JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2024, Vol. 59 ›› Issue (1): 27-34.doi: 10.6040/j.issn.1671-9352.0.2023.035

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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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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

CLC Number: 

  • O213

Fig.1

In-control image and out-of-control images"

Fig.2

ARL1 and MRL1 of nonnegative CP decomposition control chart under location shifts, area changes, shapes changes and color changes"

Fig.3

Nonwoven fabric of the original image and the nominal image"

Table 1

MRL1 for GLR statistic-based control chart, EWMA control chart, RTC-based control chart and nonnegative CP decomposition-based control chart when MRL0=150, shift region is 10×10 and shift center?s location is (125, 125)"

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

Table 2

ARL1 and MRL1 of the nonnegative CP decomposition-based control chart for different region sizes and shift center?s location when shift size is 10×10"

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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