Refinements of Jensen's inequality and applications

<abstract><p>The principal aim of this research work is to establish refinements of the integral Jensen's inequality. For the intended refinements, we mainly use the notion of convexity and the concept of majorization. We derive some inequalities for power and quasi–arithmetic means while utilizing the main results. Moreover, we acquire several refinements of Hölder inequality and also an improvement of Hermite–Hadamard inequality as consequences of obtained results. Furthermore, we secure several applications of the acquired results in information theory, which consist bounds for Shannon entropy, different divergences, Bhattacharyya coefficient, triangular discrimination and various distances.</p></abstract>

Leveraging the Bhattacharyya coefficient for uncertainty quantification in deep neural networks

Modern deep learning models achieve state-of-the-art results for many tasks in computer vision, such as image classification and segmentation. However, its adoption into high-risk applications, e.g. automated medical diagnosis systems, happens at a slow pace. One of the main reasons for this is that regular neural networks do not capture uncertainty. To assess uncertainty in classification, several techniques have been proposed casting neural network approaches in a Bayesian setting. Amongst these techniques, Monte Carlo dropout is by far the most popular. This particular technique estimates the moments of the output distribution through sampling with different dropout masks. The output uncertainty of a neural network is then approximated as the sample variance. In this paper, we highlight the limitations of such a variance-based uncertainty metric and propose an novel approach. Our approach is based on the overlap between output distributions of different classes. We show that our technique leads to a better approximation of the inter-class output confusion. We illustrate the advantages of our method using benchmark datasets. In addition, we apply our metric to skin lesion classification—a real-world use case—and show that this yields promising results.

Reduction dimensionality of hyperspectral imagery using genetic algorithm and mutual information and normalized mutual information as a fitness function

Hyperspectral images (HSI) present a wealth of information. It is distinguished by its high dimensionality. It served humanity in many fields. The quantity of HSI information represents a double-edged sword. As a consequence, their dimensionality must be reduced. Nowadays, several methods are proposed to overcome their duress. The most useful and essential solution is selection approaches of hyperspectral bands to analyze it quickly. Our work suggests a novel method to achieve this selection: we introduce a Genetic Algorithm (GA) based on mutual information (MI) and Normalized Mutual Information (NMI) as fitness functions. It selects the relevant bands from noisiest and redundant ones that don’t contain any additional information. .The proposed method is applied to three different HSI: INDIAN PINE, PAVIA, and SALINAS. The introduced algorithm provides a remarkable efficiency on the accuracy of the classification, in front of other statistical methods: the Bhattacharyya coefficient as well as the inter-bands correlation (Pearson correlation). We conclude that the measure of information (MI, NMI) provides more efficiency as a fitness function for GA selection applied to HSI; it must be more investigated.

Selecting the best product alternative in a sea of uncertainty

Introduction Most LCA studies are comparative and to an increasing extent the effects uncertainty are included in LCA results. This raises the question how the best option from a set of product alternatives can be selected when the product scores are uncertain. The starting point of this article is a set of Monte Carlo results for a number of alternative products. Indicators for single product alternatives First we discuss different ways of expressing results for product alternatives separately. This includes a discussion of centrality (mean, median, geometric mean, etc.) and dispersion (standard deviation, standard error, confidence interval, etc.). Indicators of difference for two product alternatives A critical review of approaches to single out the superior option on case of a comparison of two is given. This includes familiar approaches such as $$t$$ t tests, but also lesser known ones such the Bhattacharyya coefficient and Cohen’s $$d$$ d . All approaches are defined, discussed, and illustrated with one consistent, downloadable, example. More than two product alternatives The findings for two products are generalized for the multi-product situation. In particular, the issue of inflation of type I errors in multiple comparisons is discussed. Discussion Two main questions are identified: (1) What is the probability that a randomly selected specimen of product A performs better than a randomly selected specimen of product B? (2) How much will a randomly selected specimen of product A perform better than a randomly selected specimen of product B? These two options can both be relevant, but existing approaches for distinguishing product alternatives address one of these two only, or they even turn out to answer a different, less relevant, question. A proposal for a new indicator that addresses both questions simultaneously is offered and its use is illustrated.

An improved localization method for lesion area in gynecological ultrasound image

The false positive and false negative rates of current image localization methods in gynecological lesion area are high because the effectiveness is affected by random noise. Therefore, by using Bhattacharyya coefficient-based scale-invariant feature transform (B-SIFT), a novel localization method of lesion area in gynecological ultrasound image is proposed in this paper. Firstly, Rayleigh mean filtering is used to suppress the noise in the ultrasound image based on Rayleigh distribution characteristics of the noise. Then, the segmentation method of the lesion region is designed by using the scale-invariant feature transform (SIFT). Furthermore, the feature extraction function B-SIFT is proposed to locate the lesion region based on the Bhattacharyya coefficient. Finally, two lesion characteristics of Bhattacharyya coefficients are defined, and the B-SIFT-based feature region descriptors are obtained by constructing an eigenvector normalized based on the Bhattacharyya coefficients. Experimental results show that the proposed method has a high positioning accuracy, strong recall ratio, low energy consumption, and low time consumption, which is more effective and feasible than the traditional method for localization of lesions.