Bounding Extremal Degrees of Edge-Independent Random Graphs Using Relative Entropy

Shang, Yilun

doi:10.3390/e18020053

Cited by 11 publications

(7 citation statements)

References 23 publications

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“…Let G be a random graph on n vertices, where uv is an edge with probability p uv and each edge is independent of each other edge. It is shown that [30,39]…”

Section: Algorithmmentioning

confidence: 99%

Clustering coefficients of large networks

Shang

Yang

2017

Information Sciences

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Let G be a network with n nodes and eigenvalues λ 1 ≥ λ 2 ≥ · · · ≥ λ n . Then G is called an (n, d, λ)We show that this description also holds for strongly regular graphs and Erdős-Rényi graphs. Although most real-world networks are not theoretically constructed, we find that, interestingly, many of them have c(G) close to d/n, and many close to 1 − µ2(n−d−1) d (d−1) , where d is the average degree of G, and µ 2 is the average of the numbers of common neighbors over all non-adjacent pairs of nodes.

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“…Let G be a random graph on n vertices, where uv is an edge with probability p uv and each edge is independent of each other edge. It is shown that [30,39]…”

Section: Algorithmmentioning

confidence: 99%

Clustering coefficients of large networks

Shang

Yang

2017

Information Sciences

Self Cite

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“…Information theory, relative entropy, and the Kullback-Leibler divergence are now widely used concepts (see, e.g., References [1][2][3]). Entropy-based algorithms have enabled engineers and researchers to measure the uncertainty and irregularity of complex systems and data [4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Parameter Analysis of Multiscale Two-Dimensional Fuzzy and Dispersion Entropy Measures Using Machine Learning Classification

Furlong

Hilal

O'Brien

et al. 2021

Entropy

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Two-dimensional fuzzy entropy, dispersion entropy, and their multiscale extensions (MFuzzyEn2D and MDispEn2D, respectively) have shown promising results for image classifications. However, these results rely on the selection of key parameters that may largely influence the entropy values obtained. Yet, the optimal choice for these parameters has not been studied thoroughly. We propose a study on the impact of these parameters in image classification. For this purpose, the entropy-based algorithms are applied to a variety of images from different datasets, each containing multiple image classes. Several parameter combinations are used to obtain the entropy values. These entropy values are then applied to a range of machine learning classifiers and the algorithm parameters are analyzed based on the classification results. By using specific parameters, we show that both MFuzzyEn2D and MDispEn2D approach state-of-the-art in terms of image classification for multiple image types. They lead to an average maximum accuracy of more than 95% for all the datasets tested. Moreover, MFuzzyEn2D results in a better classification performance than that extracted by MDispEn2D as a majority. Furthermore, the choice of classifier does not have a significant impact on the classification of the extracted features by both entropy algorithms. The results open new perspectives for these entropy-based measures in textural analysis.

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“…It is possible, however, to construct an argument as to why the two quantities might be in such strong correlation. A number of approaches have been made to obtain upper and lower bounds for entropy measures in random and more general graphs [6,22] and in the analysis that follows, we will make use of a bounding approach to identify how the correlation between vertex entropy and chromatic information may arise.…”

Section: Theoretical Discussion Of the Resultsmentioning

confidence: 99%

Relating Vertex and Global Graph Entropy in Randomly Generated Graphs

Tee

Parisis

Berthouze

et al. 2018

Entropy

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Combinatoric measures of entropy capture the complexity of a graph but rely upon the calculation of its independent sets, or collections of non-adjacent vertices. This decomposition of the vertex set is a known NP-Complete problem and for most real world graphs is an inaccessible calculation. Recent work by Dehmer et al. and Tee et al. identified a number of vertex level measures that do not suffer from this pathological computational complexity, but that can be shown to be effective at quantifying graph complexity. In this paper, we consider whether these local measures are fundamentally equivalent to global entropy measures. Specifically, we investigate the existence of a correlation between vertex level and global measures of entropy for a narrow subset of random graphs. We use the greedy algorithm approximation for calculating the chromatic information and therefore Körner entropy. We are able to demonstrate strong correlation for this subset of graphs and outline how this may arise theoretically.

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Bounding Extremal Degrees of Edge-Independent Random Graphs Using Relative Entropy

Cited by 11 publications

References 23 publications

Clustering coefficients of large networks

Clustering coefficients of large networks

Parameter Analysis of Multiscale Two-Dimensional Fuzzy and Dispersion Entropy Measures Using Machine Learning Classification

Relating Vertex and Global Graph Entropy in Randomly Generated Graphs

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