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Desheng Liu - One of the best experts on this subject based on the ideXlab platform.

  • a spatial temporal contextual Markovian Kernel method for multi temporal land cover mapping
    Isprs Journal of Photogrammetry and Remote Sensing, 2015
    Co-Authors: Adam Wehmann, Desheng Liu
    Abstract:

    Abstract Due to a lack of spatial–temporal consistency, the current generation of multi-temporal land cover products is subject to significant error propagation in change detection results. To address the evolving needs of land change science, the next generation of land cover products must be derived from new classification methods that are designed specifically for multi-temporal land cover mapping. In this paper, a next generation classifier is proposed that fully exploits contextual information by combining results born from the machine learning paradigm in remote sensing with domain knowledge from multi-temporal land cover mapping. This classifier, the Spatial–Temporal Markovian Support Vector Classifier, exhibits an entirely new level of accuracy of change detection when evaluated for the classification of seven Landsat images from an Appalachian Ohio study area. It exceeds previous leading techniques employing machine learning Kernel methods and Markov Random Field models of image context on all accuracy metrics for the creation of a spatial–temporally consistent land cover product. It owes its performance to the greatly improved decision-making about contextual information afforded by the extension and integration of these previous techniques. With such a classifier, substantially more accurate and spatial–temporally consistent multi-temporal land cover products are possible that are suitable for the detailed study of land cover change.

  • A spatial–temporal contextual Markovian Kernel method for multi-temporal land cover mapping
    ISPRS Journal of Photogrammetry and Remote Sensing, 2015
    Co-Authors: Adam Wehmann, Desheng Liu
    Abstract:

    Abstract Due to a lack of spatial–temporal consistency, the current generation of multi-temporal land cover products is subject to significant error propagation in change detection results. To address the evolving needs of land change science, the next generation of land cover products must be derived from new classification methods that are designed specifically for multi-temporal land cover mapping. In this paper, a next generation classifier is proposed that fully exploits contextual information by combining results born from the machine learning paradigm in remote sensing with domain knowledge from multi-temporal land cover mapping. This classifier, the Spatial–Temporal Markovian Support Vector Classifier, exhibits an entirely new level of accuracy of change detection when evaluated for the classification of seven Landsat images from an Appalachian Ohio study area. It exceeds previous leading techniques employing machine learning Kernel methods and Markov Random Field models of image context on all accuracy metrics for the creation of a spatial–temporally consistent land cover product. It owes its performance to the greatly improved decision-making about contextual information afforded by the extension and integration of these previous techniques. With such a classifier, substantially more accurate and spatial–temporally consistent multi-temporal land cover products are possible that are suitable for the detailed study of land cover change.

Adam Wehmann - One of the best experts on this subject based on the ideXlab platform.

  • a spatial temporal contextual Markovian Kernel method for multi temporal land cover mapping
    Isprs Journal of Photogrammetry and Remote Sensing, 2015
    Co-Authors: Adam Wehmann, Desheng Liu
    Abstract:

    Abstract Due to a lack of spatial–temporal consistency, the current generation of multi-temporal land cover products is subject to significant error propagation in change detection results. To address the evolving needs of land change science, the next generation of land cover products must be derived from new classification methods that are designed specifically for multi-temporal land cover mapping. In this paper, a next generation classifier is proposed that fully exploits contextual information by combining results born from the machine learning paradigm in remote sensing with domain knowledge from multi-temporal land cover mapping. This classifier, the Spatial–Temporal Markovian Support Vector Classifier, exhibits an entirely new level of accuracy of change detection when evaluated for the classification of seven Landsat images from an Appalachian Ohio study area. It exceeds previous leading techniques employing machine learning Kernel methods and Markov Random Field models of image context on all accuracy metrics for the creation of a spatial–temporally consistent land cover product. It owes its performance to the greatly improved decision-making about contextual information afforded by the extension and integration of these previous techniques. With such a classifier, substantially more accurate and spatial–temporally consistent multi-temporal land cover products are possible that are suitable for the detailed study of land cover change.

  • A spatial–temporal contextual Markovian Kernel method for multi-temporal land cover mapping
    ISPRS Journal of Photogrammetry and Remote Sensing, 2015
    Co-Authors: Adam Wehmann, Desheng Liu
    Abstract:

    Abstract Due to a lack of spatial–temporal consistency, the current generation of multi-temporal land cover products is subject to significant error propagation in change detection results. To address the evolving needs of land change science, the next generation of land cover products must be derived from new classification methods that are designed specifically for multi-temporal land cover mapping. In this paper, a next generation classifier is proposed that fully exploits contextual information by combining results born from the machine learning paradigm in remote sensing with domain knowledge from multi-temporal land cover mapping. This classifier, the Spatial–Temporal Markovian Support Vector Classifier, exhibits an entirely new level of accuracy of change detection when evaluated for the classification of seven Landsat images from an Appalachian Ohio study area. It exceeds previous leading techniques employing machine learning Kernel methods and Markov Random Field models of image context on all accuracy metrics for the creation of a spatial–temporally consistent land cover product. It owes its performance to the greatly improved decision-making about contextual information afforded by the extension and integration of these previous techniques. With such a classifier, substantially more accurate and spatial–temporally consistent multi-temporal land cover products are possible that are suitable for the detailed study of land cover change.

Jeffrey J. Hunter - One of the best experts on this subject based on the ideXlab platform.

  • The Computation of Key Properties of Markov Chains via Perturbations
    Linear Algebra and its Applications, 2016
    Co-Authors: Jeffrey J. Hunter
    Abstract:

    Abstract Computational procedures for the stationary probability distribution, the group inverse of the Markovian Kernel and the mean first passage times of a finite irreducible Markov chain, are developed using perturbations. The derivation of these expressions involves the solution of systems of linear equations and, structurally, inevitably the inverses of matrices. By using a perturbation technique, starting from a simple base where no such derivations are formally required, we update a sequence of matrices, formed by linking the solution procedures via generalised matrix inverses and utilising matrix and vector multiplications. Four different algorithms are given, some modifications are discussed, and numerical comparisons are made using a test example. The derivations are based upon the ideas outlined by Hunter [14] .

  • Generalized inverses of Markovian Kernels in terms of properties of the Markov chain
    Linear Algebra and its Applications, 2014
    Co-Authors: Jeffrey J. Hunter
    Abstract:

    Abstract All one-condition generalized inverses of the Markovian Kernel I − P , where P is the transition matrix of a finite irreducible Markov chain, can be uniquely specified in terms of the stationary probabilities and the mean first passage times of the underlying Markov chain. Special sub-families include the group inverse of I − P , Kemeny and Snell's fundamental matrix of the Markov chain and the Moore–Penrose g-inverse. The elements of some sub-families of the generalized inverses can also be re-expressed involving the second moments of the recurrence time variables. Some applications to Kemeny's constant and perturbations of Markov chains are also considered.

  • Simple procedures for finding mean first passage times in Markov chains
    Asia-Pacific Journal of Operational Research, 2007
    Co-Authors: Jeffrey J. Hunter
    Abstract:

    The derivation of mean first passage times in Markov chains involves the solution of a family of linear equations. By exploring the solution of a related set of equations, using suitable generalized inverses of the Markovian Kernel I - P, where P is the transition matrix of a finite irreducible Markov chain, we are able to derive elegant new results for finding the mean first passage times. As a by-product we derive the stationary distribution of the Markov chain without the necessity of any further computational procedures. Standard techniques in the literature, using for example Kemeny and Snell's fundamental matrix Z, require the initial derivation of the stationary distribution followed by the computation of Z, the inverse of I - P + eπT where eT = (1, 1, …, 1) and πT is the stationary probability vector. The procedures of this paper involve only the derivation of the inverse of a matrix of simple structure, based upon known characteristics of the Markov chain together with simple elementary vectors. No prior computations are required. Various possible families of matrices are explored leading to different related procedures.

Katarzyna Pietruska-pałuba - One of the best experts on this subject based on the ideXlab platform.

  • Heat Kernel characterisation of Besov-Lipschitz spaces on metric measure spaces
    manuscripta mathematica, 2009
    Co-Authors: Katarzyna Pietruska-pałuba
    Abstract:

    We give a heat-Kernel characterisation of the Besov-Lipschitz spaces Lip ( α , p , q )( X ) on domains which support a Markovian Kernel with appropriate exponential bounds. This extends former results of Grigor’yan et al. (Trans Am Math Soc 355:2065–2095, 2008), Hu and Zähle (Studia Math 170:259–281, 2005), Pietruska-Pałuba (Stoch Stoch Rep 67:267–285, 1999; 70:153–164, 2000), which were valid for $${\alpha = \frac{d_w}{2}, p = 2, q = \infty}$$ , where d _ w is the walk dimension of the space X .

  • Probabilistic characterisation of Besov-Lipschitz spaces on metric measure spaces
    arXiv: Probability, 2008
    Co-Authors: Katarzyna Pietruska-pałuba
    Abstract:

    We give a probabilistic characterisation of the Besov-Lipschitz spaces $Lip(\alpha,p,q)(X)$ on domains which support a Markovian Kernel with appropriate exponential bounds. This extends former results of \cite{Jon,KPP1,KPP2,GHL} which were valid for $\alpha=\frac{d_w}{2},p=2$, $q=\infty,$ where $d_w$ is the walk dimension of the space $X.$

Didier Piau - One of the best experts on this subject based on the ideXlab platform.

  • Immortal branching Markov processes: Averaging properties and PCR applications
    Annals of Probability, 2004
    Co-Authors: Didier Piau
    Abstract:

    The immortal branching Markov process (iBMP) is a modification of the usual branching model, in which each particle of generation n is counted, in addition to its offspring, as a member of generation n+1, its state being unchanged. When the number of offspring is Bernoulli, iBMP accounts, for instance, for the variability of the biological sequences that are produced by polymerase chain reactions (PCRs). This variability is due to the mutations and to the incomplete replications that affect the PCR. Estimators of PCR mutation rate and efficiency have been proposed that are based, in particular, on the mean empirical law ηn of the mutations of a sequence. Unfortunately, ηn is not analytically tractable. However, the infinite-population limit η∗n of ηn is easily characterized in the two following, biologically relevant, cases. The Markovian Kernel describes a homogeneous random walk, either on the integers or on some finite Cartesian product of a finite set. In the PCR context, this corresponds to infinite or finite targets, respectively. In this paper, we provide bounds of the discrepancy between ηn and η∗n in these two cases. As a consequence, iBMP exhibits a strong averaging effect, even for surprisingly small starting populations. The bounds are explicit functions of the offspring law, the Markovian Kernel, the number of steps n, the size of the initial population and, in the finite-target case, the size of the target. They concern every moment and, what might be less expected, the histogram itself. In the finite-target case, some of the bounds undergo a phase transition at an explicit value of the mutation rate per site and per cycle. We use precise estimates of the harmonic means of classical nondecreasing branching processes, whose proofs are included in the Appendix.