, these Models are in general computationally inefficient, a fact that limits their widespread adoption in practical applications. To resolve these issues, in this paper we introduce a novel, nonparametric Bayesian formulation for the HMRF Model, the infinite HMRF Model. We describe an efficient variational Bayesian inference algorithm for the proposed Model, and we apply it to a series of image segmentation problems, demonstrating its advantages over existing methodologies.

Giuseppe Scarpa - One of the best experts on this subject based on the ideXlab platform.

  • a tree structured markov Random Field Model for bayesian image segmentation
    IEEE Transactions on Image Processing, 2003
    Co-Authors: Ciro Delia, Giovanni Poggi, Giuseppe Scarpa
    Abstract:

    We present a new image segmentation algorithm based on a tree-structured binary MRF Model. The image is recursively segmented in smaller and smaller regions until a stopping condition, local to each region, is met. Each elementary binary segmentation is obtained as the solution of a MAP estimation problem, with the region prior Modeled as an MRF. Since only binary Fields are used, and thanks to the tree structure, the algorithm is quite fast, and allows one to address the cluster validation problem in a seamless way. In addition, all Field parameters are estimated locally, allowing for some spatial adaptivity. To improve segmentation accuracy, a split-and-merge procedure is also developed and a spatially adaptive MRF Model is used. Numerical experiments on multispectral images show that the proposed algorithm is much faster than a similar reference algorithm based on "flat" MRF Models, and its performance, in terms of segmentation accuracy and map smoothness, is comparable or even superior.

  • a tree structured markov Random Field Model for bayesian image segmentation
    IEEE Transactions on Image Processing, 2003
    Co-Authors: Ciro Delia, Giovanni Poggi, Giuseppe Scarpa
    Abstract:

    We present a new image segmentation algorithm based on a tree-structured binary MRF Model. The image is recursively segmented in smaller and smaller regions until a stopping condition, local to each region, is met. Each elementary binary segmentation is obtained as the solution of a MAP estimation problem, with the region prior Modeled as an MRF. Since only binary Fields are used, and thanks to the tree structure, the algorithm is quite fast, and allows one to address the cluster validation problem in a seamless way. In addition, all Field parameters are estimated locally, allowing for some spatial adaptivity. To improve segmentation accuracy, a split-and-merge procedure is also developed and a spatially adaptive MRF Model is used. Numerical experiments on multispectral images show that the proposed algorithm is much faster than a similar reference algorithm based on "flat" MRF Models, and its performance, in terms of segmentation accuracy and map smoothness, is comparable or even superior.

Gregory C Beroza - One of the best experts on this subject based on the ideXlab platform.

  • a spatial Random Field Model to characterize complexity in earthquake slip
    Journal of Geophysical Research, 2002
    Co-Authors: Martin P Mai, Gregory C Beroza
    Abstract:

    [1] Finite-fault source inversions reveal the spatial complexity of earthquake slip over the fault plane. We develop a stochastic characterization of earthquake slip complexity, based on published finite-source rupture Models, in which we Model the distribution of slip as a spatial Random Field. The Model most consistent with the data follows a von Karman autocorrelation function (ACF) for which the correlation lengths a increase with source dimension. For earthquakes with large fault aspect ratios, we observe substantial differences of the correlation length in the along-strike (a x ) and downdip (a z ) directions. Increasing correlation length with increasing magnitude can be understood using concepts of dynamic rupture propagation. The power spectrum of the slip distribution can also be well described with a power law decay (i.e., a fractal distribution) in which the fractal dimension D remains scale invariant, with a median value D = 2.29 ±0.23, while the comer wave number k c , which is inversely proportional to source size, decreases with earthquake magnitude, accounting for larger slip patches for large-magnitude events. Our stochastic slip Model can be used to generate realizations of scenario earthquakes for near-source ground motion simulations.