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《山东大学学报(理学版)》 ›› 2024, Vol. 59 ›› Issue (1): 27-34.doi: 10.6040/j.issn.1671-9352.0.2023.035

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基于非负CP分解的图像数据监控方法

范金宇1,2(),邹杨1,2,熊健3,古勇毅1,2,*()   

  1. 1. 广东财经大学统计与数学学院, 广东 广州 510320
    2. 广东财经大学大数据与教育统计实验室, 广东 广州 510320
    3. 广州大学经济与统计学院, 广东 广州 510320
  • 收稿日期:2023-01-13 出版日期:2024-01-20 发布日期:2024-01-19
  • 通讯作者: 古勇毅 E-mail:jinyufan@gdufe.edu.cn;gdguyongyi@163.com
  • 作者简介:范金宇(1988—), 女, 讲师, 博士, 研究方向为统计过程控制、高维数据分析, E-mail: jinyufan@gdufe.edu.cn
  • 基金资助:
    国家自然科学基金面上资助项目(12271111);广州市科技计划项目(202102020419);全国统计科学研究项目(2021LY014)

Imagedata control chart based on nonnegative CP tensor decomposition

Jin-yu FAN1,2(),Yang ZOU1,2,Jian XIONG3,Yongyi GU1,2,*()   

  1. 1. School of Statistics and Mathematics, Guangdong University of Finance & Economics, Guangzhou 510320, Guangdong, China
    2. Big data and Educational Statistical Application Laboratory, Guangdong University of Finance & Economics, Guangzhou 510320, Guangdong, China
    3. School of Economics and Statistics, Guangzhou University, Guangzhou 510320, Guangdong, China
  • Received:2023-01-13 Online:2024-01-20 Published:2024-01-19
  • Contact: Yongyi GU E-mail:jinyufan@gdufe.edu.cn;gdguyongyi@163.com

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摘要：

非负张量分解不仅能有效提取图像数据特征, 而且不破坏图像数据的内部结构。因此, 本文基于非负CANDECOMP/PARAFAC(CP)分解建立无需额外参数设置和调优的图像数据控制图, 并基于仿真模拟分析该控制图在不同偏移情形下的监控性能。仿真结果显示, 该控制图对图像的位置偏移、面积变化、形状变化和颜色变化都能做出快速预警。为了比较所建立的控制图的性能优劣, 通过一个实际的工业生产中的无纺布图像, 基于相同的参数设置, 将所提出的非负CP分解控制图与广义似然比(generalized likelihood ratio, GLR)时空控制图、区域增长的指数加权移动平均(exponentially weighted moving average, EWMA)时空控制图和基于实时对比(real time contrasts, RTC)控制图进行比较。模拟结果显示, 当偏移量大于2的时候, 非负CP分解控制图的检测性能媲美现有的检测方法; 当偏移量不超过2时, 非负CP分解控制图能更快速地检测出异常。

关键词: 图像数据, 非负张量分解, 特征提取, 控制图

Abstract:

Nonnegative tensor decomposition is well known for extracting the features of image data effectively and do not destroy the internal structure features of the data at the same time. This paper establishes a control chart for image data based on nonnegative tensor decomposition without any additional parameters. The monitoring performance of the proposed chart is verified by simulation under location changes, area changes, shape changes and color changes of images. Meanwhile, through a real industrial nonwoven fabric image, comparisons of the proposed control chart, the GLR-based spatiotemporal chart, the EWMA and region growing based chart and the RTC chart are conducted with the same parameter settings. The results show that our proposed method is superior to the other methods when shift size is less than or equal to 2 and performs similarly with the other method when the shift size is large than 2.

Key words: image data, nonnegative tensor decomposition, feature extraction, control chart

中图分类号: 

  • O213

图1

受控图像样本和失控图像样本"

图2

非负CP分解控制图对位置偏移、区域变化、形状变化和颜色变化的ARL1和MRL1"

图3

非织物纺织原始图像和其名义图像"

表1

MRL0=150, 偏移区域10×10和偏移中心(125, 125)时，GLR时空控制图，EWMA时空控制图，RTC方法控制图和非负CP分解控制图的MRL1"

δ GLR时空控制图[10] EWMA时空控制图[15] RTC方法控制图[16] 非负CP分解控制图
-10 2.0 3.0 6.5 4.0
-5 8.0 6.0 10.0 8.0
-3 31.0 12.0 22.0 16.0
-2 78.0 30.0 49.0 29.0
-1 141.5 101.0 107.5 72.0
1 134.5 85.5 112.0 65.0
2 81.0 29.0 47.5 27.0
3 29.0 12.0 23.0 16.0
5 7.0 6.0 9.0 8.0
10 2.0 3.0 7.0 4.0

表2

偏移范围10×10时，不同区域划分及偏移中心下非负CP控制图的ARL1和MRL1"

ARL0=200(MRL0=150) 偏移量δ
-10 -5 -3 -2 -1 1 2 3 5 10
区域大小 偏移中心(125, 125)
10×10 4.0(4) 9.1(8) 18.6(16) 36.0(29) 98.4(72) 90.0(65) 33.6(27) 18.3(16) 8.5(8) 3.8(4)
15×15 3.9(4) 8.8(8) 18.3(16) 36.0(29) 96.5(68) 95.1(67) 35.0(28) 18.0(15) 8.8(8) 3.8(4)
20×20 3.9(4) 8.8(8) 19.3(16) 36.0(28) 103.2(75) 90.0(65) 34.1(27) 18.4(15.5) 8.6(8) 3.9(4)
区域大小 偏移中心(188, 206)
10×10 4.0(4) 8.8(8) 18.9(17) 38.1(29) 97.5(70.5) 96.1(67) 34.5(27) 18.3(16) 8.7(8) 3.8(4)
15×15 4.0(4) 9.2(8) 18.7(15.5) 35.2(27) 100.8(72) 94.1(66) 35.0(27) 18.6(16) 8.9(8) 3.9(4)
20×20 3.9(4) 9.1(8) 18.6(16) 34.9(28) 99.1(70) 93.4(66.5) 36.3(27) 18.3(16) 8.7(8) 3.9(4)
区域大小 偏移中心(158, 78)
10×10 4.0(4) 9.0(8) 18.5(16) 34.7(27) 99.2(71) 95.7(68) 33.4(26) 18.2(16) 8.9(8) 3.9(4)
15×15 4.0(4) 9.1(8) 18.8(16) 35.1(27) 97.0(72) 90.1(65) 33.4(26) 17.6(15) 9.0(8) 3.9(4)
20×20 4.0(4) 9.0(8) 18.5(16) 34.7(27) 99.2(71) 95.6(68) 33.4(26) 18.2(16) 8.9(8) 3.9(4)
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