• Journal of Communications and Networks
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• v.10 no.1
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• pp.89-97
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• 2008

Anomaly detection systems playa significant role in protection mechanism against attacks launched on a network. The greatest challenge in designing systems detecting anomalous exploits is defining what to measure. Effective yet simple, Shannon entropy metrics have been successfully used to detect specific types of malicious traffic in a number of commercially available IDS's. We believe that Renyi entropy measures can also adequately describe the characteristics of a network as a whole as well as detect abnormal traces in the observed traffic. In addition, Renyi entropy metrics might boost sensitivity of the methods when disambiguating certain anomalous patterns. In this paper we describe our efforts to understand how Renyi mutual information can be applied to anomaly detection as an offline computation. An initial analysis has been performed to determine how well fast spreading worms (Slammer, Code Red, and Welchia) can be detected using our technique. We use both synthetic and real data audits to illustrate the potentials of our method and provide a tentative explanation of the results.

• Journal of Information Processing Systems
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• v.15 no.1
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• pp.7-21
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• 2019

In order to improve the edge segmentation effect of the level set image segmentation and avoid the influence of the initial contour on the level set method, a saliency level set image segmentation model based on local Renyi entropy is proposed. Firstly, the saliency map of the original image is extracted by using saliency detection algorithm. And the outline of the saliency map can be used to initialize the level set. Secondly, the local energy and edge energy of the image are obtained by using local Renyi entropy and Canny operator respectively. At the same time, new adaptive weight coefficient and boundary indication function are constructed. Finally, the local binary fitting energy model (LBF) as an external energy term is introduced. In this paper, the contrast experiments are implemented in different image database. The robustness of the proposed model for segmentation of images with intensity inhomogeneity and complicated edges is verified.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.123-132
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• 2023

We define an operator version of the relative Rényi entropy as the generalization of relative von Neumann entropy, and provide its fundamental properties and the bounds for its trace value. Moreover, we see an effect of the relative Rényi entropy under tensor product, and show the sub-additivity for density matrices.

• Journal of the Korean Data and Information Science Society
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• v.21 no.3
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• pp.561-567
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• 2010

Multiclassification is typically performed using voting scheme methods based on combining a set of binary classifications. In this paper we use multiclassification method with a hat matrix of least squares support vector machine (LS-SVM), which can be regarded as the revised one-against-all method. To tackle multiclass problems for large data, we use the $Nystr\ddot{o}m$ approximation and the quadratic Renyi entropy with estimation in the primal space such as used in xed size LS-SVM. For the selection of hyperparameters, generalized cross validation techniques are employed. Experimental results are then presented to indicate the performance of the proposed procedure.

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.17 no.2
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• pp.391-411
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• 2023

Aggregates play the skeleton and supporting role in the construction field, high-precision measurement and high-efficiency analysis of aggregates are frequently employed to evaluate the project quality. Aiming at the unbalanced operation time and segmentation accuracy for multi-class segmentation algorithms of aggregate images, a Chaotic Sparrow Search Algorithm (CSSA) is put forward to optimize it. In this algorithm, the chaotic map is combined with the sinusoidal dynamic weight and the elite mutation strategies; and it is firstly proposed to promote the SSA's optimization accuracy and stability without reducing the SSA's speed. The CSSA is utilized to optimize the popular multi-class segmentation algorithm-Multiple Entropy Thresholding (MET). By taking three METs as objective functions, i.e., Kapur Entropy, Minimum-cross Entropy and Renyi Entropy, the CSSA is implemented to quickly and automatically calculate the extreme value of the function and get the corresponding correct thresholds. The image adaptive multi-class segmentation model is called CSSA-MET. In order to comprehensively evaluate it, a new parameter I based on the segmentation accuracy and processing speed is constructed. The results reveal that the CSSA outperforms the other seven methods of optimization performance, as well as the quality evaluation of aggregate images segmented by the CSSA-MET, and the speed and accuracy are balanced. In particular, the highest I value can be obtained when the CSSA is applied to optimize the Renyi Entropy, which indicates that this combination is more suitable for segmenting the aggregate images.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.751-760
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• 2021

We study in this paper the right Rényi mean for a quantum divergence induced from the α - z Rényi relative entropy. Many properties including homogeneity, invariance under permutation, repetition and unitary congruence transformation, and determinantal inequality have been presented. Moreover, we give the identity of two right Rényi means with respect to tensor product.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.22 no.3
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• pp.291-297
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• 2012

Conventional Fourier analysis can give only limited information about the dynamic characteristics of nonstationary signals. Instead, time-frequency analysis is widely used to investigate the nonstationary signal in detail. Several time-frequency analysis methods are compared for a typical acoustic emission burst generated during the impact between a ferrite ceramic and aluminum plate. This AE burst is inherently nonstationary and random containing many frequency contents, which leads to severe interference between cross terms in bilinear convolution type distributions. The smoothing and reassignment processes can improve the readability and resolution of the results. Spectrogram and scalogram of the AE burst are obtained and compared to get the characteristics information. Renyi entropies are computed for various bilinear time-frequency transforms to evaluate the randomness. These bilinear transforms are reassigned by using the improved algorithm in discrete computation.

• Journal of the Korean Statistical Society
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• v.36 no.1
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• pp.93-109
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• 2007

Gamma distributions are some of the most popular models for hydrological processes. In this paper, a very flexible family which contains the gamma distribution as a particular case is introduced. Evidence of flexibility is shown by examining the shape of its pdf and the associated hazard rate function. A comprehensive treatment of the mathematical properties is provided by deriving expressions for the nth moment, moment generating function, characteristic function, Renyi entropy and the asymptotic distribution of the extreme order statistics. Estimation and simulation issues are also considered. Finally, a detailed application to drought data from the State of Nebraska is illustrated.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2003.09a
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• pp.403-406
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• 2003

This paper presents a robust algorithm for edge detection based on fuzzy fusion, using a novel local edge information measure based on Renyi's a-order entropy. The calculation of the proposed measure is carried out using a parametric classification scheme based on local statistics. By suitably tuning its parameters, the local edge information measure is capable of extracting different types of edges, while exhibiting high immunity to noise. The notions of fuzzy measures and the Choquet fuzzy integral are applied to combine the different sources of information obtained using the local edge information measure with different sets of parameters. The effectiveness and the robustness of the new method are demonstrated by applying our algorithm to various synthetic computer-generated and real-world images.