Efficient ECG classification based on Chi-square distance for arrhythmia detection

This study introduces a new classifier tailored to address the limitations inherent in conventional classifiers such as K-nearest neighbor(KNN),random forest(RF),decision tree(DT),and support vector machine(SVM)for arrhythmia detection.The proposed classifier leverages the Chi-square distance as a primary metric,providing a specialized and original approach for precise arrhythmia detection.To optimize feature selection and refine the classifier’s performance,particle swarm optimization(PSO)is integrated with the Chi-square distance as a fitness function.This synergistic integration enhances the classifier’s capabilities,resulting in a substantial improvement in accuracy for arrhythmia detection.Experimental results demonstrate the efficacy of the proposed method,achieving a noteworthy accuracy rate of 98% with PSO,higher than 89% achieved without any previous optimization.The classifier outperforms machine learning(ML)and deep learning(DL)techniques,underscoring its reliability and superiority in the realm of arrhythmia classification.The promising results render it an effective method to support both academic and medical communities,offering an advanced and precise solution for arrhythmia detection in electrocardiogram(ECG)data.

Use of Pearson’s Chi-Square for Testing Equality of Percentile Profiles across Multiple Populations

In large sample studies where distributions may be skewed and not readily transformed to symmetry, it may be of greater interest to compare different distributions in terms of percentiles rather than means. For example, it may be more informative to compare two or more populations with respect to their within population distributions by testing the hypothesis that their corresponding respective 10th, 50th, and 90th percentiles are equal. As a generalization of the median test, the proposed test statistic is asymptotically distributed as Chi-square with degrees of freedom dependent upon the number of percentiles tested and constraints of the null hypothesis. Results from simulation studies are used to validate the nominal 0.05 significance level under the null hypothesis, and asymptotic power properties that are suitable for testing equality of percentile profiles against selected profile discrepancies for a variety of underlying distributions. A pragmatic example is provided to illustrate the comparison of the percentile profiles for four body mass index distributions.

单值分解和Chi-square技术在生化反应过程控制中的应用

In this paper Singular Decompositon Value (SVD) formula and modified Chi-square solution are provided, and the modified Chi-square is combined with FT-IR instrument to control biochemical reaction process. Using the modified Chi-square technique, the unknown concentration of reactants and products in test samples withdrawn from the process is determined. The technique avoids the need for the spectral data to conform to Beer’s Law and the best spectral range is determined automatically.

基于Chi-square检验的分布式网络入侵检测系统

针对网络攻击的新特点,本文提出了一种基于Chi-square检验的分布式网络入侵检测系统模型CTDIDS。设计并实现了一个基于异常检测的入侵分析引擎。通过对网络数据包的分析,运用Chi-square值比较对系统的行为进行检测。与现有的入侵检测方法相比,本文提出的方法具有更好的环境适应性和数据协同分析能力。实验证明,分布式入侵检测系统CTDIDS具有更高的准确性和扩展性。

一种新的Pearson相关系数稳健估计法

传统Pearson相关系数计算公式具有不稳健性,离群值的存在会导致计算结果与实际不符。针对此问题,文章给出了一种稳健估计方法。在模拟样本量分别为20、50、100、200,污染率分别为1%、5%、10%情形下,比较传统相关系数值与稳健相关系数值,发现:稳健相关系数公式正确率均显著高于传统相关系数。在实例分析中进一步验证了稳健相关系数的可行性和有效性。文章研究结论可用于含离群值变量的相关系数稳健估计。The traditional Pearson correlation coefficient calculation formula is not robust, and the existence of outliers will cause the calculation results to be inconsistent with reality. To solve this problem, this paper presents a robust estimation method. When the simulated sample size is 20, 50, 100 and 200 respectively, the pollution rate is 1%, 5% and 10% respectively, it is found that the accuracy of the robust correlation coefficient formula is significantly higher than that of the traditional correlation coefficient. The feasibility and effectiveness of a robust correlation coefficient are further verified in the example analysis. The conclusions of this paper can be used for robust estimation of correlation coefficients with outlier variables.

Visualising data distributions with kernel density estimation and reduced chi-squared statistic

The application of frequency distribution statistics to data provides objective means to assess the nature of the data distribution and viability of numerical models that are used to visualize and interpret data.Two commonly used tools are the kernel density estimation and reduced chi-squared statistic used in combination with a weighted mean.Due to the wide applicability of these tools,we present a Java-based computer application called KDX to facilitate the visualization of data and the utilization of these numerical tools.

Chi-Square and PCA Based Feature Selection for Diabetes Detection with Ensemble Classifier

Diabetes mellitus is a metabolic disease that is ranked among the top 10 causes of death by the world health organization.During the last few years,an alarming increase is observed worldwide with a 70%rise in the disease since 2000 and an 80%rise in male deaths.If untreated,it results in complications of many vital organs of the human body which may lead to fatality.Early detection of diabetes is a task of significant importance to start timely treatment.This study introduces a methodology for the classification of diabetic and normal people using an ensemble machine learning model and feature fusion of Chi-square and principal component analysis.An ensemble model,logistic tree classifier(LTC),is proposed which incorporates logistic regression and extra tree classifier through a soft voting mechanism.Experiments are also performed using several well-known machine learning algorithms to analyze their performance including logistic regression,extra tree classifier,AdaBoost,Gaussian naive Bayes,decision tree,random forest,and k nearest neighbor.In addition,several experiments are carried out using principal component analysis(PCA)and Chi-square(Chi-2)fea-tures to analyze the influence of feature selection on the performance of machine learning classifiers.Results indicate that Chi-2 features show high performance than both PCA features and original features.However,the highest accuracy is obtained when the proposed ensemble model LTC is used with the proposed fea-ture fusion framework-work which achieves a 0.85 accuracy score which is the highest of the available approaches for diabetes prediction.In addition,the statis-tical T-test proves the statistical significance of the proposed approach over other approaches.

基于Pearson相关性分析的双V型永磁同步电机失磁故障动态识别方法

针对电驱动系统用高功率密度永磁驱动电机存在的不可逆退磁问题,以一款8极48槽的双V型永磁同步电机为例对退磁故障的动态识别方法进行了研究。在考虑电机闭合磁路对永磁体退磁故障影响的基础上,通过分析高退磁率电机模型退磁前后的空载和负载参数变化,采用Pearson相关性分析的方法提取了表征退磁故障的特征参量,给出了一种退磁故障的动态识别方法,并分析了转速和电流对特征参量的影响,完成了对退磁故障动态识别方法的修正。通过仿真和实验测试的方法对退磁故障动态识别方法的准确性进行了验证,结果表明,仿真结果的误差为0.68%,实验测试的预测结果最大误差为1.765%,误差均在可接受范围内。

大锻件统计学Chi-square test的研究和应用

根据大锻件生产的特点和统计学的基本理论方法,首次深入浅出地论述了大锻件的Chi-square test,即X2检验,并给出了具体应用示例。该方法可用于大锻件工艺参数的科学分析和生产验证,可用于大锻件质量分析和判断,可帮助逐步建立起大锻件的工序能力,帮助实现稳定并提升大锻件工艺和质量控制水平。

基于暂态电压Pearson相关系数的柔性直流配电网纵联保护方法

柔性直流配电网故障特征复杂,快速可靠的故障保护方法是柔性直流配电网亟需突破的关键技术。基于此提出了一种基于直流线路限流电抗器暂态电压皮尔逊(Pearson)相关系数的直流配电网纵联保护方法。首先,分析了区内外不同故障类型下直流线路两端限流电抗器暂态电压的特征差异。其次,利用正、负极线路电压的变化率构成保护启动判据,通过直流线路两端限流电抗器暂态电压的Pearson相关系数识别区内、外故障,并利用直流线路正负极电压变化率间的正负关系设计故障选极判据。最后,在Matlab/Simulink仿真软件中搭建柔性直流配电网仿真模型验证所提保护方法的可行性。结果表明所提保护方法能满足柔性直流配电网保护速动性和选择性的要求,且耐过渡电阻能力强,受通信延迟影响小,具有一定的抗干扰能力。

基于Bhattacharyya系数和Pearson相关系数的交直流混联电网电压波形相似度纵联保护方法

当交直流混联电网的联络线中有故障发生时,直流逆变侧电气故障特征和无穷大交流电源截然不同,难以保证传统交流保护方法的可靠与灵敏。因此提出了一种基于Bhattacharyya系数和Pearson相关系数的交直流混联电网电压波形相似度纵联保护方法,线路两侧的保护单元对各自的测量电压和通过计算得到的参考点参考电压波形相似性进行比较。综合Pearson相关系数和Bhattacharyya系数对待判断的两电压波形相似度进行判断,此后对线路两端保护装置的故障区域相似性判断结果采用纵联保护逻辑进行比较,从而实现对全线范围内区内外故障进行可靠识别与判断。PSCAD仿真结果表明,所提方法可以准确识别交直流混联电网联络线故障,具有较高的可靠性和良好的适用性。

Large Deviations and Moderate Deviations for the Chi-Square Test in Type Ⅱ Error

We study the asymptotics tot the statistic of chi-square in type Ⅱ error. By the contraction principle, the large deviations and moderate deviations are obtained, and the rate function of moderate deviations can be calculated explicitly which is a squared function.

基于Pearson相关性的VAR模型煤电水煤比寻优应用

本文为解决350MW燃煤机组在煤质频繁变化情况下水煤比失衡的问题,使用向量自回归(VAR)模型在机组参数波动工况下进行水煤比寻优。通过使用Pearson相关系数分析机组运行参数,确定寻优模型的输入数据,计算VAR模型最优阶数,并建立VAR模型从多个参数的时间序列寻找对应工况下水煤比最优值,同时使用三种不同分析方法确保该最优值的准确性和安全性。实践证明,该方法能有效解决机组由于煤质频繁变化导致锅炉给水策略不适配引发的主蒸汽温度和主蒸汽压力偏差大等问题。

Assessment of Dependent Performance Shaping Factors in SPAR-H Based on Pearson Correlation Coefficient

With the improvement of equipment reliability,human factors have become the most uncertain part in the system.The standardized Plant Analysis of Risk-Human Reliability Analysis(SPAR-H)method is a reliable method in the field of human reliability analysis(HRA)to evaluate human reliability and assess risk in large complex systems.However,the classical SPAR-H method does not consider the dependencies among performance shaping factors(PSFs),whichmay cause overestimation or underestimation of the risk of the actual situation.To address this issue,this paper proposes a new method to deal with the dependencies among PSFs in SPAR-H based on the Pearson correlation coefficient.First,the dependence between every two PSFs is measured by the Pearson correlation coefficient.Second,the weights of the PSFs are obtained by considering the total dependence degree.Finally,PSFs’multipliers are modified based on the weights of corresponding PSFs,and then used in the calculating of human error probability(HEP).A case study is used to illustrate the procedure and effectiveness of the proposed method.

Chi-Square Distribution: New Derivations and Environmental Application

We describe two new derivations of the chi-square distribution. The first derivation uses the induction method, which requires only a single integral to calculate. The second derivation uses the Laplace transform and requires minimum assumptions. The new derivations are compared with the established derivations, such as by convolution, moment generating function, and Bayesian inference. The chi-square testing has seen many applications to physics and other fields. We describe a unique version of the chi-square test where both the variance and location are tested, which is then applied to environmental data. The chi-square test is used to make a judgment whether a laboratory method is capable of detection of gross alpha and beta radioactivity in drinking water for regulatory monitoring to protect health of population. A case of a failure of the chi-square test and its amelioration are described. The chi-square test is compared to and supplemented by the t-test.

Generalized Kumaraswamy Generalized Power Gompertz Distribution: Statistical Properties, Application, and Validation Using a Modified Chi-Squared Goodness of Fit Test

A new six-parameter continuous distribution called the Generalized Kumaraswamy Generalized Power Gompertz (GKGPG) distribution is proposed in this study, a graphical illustration of the probability density function and cumulative distribution function is presented. The statistical features of the Generalized Kumaraswamy Generalized Power Gompertz distribution are systematically derived and adequately studied. The estimation of the model parameters in the absence of censoring and under-right censoring is performed using the method of maximum likelihood. The test statistic for right-censored data, criteria test for GKGPG distribution, estimated matrix Ŵ, Ĉ, and Ĝ, criteria test Y2n, alongside the quadratic form of the test statistic is derived. Mean simulated values of maximum likelihood estimates and their corresponding square mean errors are presented and confirmed to agree closely with the true parameter values. Simulated levels of significance for Y2n (γ) test for the GKGPG model against their theoretical values were recorded. We conclude that the null hypothesis for which simulated samples are fitted by GKGPG distribution is widely validated for the different levels of significance considered. From the summary of the results of the strength of a specific type of braided cord dataset on the GKGPG model, it is observed that the proposed GKGPG model fits the data set for a significance level ε = 0.05.

A Simple Chi-Square Statistic for Testing Homogeneity of Zero-Inflated Distributions

Zero-inflated distributions are common in statistical problems where there is interest in testing homogeneity of two or more independent groups. Often, the underlying distribution that has an inflated number of zero-valued observations is asymmetric, and its functional form may not be known or easily characterized. In this case, comparisons of the groups in terms of their respective percentiles may be appropriate as these estimates are nonparametric and more robust to outliers and other irregularities. The median test is often used to compare distributions with similar but asymmetric shapes but may be uninformative when there are excess zeros or dissimilar shapes. For zero-inflated distributions, it is useful to compare the distributions with respect to their proportion of zeros, coupled with the comparison of percentile profiles for the observed non-zero values. A simple chi-square test for simultaneous testing of these two components is proposed, applicable to both continuous and discrete data. Results of simulation studies are reported to summarize empirical power under several scenarios. We give recommendations for the minimum sample size which is necessary to achieve suitable test performance in specific examples.

Prediction of Bandwidth of Metamaterial Antenna Using Pearson Kernel-Based Techniques

The use of metamaterial enhances the performance of a specific class of antennas known as metamaterial antennas.The radiation cost and quality factor of the antenna are influenced by the size of the antenna.Metamaterial antennas allow for the circumvention of the bandwidth restriction for small antennas.Antenna parameters have recently been predicted using machine learning algorithms in existing literature.Machine learning can take the place of the manual process of experimenting to find the ideal simulated antenna parameters.The accuracy of the prediction will be primarily dependent on the model that is used.In this paper,a novel method for forecasting the bandwidth of the metamaterial antenna is proposed,based on using the Pearson Kernel as a standard kernel.Along with these new approaches,this paper suggests a unique hypersphere-based normalization to normalize the values of the dataset attributes and a dimensionality reduction method based on the Pearson kernel to reduce the dimension.A novel algorithm for optimizing the parameters of Convolutional Neural Network(CNN)based on improved Bat Algorithm-based Optimization with Pearson Mutation(BAO-PM)is also presented in this work.The prediction results of the proposed work are better when compared to the existing models in the literature.

Using Pearson’s System of Curves to Approximate the Distributions of the Difference between Two Correlated Estimates of Signal-to-Noise Ratios: The Cases of Bivariate Normal and Bivariate Lognormal Distributions

Background: The signal-to-noise ratio (SNR) is recognized as an index of measurements reproducibility. We derive the maximum likelihood estimators of SNR and discuss confidence interval construction on the difference between two correlated SNRs when the readings are from bivariate normal and bivariate lognormal distribution. We use the Pearsons system of curves to approximate the difference between the two estimates and use the bootstrap methods to validate the approximate distributions of the statistic of interest. Methods: The paper uses the delta method to find the first four central moments, and hence the skewness and kurtosis which are important in the determination of the parameters of the Pearsons distribution. Results: The approach is illustrated in two examples;one from veterinary microbiology and food safety data and the other on data from clinical medicine. We derived the four central moments of the target statistics, together with the bootstrap method to evaluate the parameters of Pearsons distribution. The fitted Pearsons curves of Types I and II were recommended based on the available data. The R-codes are also provided to be readily used by the readers.