The Divergence and Bhattacharyya Distance Measures in Signal Selection

Kailath, T.

doi:10.1109/tcom.1967.1089532

Cited by 1,617 publications

(833 citation statements)

References 24 publications

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“…Wlog., let the class-conditional probabilities p 1 and p 2 belong to the same exponential family, then we have [11,16]:…”

Section: Closed-form Bhattacharrya/chernoff Coefficients For Exponentmentioning

confidence: 99%

Generalized Bhattacharyya and Chernoff upper bounds on Bayes error using quasi-arithmetic means

Nielsen

2014

Pattern Recognition Letters

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Bayesian classification labels observations based on given prior information, namely class-a priori and class-conditional probabilities. Bayes' risk is the minimum expected classification cost that is achieved by the Bayes' test, the optimal decision rule. When no cost incurs for correct classification and unit cost is charged for misclassification, Bayes' test reduces to the maximum a posteriori decision rule, and Bayes risk simplifies to Bayes' error, the probability of error. Since calculating this probability of error is often intractable, several techniques have been devised to bound it with closed-form formula, introducing thereby measures of similarity and divergence between distributions like the Bhattacharyya coefficient and its associated Bhattacharyya distance. The Bhattacharyya upper bound can further be tightened using the Chernoff information that relies on the notion of best error exponent. In this paper, we first express Bayes' risk using the total variation distance on scaled distributions. We then elucidate and extend the Bhattacharyya and the Chernoff upper bound mechanisms using generalized weighted means. We provide as a byproduct novel notions of statistical divergences and affinity coefficients. We illustrate our technique by deriving new upper bounds for the univariate Cauchy and the multivariate t-distributions, and show experimentally that those bounds are not too distant to the computationally intractable Bayes' error.

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“…Wlog., let the class-conditional probabilities p 1 and p 2 belong to the same exponential family, then we have [11,16]:…”

Section: Closed-form Bhattacharrya/chernoff Coefficients For Exponentmentioning

confidence: 99%

Generalized Bhattacharyya and Chernoff upper bounds on Bayes error using quasi-arithmetic means

Nielsen

2014

Pattern Recognition Letters

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“…KullbackLeibler divergence [16], Lin-Wong divergence (modified Kullback-Leibler) [17], Bhattacharrya measure [13], Kolmogorov measure [5], entropy-based measure [20], cosine distance measure [19], and others (more measures could be found in [5]). Obviously, they differ in forms and mathematical properties.…”

Section: Dissimilarity Measuresmentioning

confidence: 99%

Context Change Detection for Resource Allocation in Service-Oriented Systems

Rygielski

Tomczak

2011

Knowlege-Based and Intelligent Information and Engineering Systems

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Abstract. In this paper, the problem of detecting the major changes in the stream of service requests is formulated. The change of stream component varies over time and depends on, e.g., a time of a day. The underlying cause of the change is called a context. Hence, at each moment there exists a probability distribution determining the probability of requesting the system service conditioned by the context. The aim is to find such a moment in which the distributions change. To solve that problem dissimilarity measures between two probability distributions are given. Nevertheless, detecting every change is not interesting but only long-lasting changes because of the costs of the service system resources reallocation. Therefore, in the proposed algorithm an issue of sensitivity to temporary changes detection is considered.

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“…Here we use Bhattacharyya coefficient [29,30,31,32] to measure the similarity between two regions say R and Q is:…”

Section: A Similarity Measurementioning

confidence: 99%

Unsupervised Method of Object Retrieval Using Similar Region Merging and Flood Fill

Saxena¹,

Jain²,

Singh³

2011

SpecialIssue

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Abstract-In this work; we address a novel interactive framework for object retrieval using unsupervised similar region merging and flood fill method which models the spatial and appearance relations among image pixels. Efficient and effective image segmentation is usually very hard for natural and complex images. This paper presents a new technique for similar region merging and objects retrieval. The users only need to roughly indicate the after which steps desired objects boundary is obtained during merging of similar regions. A novel similarity based region merging mechanism is proposed to guide the merging process with the help of mean shift technique. A region R is merged with its adjacent regions Q if Q has highest similarity with R among all Q's adjacent regions. The proposed method automatically merges the regions that are initially segmented through mean shift technique, and then effectively extracts the object contour by merging all similar regions. Extensive experiments are performed on 22 object classes (524 images total) show promising results.

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The Divergence and Bhattacharyya Distance Measures in Signal Selection

Cited by 1,617 publications

References 24 publications

Generalized Bhattacharyya and Chernoff upper bounds on Bayes error using quasi-arithmetic means

Generalized Bhattacharyya and Chernoff upper bounds on Bayes error using quasi-arithmetic means

Context Change Detection for Resource Allocation in Service-Oriented Systems

Unsupervised Method of Object Retrieval Using Similar Region Merging and Flood Fill

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