Derivation of separability measures based on central complex Gaussian and Wishart distributions

Lee, Ken Yoong; Bretschneider, T.

doi:10.1109/igarss.2011.6050038

Cited by 5 publications

(5 citation statements)

References 12 publications

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“…For convenience we report the similarity as the Bhattacharyya coefficient: BC ( A 1 , A 2 ) = normale − ND normalB 2 ( A 1 , A 2 ) which is maximally 1, obtained when A 1 = A 2 . Viewing the proteins’ Boltzmann distributions as central Gaussian distributions, p A 1 with covariance matrix A 1 and p A 2 with covariance matrix A 2 , eq can be derived from the more general form: BC ( A 1 , A 2 ) = prefix∫ normalp boldA 1 false( boldr false) 1 / 2 normalp boldA 2 false( boldr false) 1 / 2 d boldr See for instance Lee Brestschneider . The Gaussian assumption implied in deriving eq from eq is approximate for the MD covariances, while strictly justified for the ENMs.…”

Section: Methodsmentioning

confidence: 99%

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Evaluation of Protein Elastic Network Models Based on an Analysis of Collective Motions

Fuglebakk

Reuter

Hinsen

2013

J. Chem. Theory Comput.

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Elastic network models (ENMs) are valuable tools for investigating collective motions of proteins, and a rich variety of simple models have been proposed over the past decade. A good representation of the collective motions requires a good approximation of the covariances between the fluctuations of the individual atoms. Nevertheless, most studies have validated such models only by the magnitudes of the single-atom fluctuations they predict. In the present study, we have quantified the agreement between the covariance structure predicted by molecular dynamics (MD) simulations and those predicted by a representative selection of proposed coarse-grained ENMs. We then contrast this approach with the comparison to MD-predicted atomic fluctuations and comparison to crystallographic B-factors. While all the ENMs yield approximations to the MD-predicted covariance structure, we report large and consistent differences between proposed models. We also find that the ability of the ENMs to predict atomic fluctuations is correlated with their ability to capture the covariance structure. In contrast, we find that the models that agree best with B-factors model collective motions less reliably and recommend against using B-factors as a benchmark.

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Section: Methodsmentioning

confidence: 99%

“…See for instance Lee Brestschneider. 53 The Gaussian assumption implied in deriving eq 24 from eq 25 is approximate for the MD covariances, while strictly justified for the ENMs.…”

Section: ■ Materials and Methodsmentioning

confidence: 99%

Evaluation of Protein Elastic Network Models Based on an Analysis of Collective Motions

Fuglebakk

Reuter

Hinsen

2013

J. Chem. Theory Comput.

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“…This result was also derived by Lee and Bretschneider [43] and applied to real PolSAR data for assessing separability of target classes. Case (iii):…”

Section: Inequalities and Finite Sample Size Behaviormentioning

confidence: 65%

Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions

Frery

Nascimento

Cintra

2014

IEEE Trans. Geosci. Remote Sensing

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The scaled complex Wishart distribution is a widely used model for multilook full polarimetric SAR data whose adequacy has been attested in the literature. Classification, segmentation, and image analysis techniques which depend on this model have been devised, and many of them employ some type of dissimilarity measure. In this paper we derive analytic expressions for four stochastic distances between relaxed scaled complex Wishart distributions in their most general form and in important particular cases. Using these distances, inequalities are obtained which lead to new ways of deriving the Bartlett and revised Wishart distances. The expressiveness of the four analytic distances is assessed with respect to the variation of parameters. Such distances are then used for deriving new tests statistics, which are proved to have asymptotic chi-square distribution. Adopting the test size as a comparison criterion, a sensitivity study is performed by means of Monte Carlo experiments suggesting that the Bhattacharyya statistic outperforms all the others. The power of the tests is also assessed. Applications to actual data illustrate the discrimination and homogeneity identification capabilities of these distances.

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“…19 shows that all of the standard filters(Lee, Kuan, Frost and Gamma MAP) preserve this consistency in their filtered output. Intuitively, as the boxcar filter is actually similar to multi-look processing, its output also exhibits this consistency.…”

mentioning

confidence: 80%

“…proposed [17,18,19,20,4], but all of them are based on the likelihood test statistics, which so far have only shown to be based on an asymptotic distribution.…”

Section: Research Objectivementioning

confidence: 99%

Scalar and homoskedastic models for SAR and POLSAR data

Le¹

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Derivation of separability measures based on central complex Gaussian and Wishart distributions

Cited by 5 publications

References 12 publications

Evaluation of Protein Elastic Network Models Based on an Analysis of Collective Motions

Evaluation of Protein Elastic Network Models Based on an Analysis of Collective Motions

Analytic Expressions for Stochastic Distances Between Relaxed Complex Wishart Distributions

Scalar and homoskedastic models for SAR and POLSAR data

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