Combinatorics and Statistical Issues Related to the Kruskal–Wallis Statistic

Bargagliotti, Anna E.; Greenwell, Raymond N.

doi:10.1080/03610918.2013.786781

Cited by 6 publications

(3 citation statements)

References 15 publications

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“…The Kruskal–Wallis test is applied for all three samples. What is notable, the relatively small dimension of the samples significantly simplified mathematical calculations (Bargagliotti and Greenwell 2015).…”

Section: Methodsmentioning

confidence: 99%

A comparative statistical analysis of music styles (seventeenth–nineteenth centuries)

Chang

2020

Interdisciplinary Science Reviews

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This article is devoted to the study of instrumental sonatas by composers of Baroque, Classicism, and Romanticism periods. Within the study, the overall number of notes, number of repeated, lowered and raised notes, maximum interval, and range of musical passage are examined. Six subhypotheses are tested to learn the differences in musical works. The analysis is carried out by Student's t-test and Kruskal-Wallis test. The analysis results manifest that four of the six analysed parameters depend on the era of composing. Therefore, these parameters can be used to identify the period of writing a musical piece.

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Section: Methodsmentioning

confidence: 99%

A comparative statistical analysis of music styles (seventeenth–nineteenth centuries)

Chang

2020

Interdisciplinary Science Reviews

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“…To address this issue, we have integrated Kruskal-Wallis test (KW) into KECA. KW is a nonparametric form of the Analysis of Variance (ANOVA) and can be used to assess whether the difference between two or more independent data groups is statistically significant [32]. The popularity of KW may be attributed to its nonnecessity of the assumptions about normal distribution.…”

Section: B Kruskal-wallis Testmentioning

confidence: 99%

Classification Epileptic Seizures in EEG Using Time-Frequency Image and Block Texture Features

Sun

Chen

et al. 2020

IEEE Access

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With the rapid development in technology, computer aided detection or diagnosis has become an indispensable part of the medical industry. Automatic detection of epileptic events is one of the important subjects that have aroused wide interest from more and more investigators. This paper proposes a new model in classification of multi-category electroencephalogram (EEG) signals using time-frequency image and block texture features. The one-dimensional EEG is first mapped to time-frequency domain by means of short-time Fourier transform (STFT), which is adapted to obtain a two-dimensional time-frequency image (2D-TFI). With the idea of multi-scale blocking, the obtained phase images and amplitude images are divided into several sub-blocks corresponding to different frequency ranges and time periods. Then the texture features are calculated to describe the behaviour of EEG signals. Particularly, a novel quadratic feature selection method based on kernel entropy component analysis (KECA) and Kruskal-Wallis test (KW) has been proposed for dimension reduction, by which the features that contained most distinctive information were provided. Eventually, the optimal KECA-based features are fed to support vector machine (SVM) for deciding the class of corresponding EEG. The proposed model is found to achieve at least 99.30% accuracy, 98.0% sensitivity and 100% specificity for each of the eight clinical problems. Our scheme is proven to be effective for seizure detection, which can help doctors optimize the diagnosis workflow, reduce workload and improve detection precision. INDEX TERMS Seizure, EEG, two-dimensional time-frequency image, multi-scale blocking, texture features, kernel entropy component analysis, quadratic feature selection.

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“…The parameters of the GKM clustering algorithm are as follows: the crossover probability P c GKM is 0.85, the mutation probability P m GKM is 0.1, the population P GKM is 5, the maximum number of iterations TM GKM is 10, the initial value of k is 2, and the positive coefficients a and b are 2 and 1.2, respectively. In order to test the differences for statistical significance, the Kruskal-Wallis test [33] with a 5% significance level is applied for all pairwise comparisons, and the performance score [34] is adopted to rank all the algorithms: the smaller the score is, the better the algorithm is.…”

Section: A Simulationsmentioning

confidence: 99%

An Improved NSGA-III Algorithm Using Genetic K-Means Clustering Algorithm

Liu

et al. 2019

IEEE Access

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The non-dominated sorting genetic algorithm III (NSGA-III) has recently been proposed to solve many-objective optimization problems (MaOPs). While this algorithm achieves good diversity, its convergence is unsatisfactory. In order to improve the convergence, we propose an improved NSGA-III using a genetic K-means clustering algorithm (NSGA-III-GKM), which can also ensure diversity and automatically provide the number and direction vector of the subspaces. Compared with the NSGA-III, the proposed NSGA-III-GKM has two key features. First, the initial reference points are clustered using a GKM clustering algorithm, which realizes automatic learning of the number of clusters. Second, as the reference points are replaced by cluster centers, a penalty-based boundary intersection (PBI) aggregation function is introduced to replace the perpendicular distance. The proposed NSGA-III-GKM and other similar optimization algorithms (NSGA-III, MOEA/D, U-NSGA-III, DC-NSGA-III and B-NSGA-III) are tested on DTLZ test problems and UF test problems. The simulation results demonstrate that the NSGA-III-GKM exhibits better diversity and convergence performance than the other algorithms.INDEX TERMS Many-objective optimization, genetic K-means clustering algorithm, NSGA-III, automatic learning.

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Combinatorics and Statistical Issues Related to the Kruskal–Wallis Statistic

Cited by 6 publications

References 15 publications

A comparative statistical analysis of music styles (seventeenth–nineteenth centuries)

A comparative statistical analysis of music styles (seventeenth–nineteenth centuries)

Classification Epileptic Seizures in EEG Using Time-Frequency Image and Block Texture Features

An Improved NSGA-III Algorithm Using Genetic K-Means Clustering Algorithm

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