On a Variational Definition for the Jensen-Shannon Symmetrization of Distances Based on the Information Radius

Nielsen, Frank

doi:10.3390/e23040464

Cited by 23 publications

(19 citation statements)

References 63 publications

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“…To evaluate the overall parameter difference, we adopted the Jessen-Shannon divergence (JSD) 38 with Bootstrap test 39 as a metric for quantifying the difference of the parameter value distributions in tumor and tissue ROIs. To empirically calculate JSD, the probability distributions of the parameter values in tumor and tissue ROIs were estimated from the histogram, consisting of 50 bins ranging from 0.5% quartile to 99.5% quartile of all parameter values (pooling parameter values in both tumor and tissue ROIs).…”

Section: Methodsmentioning

confidence: 99%

The unique second wave phenomenon in contrast enhanced ultrasound imaging with nanobubbles

Chen

Perera

Kolios

et al. 2022

Sci Rep

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Investigation of nanobubble (NB) pharmacokinetics in contrast-enhanced ultrasound (CEUS) at the pixel level shows a unique phenomenon where the first pass of the contrast agent bolus is accompanied by a second wave. This effect has not been previously observed in CEUS with microbubbles. The objective of this study was to investigate this second-wave phenomenon and its potential clinical applications. Seven mice with a total of fourteen subcutaneously-implanted tumors were included in the experiments. After injecting a bolus of NBs, the NB-CEUS images were acquired to record the time-intensity curves (TICs) at each pixel. These TICs are fitted to a pharmacokinetic model which we designed to describe the observed second-wave phenomenon. The estimated model parameters are presented as parametric maps to visualize the characteristics of tumor lesions. Histological analysis was also conducted in one mouse to compare the molecular features of tumor tissue with the obtained parametric maps. The second-wave phenomenon is evidently shown in a series of pixel-based TICs extracted from either tumor or tissues. The value of two model parameters, the ratio of the peak intensities of the second over the first wave, and the decay rate of the wash-out process present large differences between malignant tumor and normal tissue (0.04 < Jessen-Shannon divergence < 0.08). The occurrence of a second wave is a unique phenomenon that we have observed in NB-CEUS imaging of both mouse tumor and tissue. As the characteristics of the second wave are different between tumor and tissue, this phenomenon has the potential to support the diagnosis of cancerous lesions.

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Section: Methodsmentioning

confidence: 99%

The unique second wave phenomenon in contrast enhanced ultrasound imaging with nanobubbles

Chen

Perera

Kolios

et al. 2022

Sci Rep

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“…The second identity shows that the Chernoff symmetrization can be interpreted as a variational Jensen-Shannon-type divergence [50].…”

Section: Chernoff-bregman Divergencementioning

confidence: 99%

Revisiting Chernoff Information with Likelihood Ratio Exponential Families

Nielsen¹

2022

Preprint

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The Chernoff information between two probability measures is a statistical divergence measuring their deviation defined as their maximally skewed Bhattacharyya distance. Although the Chernoff information was originally introduced for bounding the Bayes error in statistical hypothesis testing, the divergence found many other applications due to its empirical robustness property found in applications ranging from information fusion to quantum information. From the viewpoint of information theory, the Chernoff information can also be interpreted as a minmax symmetrization of the Kullback-Leibler divergence. In this paper, we first revisit the Chernoff information between two densities of a measurable Lebesgue space by considering the exponential families induced by their geometric mixtures: The so-called likelihood ratio exponential families. Second, we show how to (i) solve exactly the Chernoff information between any two univariate Gaussian distributions or get a closed-form formula using symbolic computing, (ii) report a closed-form formula of the Chernoff information of centered Gaussians with scaled covariance matrices and (iii) use a fast numerical scheme to approximate the Chernoff information between any two multivariate Gaussian distributions.

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“…Furthermore,

-geodesical skew divergence is a special form of the generalized skew K-divergence [ 10 , 38 ], which is a family of abstract means-based divergences. In this paper, the skew K-divergence touched upon in [ 10 ] is characterized in terms of

-geodesic on positive measures, and its geometric and functional analytic properties are investigated.…”

Section: α -Geodesical Skew Divergencementioning

confidence: 99%

α-Geodesical Skew Divergence

Kimura

Hino

2021

Entropy

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The asymmetric skew divergence smooths one of the distributions by mixing it, to a degree determined by the parameter λ, with the other distribution. Such divergence is an approximation of the KL divergence that does not require the target distribution to be absolutely continuous with respect to the source distribution. In this paper, an information geometric generalization of the skew divergence called the α-geodesical skew divergence is proposed, and its properties are studied.

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On a Variational Definition for the Jensen-Shannon Symmetrization of Distances Based on the Information Radius

Cited by 23 publications

References 63 publications

The unique second wave phenomenon in contrast enhanced ultrasound imaging with nanobubbles

The unique second wave phenomenon in contrast enhanced ultrasound imaging with nanobubbles

Revisiting Chernoff Information with Likelihood Ratio Exponential Families

α-Geodesical Skew Divergence

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