scholarly journals Regularized Auto-Encoder-Based Separation of Defects from Backgrounds for Inspecting Display Devices

Electronics ◽  
2019 ◽  
Vol 8 (5) ◽  
pp. 533 ◽  
Author(s):  
Heeyeon Jo ◽  
Jeongtae Kim
Keyword(s):  
Experimental Studies ◽  
Low Rank ◽  
Reconstruction Method ◽  
Low Rank Approximation ◽  
Display Devices ◽  
Singular Value Decomposition Method ◽  
Novel Method ◽  
Rank Approximation ◽  
Improved Performance ◽  
Value Decomposition

We investigated a novel method for separating defects from the background for inspecting display devices. Separation of defects has important applications such as determining whether the detected defects are truly defective and the quantification of the degree of defectiveness. Although many studies on estimating patterned background have been conducted, the existing studies are mainly based on the approach of approximation by low-rank matrices. Because the conventional methods face problems such as imperfect reconstruction and difficulty of selecting the bases for low-rank approximation, we have studied a deep-learning-based foreground reconstruction method that is based on the auto-encoder structure with a regression layer for the output. In the experimental studies carried out using mobile display panels, the proposed method showed significantly improved performance compared to the existing singular value decomposition method. We believe that the proposed method could be useful not only for inspecting display devices but also for many applications that involve the detection of defects in the presence of a textured background.

Numerical linear algebra in data mining

Acta Numerica ◽  
2006 ◽  
Vol 15 ◽  
pp. 327-384 ◽  
Author(s):  
Lars Eldén
Keyword(s):  
Data Mining ◽  
Linear Algebra ◽  
Web Search ◽  
Numerical Linear Algebra ◽  
Low Rank ◽  
Data Matrix ◽  
Low Rank Approximation ◽  
Rank Reduction ◽  
Rank Approximation ◽  
Value Decomposition

Ideas and algorithms from numerical linear algebra are important in several areas of data mining. We give an overview of linear algebra methods in text mining (information retrieval), pattern recognition (classification of handwritten digits), and PageRank computations for web search engines. The emphasis is on rank reduction as a method of extracting information from a data matrix, low-rank approximation of matrices using the singular value decomposition and clustering, and on eigenvalue methods for network analysis.

scholarly journals Least upper bound of truncation error of low-rank matrix approximation algorithm using QR decomposition with pivoting

2021 ◽  
Author(s):  
Haruka Kawamura ◽  
Reiji Suda
Keyword(s):  
Upper Bound ◽  
Truncation Error ◽  
Qr Decomposition ◽  
Low Rank ◽  
Matrix Approximation ◽  
Low Rank Approximation ◽  
Rank Matrix ◽  
Rank Approximation ◽  
Value Decomposition ◽  
Low Rank Matrix

AbstractLow-rank approximation by QR decomposition with pivoting (pivoted QR) is known to be less accurate than singular value decomposition (SVD); however, the calculation amount is smaller than that of SVD. The least upper bound of the ratio of the truncation error, defined by $$\Vert A-BC\Vert _2$$ ‖ A - B C ‖ 2 , using pivoted QR to that using SVD is proved to be $$\sqrt{\frac{4^k-1}{3}(n-k)+1}$$ 4 k - 1 3 ( n - k ) + 1 for $$A\in {\mathbb {R}}^{m\times n}$$ A ∈ R m × n $$(m\ge n)$$ ( m ≥ n ) , approximated as a product of $$B\in {\mathbb {R}}^{m\times k}$$ B ∈ R m × k and $$C\in {\mathbb {R}}^{k\times n}$$ C ∈ R k × n in this study.

Improved MR image denoising via low- rank approximation and Laplacian-of-Gaussian edge detector

2020 ◽  
Vol 14 (12) ◽  
pp. 2791-2798
Author(s):  
Xiaoqun Qiu ◽  
Zhen Chen ◽  
Saifullah Adnan ◽  
Hongwei He
Keyword(s):  
Image Denoising ◽  
Low Rank ◽  
Edge Detector ◽  
Low Rank Approximation ◽  
Mr Image ◽  
Rank Approximation

scholarly journals Fast Joint Multiband Reconstruction From Wideband Images Based on Low-Rank Approximation

2020 ◽  
Vol 6 ◽  
pp. 922-933
Author(s):  
M. Amine Hadj-Youcef ◽  
Francois Orieux ◽  
Alain Abergel ◽  
Aurelia Fraysse
Keyword(s):  
Low Rank ◽  
Low Rank Approximation ◽  
Rank Approximation

scholarly journals Low-Rank Approximation of Difference between Correlation Matrices Using Inner Product

2021 ◽  
Vol 11 (10) ◽  
pp. 4582
Author(s):  
Kensuke Tanioka ◽  
Satoru Hiwa
Keyword(s):  
Dimensional Reduction ◽  
Low Rank ◽  
Inner Product ◽  
Low Rank Approximation ◽  
Correlation Matrices ◽  
Rank Matrix ◽  
Clustering Approach ◽  
Rank Approximation ◽  
The Difference ◽  
Low Rank Matrix

In the domain of functional magnetic resonance imaging (fMRI) data analysis, given two correlation matrices between regions of interest (ROIs) for the same subject, it is important to reveal relatively large differences to ensure accurate interpretation. However, clustering results based only on differences tend to be unsatisfactory and interpreting the features tends to be difficult because the differences likely suffer from noise. Therefore, to overcome these problems, we propose a new approach for dimensional reduction clustering. Methods: Our proposed dimensional reduction clustering approach consists of low-rank approximation and a clustering algorithm. The low-rank matrix, which reflects the difference, is estimated from the inner product of the difference matrix, not only from the difference. In addition, the low-rank matrix is calculated based on the majorize–minimization (MM) algorithm such that the difference is bounded within the range −1 to 1. For the clustering process, ordinal k-means is applied to the estimated low-rank matrix, which emphasizes the clustering structure. Results: Numerical simulations show that, compared with other approaches that are based only on differences, the proposed method provides superior performance in recovering the true clustering structure. Moreover, as demonstrated through a real-data example of brain activity measured via fMRI during the performance of a working memory task, the proposed method can visually provide interpretable community structures consisting of well-known brain functional networks, which can be associated with the human working memory system. Conclusions: The proposed dimensional reduction clustering approach is a very useful tool for revealing and interpreting the differences between correlation matrices, even when the true differences tend to be relatively small.

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