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二次判别函数对偏态训练样本的渐近性能。

Asymptotic performance of the quadratic discriminant function to skewed training samples.

作者信息

Adebanji Atinuke, Asamoah-Boaheng Michael, Osei-Tutu Olivia

机构信息

Department of Mathematics, Kwame Nkrumah University of Science and Technology, PMB KNUST, Kumasi, Ghana.

Institute of Research, Innovation and Development (IRID), Kumasi Polytechnic, Box 854, Kumasi, Ghana.

出版信息

Springerplus. 2016 Sep 13;5(1):1530. doi: 10.1186/s40064-016-3204-3. eCollection 2016.

DOI:10.1186/s40064-016-3204-3
PMID:27652103
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC5020039/
Abstract

This study investigates the asymptotic performance of the quadratic discriminant function (QDF) under skewed training samples. The main objective of this study is to evaluate the performance of the QDF under skewed distribution considering different sample size ratios, varying the group centroid separators and the number of variables. Three populations [Formula: see text] with increasing group centroid separator function were considered. A multivariate normal distributed data was simulated with MatLab R2009a. There was an increase in the average error rates of the sample size ratios 1:2:2 and 1:2:3 as the total sample size increased asymptotically in the skewed distribution when the centroid separator increased from 1 to 3. The QDF under the skewed distribution performed better for the sample size ratio 1:1:1 as compared to the other sampling ratios and under centroid separator [Formula: see text].

摘要

本研究调查了在倾斜训练样本下二次判别函数（QDF）的渐近性能。本研究的主要目的是在倾斜分布下，考虑不同的样本量比例、改变组质心分隔符和变量数量，评估QDF的性能。考虑了三个总体[公式：见原文]，其组质心分隔函数不断增加。使用MatLab R2009a模拟了多元正态分布数据。当质心分隔符从1增加到3时，在倾斜分布中，随着总样本量渐近增加，样本量比例为1:2:2和1:2:3的平均错误率有所增加。与其他抽样比例相比，在倾斜分布下，样本量比例为1:1:1且在质心分隔符[公式：见原文]时，QDF的表现更好。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/227a/5020039/3febf45d92ce/40064_2016_3204_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/227a/5020039/409745b36c7a/40064_2016_3204_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/227a/5020039/ddd007fbca44/40064_2016_3204_Fig2_HTML.jpg
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https://cdn.ncbi.nlm.nih.gov/pmc/blobs/227a/5020039/3d8f86786140/40064_2016_3204_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/227a/5020039/e1ea9cc17f32/40064_2016_3204_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/227a/5020039/fee8c90a1115/40064_2016_3204_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/227a/5020039/508f4c575014/40064_2016_3204_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/227a/5020039/8ea4328c8c3b/40064_2016_3204_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/227a/5020039/3febf45d92ce/40064_2016_3204_Fig9_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/227a/5020039/409745b36c7a/40064_2016_3204_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/227a/5020039/ddd007fbca44/40064_2016_3204_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/227a/5020039/bd785054fbae/40064_2016_3204_Fig3_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/227a/5020039/3d8f86786140/40064_2016_3204_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/227a/5020039/e1ea9cc17f32/40064_2016_3204_Fig5_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/227a/5020039/fee8c90a1115/40064_2016_3204_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/227a/5020039/508f4c575014/40064_2016_3204_Fig7_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/227a/5020039/8ea4328c8c3b/40064_2016_3204_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/227a/5020039/3febf45d92ce/40064_2016_3204_Fig9_HTML.jpg

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