主成分分析阈值选择差异性分析研究
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1.兰州石化职业技术大学,兰州 730070;2.国家电网兰州供电公司,兰州 730050

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Difference Analysis Research of Threshold Selection in Principal Component Analysis
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1.Lanzhou Petrochemical University of Vocational Technology, Lanzhou 730070, China;2.State Grid Lanzhou Electric Power Supply Company, Lanzhou 730050, China

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    摘要:

    主成分分析是特征提取和数据降维中常用的方法,在很多应用中一般选择平均特征值作为主成分选择的标准。但是主成分的多少与应用结果之间的关系目前还没有具体的分析结果。因此,提出一种主成分阈值选择差异性的实验分析方法,为不同应用中主成分分析阈值的选择提供依据。将本文分析方法应用于手写数字样本集MNIST进行降维处理,根据不同的阈值构建不同的神经网络进行分类,分析不同阈值下分类准确率的变化情况。实验结果表明主成分阈值选择在79%~81%之间(维度为41~50)时,分类准确率最高;低于或高于该区间,准确率随之下降。实验结果证明了主成分分析阈值的选择与应用结果之间不为正相关关系,且平均特征值不是一个硬性的选择标准。

    Abstract:

    Principal component analysis (PCA) is a commonly used method for feature extraction and data dimension reduction. In many applications, the components whose eigenvalues are greater than the average value are retained. However, there is no specific analysis result for the relationship between the number of principal components and the application results. Therefore, an experimental analysis of the difference in selection of PCA threshold is carried out to provide basis for the PCA threshold selection in different applications. The experiment analysis is used to reduce the dimension of handwritten digital sample set MNIST, and different neural networks are constructed according to different thresholds for classification. Furthermore, the change of classification accuracy under different thresholds is analyzed. The experimental results show that when the threshold of PCA is between 79%—81% (dimension is 41—50), the classification accuracy is the highest, and the accuracy decreases accordingly when the threshold is lower or higher than that region. It is proved that there is no positive correlation between application results and threshold selection of PCA, and the average of the eigenvalues is not a mandatory criterion.

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张婧,刘倩.主成分分析阈值选择差异性分析研究[J].数据采集与处理,2022,37(5):1012-1017

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  • 收稿日期:2020-04-28
  • 最后修改日期:2021-01-30
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  • 在线发布日期: 2022-09-25