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Journal articles on the topic 'Low-Rank matrix approximation'

Author: Grafiati

Published: 7 December 2024

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1

Ting Liu, Ting Liu, Mingjian Sun Mingjian Sun, Naizhang Feng Naizhang Feng, Minghua Wang Minghua Wang, Deying Chen Deying Chen, and and Yi Shen and Yi Shen. "Sparse photoacoustic microscopy based on low-rank matrix approximation." Chinese Optics Letters 14, no. 9 (2016): 091701–91705. http://dx.doi.org/10.3788/col201614.091701.

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2

Parekh, Ankit, and Ivan W. Selesnick. "Enhanced Low-Rank Matrix Approximation." IEEE Signal Processing Letters 23, no. 4 (April 2016): 493–97. http://dx.doi.org/10.1109/lsp.2016.2535227.

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3

Fomin, Fedor V., Petr A. Golovach, and Fahad Panolan. "Parameterized low-rank binary matrix approximation." Data Mining and Knowledge Discovery 34, no. 2 (January 2, 2020): 478–532. http://dx.doi.org/10.1007/s10618-019-00669-5.

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4

Fomin, Fedor V., Petr A. Golovach, Daniel Lokshtanov, Fahad Panolan, and Saket Saurabh. "Approximation Schemes for Low-rank Binary Matrix Approximation Problems." ACM Transactions on Algorithms 16, no. 1 (January 11, 2020): 1–39. http://dx.doi.org/10.1145/3365653.

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5

Zhenyue Zhang and Keke Zhao. "Low-Rank Matrix Approximation with Manifold Regularization." IEEE Transactions on Pattern Analysis and Machine Intelligence 35, no. 7 (July 2013): 1717–29. http://dx.doi.org/10.1109/tpami.2012.274.

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6

Xu, An-Bao, and Dongxiu Xie. "Low-rank approximation pursuit for matrix completion." Mechanical Systems and Signal Processing 95 (October 2017): 77–89. http://dx.doi.org/10.1016/j.ymssp.2017.03.024.

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7

Barlow, Jesse L., and Hasan Erbay. "Modifiable low-rank approximation to a matrix." Numerical Linear Algebra with Applications 16, no. 10 (October 2009): 833–60. http://dx.doi.org/10.1002/nla.651.

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8

Jia, Yuheng, Hui Liu, Junhui Hou, and Qingfu Zhang. "Clustering Ensemble Meets Low-rank Tensor Approximation." Proceedings of the AAAI Conference on Artificial Intelligence 35, no. 9 (May 18, 2021): 7970–78. http://dx.doi.org/10.1609/aaai.v35i9.16972.

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This paper explores the problem of clustering ensemble, which aims to combine multiple base clusterings to produce better performance than that of the individual one. The existing clustering ensemble methods generally construct a co-association matrix, which indicates the pairwise similarity between samples, as the weighted linear combination of the connective matrices from different base clusterings, and the resulting co-association matrix is then adopted as the input of an off-the-shelf clustering algorithm, e.g., spectral clustering. However, the co-association matrix may be dominated by poor base clusterings, resulting in inferior performance. In this paper, we propose a novel low-rank tensor approximation based method to solve the problem from a global perspective. Specifically, by inspecting whether two samples are clustered to an identical cluster under different base clusterings, we derive a coherent-link matrix, which contains limited but highly reliable relationships between samples. We then stack the coherent-link matrix and the co-association matrix to form a three-dimensional tensor, the low-rankness property of which is further explored to propagate the information of the coherent-link matrix to the co-association matrix, producing a refined co-association matrix. We formulate the proposed method as a convex constrained optimization problem and solve it efficiently. Experimental results over 7 benchmark data sets show that the proposed model achieves a breakthrough in clustering performance, compared with 12 state-of-the-art methods. To the best of our knowledge, this is the first work to explore the potential of low-rank tensor on clustering ensemble, which is fundamentally different from previous approaches. Last but not least, our method only contains one parameter, which can be easily tuned.

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9

Tropp, Joel A., Alp Yurtsever, Madeleine Udell, and Volkan Cevher. "Practical Sketching Algorithms for Low-Rank Matrix Approximation." SIAM Journal on Matrix Analysis and Applications 38, no. 4 (January 2017): 1454–85. http://dx.doi.org/10.1137/17m1111590.

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10

Liu, Huafeng, Liping Jing, Yuhua Qian, and Jian Yu. "Adaptive Local Low-rank Matrix Approximation for Recommendation." ACM Transactions on Information Systems 37, no. 4 (December 10, 2019): 1–34. http://dx.doi.org/10.1145/3360488.

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11

Amini, Arash, Amin Karbasi, and Farokh Marvasti. "Low-Rank Matrix Approximation Using Point-Wise Operators." IEEE Transactions on Information Theory 58, no. 1 (January 2012): 302–10. http://dx.doi.org/10.1109/tit.2011.2167714.

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12

Hou, Junhui, Lap-Pui Chau, Nadia Magnenat-Thalmann, and Ying He. "Sparse Low-Rank Matrix Approximation for Data Compression." IEEE Transactions on Circuits and Systems for Video Technology 27, no. 5 (May 2017): 1043–54. http://dx.doi.org/10.1109/tcsvt.2015.2513698.

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13

Zhang, Zhenyue, and Lixin Wu. "Optimal low-rank approximation to a correlation matrix." Linear Algebra and its Applications 364 (May 2003): 161–87. http://dx.doi.org/10.1016/s0024-3795(02)00551-7.

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14

Gillis, Nicolas, and Yaroslav Shitov. "Low-rank matrix approximation in the infinity norm." Linear Algebra and its Applications 581 (November 2019): 367–82. http://dx.doi.org/10.1016/j.laa.2019.07.017.

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15

Song, Guang-Jing, and Michael K. Ng. "Nonnegative low rank matrix approximation for nonnegative matrices." Applied Mathematics Letters 105 (July 2020): 106300. http://dx.doi.org/10.1016/j.aml.2020.106300.

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16

van der Veen, Alle-Jan. "A Schur Method for Low-Rank Matrix Approximation." SIAM Journal on Matrix Analysis and Applications 17, no. 1 (January 1996): 139–60. http://dx.doi.org/10.1137/s0895479893261340.

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17

Sun, Dongxia, and Lihong Zhi. "Structured Low Rank Approximation of a Bezout Matrix." Mathematics in Computer Science 1, no. 2 (October 5, 2007): 427–37. http://dx.doi.org/10.1007/s11786-007-0014-6.

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18

Mena, Hermann, Alexander Ostermann, Lena-Maria Pfurtscheller, and Chiara Piazzola. "Numerical low-rank approximation of matrix differential equations." Journal of Computational and Applied Mathematics 340 (October 2018): 602–14. http://dx.doi.org/10.1016/j.cam.2018.01.035.

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19

Persson, David, and Daniel Kressner. "Randomized Low-Rank Approximation of Monotone Matrix Functions." SIAM Journal on Matrix Analysis and Applications 44, no. 2 (June 8, 2023): 894–918. http://dx.doi.org/10.1137/22m1523923.

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20

Soto-Quiros, Pablo. "Error analysis of the generalized low-rank matrix approximation." Electronic Journal of Linear Algebra 37 (July 23, 2021): 544–48. http://dx.doi.org/10.13001/ela.2021.5961.

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In this paper, we propose an error analysis of the generalized low-rank approximation, which is a generalization of the classical approximation of a matrix $A\in\mathbb{R}^{m\times n}$ by a matrix of a rank at most $r$, where $r\leq\min\{m,n\}$.

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21

Zhang, Jiani, Jennifer Erway, Xiaofei Hu, Qiang Zhang, and Robert Plemmons. "Randomized SVD Methods in Hyperspectral Imaging." Journal of Electrical and Computer Engineering 2012 (2012): 1–15. http://dx.doi.org/10.1155/2012/409357.

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We present a randomized singular value decomposition (rSVD) method for the purposes of lossless compression, reconstruction, classification, and target detection with hyperspectral (HSI) data. Recent work in low-rank matrix approximations obtained from random projections suggests that these approximations are well suited for randomized dimensionality reduction. Approximation errors for the rSVD are evaluated on HSI, and comparisons are made to deterministic techniques and as well as to other randomized low-rank matrix approximation methods involving compressive principal component analysis. Numerical tests on real HSI data suggest that the method is promising and is particularly effective for HSI data interrogation.

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22

Zhu, E., M. Xu, and D. Pi. "A Novel Robust Principal Component Analysis Algorithm of Nonconvex Rank Approximation." Mathematical Problems in Engineering 2020 (September 30, 2020): 1–17. http://dx.doi.org/10.1155/2020/9356935.

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Noise exhibits low rank or no sparsity in the low-rank matrix recovery, and the nuclear norm is not an accurate rank approximation of low-rank matrix. In the present study, to solve the mentioned problem, a novel nonconvex approximation function of the low-rank matrix was proposed. Subsequently, based on the nonconvex rank approximation function, a novel model of robust principal component analysis was proposed. Such model was solved with the alternating direction method, and its convergence was verified theoretically. Subsequently, the background separation experiments were performed on the Wallflower and SBMnet datasets. Furthermore, the effectiveness of the novel model was verified by numerical experiments.

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23

Fernández-Val, Iván, Hugo Freeman, and Martin Weidner. "Low-rank approximations of nonseparable panel models." Econometrics Journal 24, no. 2 (March 18, 2021): C40—C77. http://dx.doi.org/10.1093/ectj/utab007.

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Summary We provide estimation methods for nonseparable panel models based on low-rank factor structure approximations. The factor structures are estimated by matrix-completion methods to deal with the computational challenges of principal component analysis in the presence of missing data. We show that the resulting estimators are consistent in large panels, but suffer from approximation and shrinkage biases. We correct these biases using matching and difference-in-differences approaches. Numerical examples and an empirical application to the effect of election day registration on voter turnout in the US illustrate the properties and usefulness of our methods.

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24

Chen, Zhilong, Peng Wang, and Detong Zhu. "Approximation Conjugate Gradient Method for Low-Rank Matrix Recovery." Symmetry 16, no. 5 (May 2, 2024): 547. http://dx.doi.org/10.3390/sym16050547.

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Large-scale symmetric and asymmetric matrices have emerged in predicting the relationship between genes and diseases. The emergence of large-scale matrices increases the computational complexity of the problem. Therefore, using low-rank matrices instead of original symmetric and asymmetric matrices can greatly reduce computational complexity. In this paper, we propose an approximation conjugate gradient method for solving the low-rank matrix recovery problem, i.e., the low-rank matrix is obtained to replace the original symmetric and asymmetric matrices such that the approximation error is the smallest. The conjugate gradient search direction is given through matrix addition and matrix multiplication. The new conjugate gradient update parameter is given by the F-norm of matrix and the trace inner product of matrices. The conjugate gradient generated by the algorithm avoids SVD decomposition. The backtracking linear search is used so that the approximation conjugate gradient direction is computed only once, which ensures that the objective function decreases monotonically. The global convergence and local superlinear convergence of the algorithm are given. The numerical results are reported and show the effectiveness of the algorithm.

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25

Chang, Xiangyu, Yan Zhong, Yao Wang, and Shaobo Lin. "Unified Low-Rank Matrix Estimate via Penalized Matrix Least Squares Approximation." IEEE Transactions on Neural Networks and Learning Systems 30, no. 2 (February 2019): 474–85. http://dx.doi.org/10.1109/tnnls.2018.2844242.

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26

Nie, Feiping, Zhanxuan Hu, and Xuelong Li. "Matrix Completion Based on Non-Convex Low-Rank Approximation." IEEE Transactions on Image Processing 28, no. 5 (May 2019): 2378–88. http://dx.doi.org/10.1109/tip.2018.2886712.

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27

Zheng, Jianwei, Mengjie Qin, Xiaolong Zhou, Jiafa Mao, and Hongchuan Yu. "Efficient Implementation of Truncated Reweighting Low-Rank Matrix Approximation." IEEE Transactions on Industrial Informatics 16, no. 1 (January 2020): 488–500. http://dx.doi.org/10.1109/tii.2019.2916986.

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28

Horasan, Fahrettin, Hasan Erbay, Fatih Varçın, and Emre Deniz. "Alternate Low-Rank Matrix Approximation in Latent Semantic Analysis." Scientific Programming 2019 (February 3, 2019): 1–12. http://dx.doi.org/10.1155/2019/1095643.

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The latent semantic analysis (LSA) is a mathematical/statistical way of discovering hidden concepts between terms and documents or within a document collection (i.e., a large corpus of text). Each document of the corpus and terms are expressed as a vector with elements corresponding to these concepts to form a term-document matrix. Then, the LSA uses a low-rank approximation to the term-document matrix in order to remove irrelevant information, to extract more important relations, and to reduce the computational time. The irrelevant information is called as “noise” and does not have a noteworthy effect on the meaning of the document collection. This is an essential step in the LSA. The singular value decomposition (SVD) has been the main tool obtaining the low-rank approximation in the LSA. Since the document collection is dynamic (i.e., the term-document matrix is subject to repeated updates), we need to renew the approximation. This can be done via recomputing the SVD or updating the SVD. However, the computational time of recomputing or updating the SVD of the term-document matrix is very high when adding new terms and/or documents to preexisting document collection. Therefore, this issue opened the door of using other matrix decompositions for the LSA as ULV- and URV-based decompositions. This study shows that the truncated ULV decomposition (TULVD) is a good alternative to the SVD in the LSA modeling.

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29

Pitaval, Renaud-Alexandre, Wei Dai, and Olav Tirkkonen. "Convergence of Gradient Descent for Low-Rank Matrix Approximation." IEEE Transactions on Information Theory 61, no. 8 (August 2015): 4451–57. http://dx.doi.org/10.1109/tit.2015.2448695.

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30

Pei Chen. "Heteroscedastic Low-Rank Matrix Approximation by the Wiberg Algorithm." IEEE Transactions on Signal Processing 56, no. 4 (April 2008): 1429–39. http://dx.doi.org/10.1109/tsp.2007.909353.

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31

Duan, Xuefeng, Jiaofen Li, Qingwen Wang, and Xinjun Zhang. "Low rank approximation of the symmetric positive semidefinite matrix." Journal of Computational and Applied Mathematics 260 (April 2014): 236–43. http://dx.doi.org/10.1016/j.cam.2013.09.080.

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32

Mohd Sagheer, Sameera V., and Sudhish N. George. "Ultrasound image despeckling using low rank matrix approximation approach." Biomedical Signal Processing and Control 38 (September 2017): 236–49. http://dx.doi.org/10.1016/j.bspc.2017.06.011.

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33

Luo, Yu, and Jie Ling. "Single-image de-raining using low-rank matrix approximation." Neural Computing and Applications 32, no. 11 (June 7, 2019): 7503–14. http://dx.doi.org/10.1007/s00521-019-04271-0.

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34

Matveev, Sergey, and Stanislav Budzinskiy. "Sketching for a low-rank nonnegative matrix approximation: Numerical study." Russian Journal of Numerical Analysis and Mathematical Modelling 38, no. 2 (March 1, 2023): 99–114. http://dx.doi.org/10.1515/rnam-2023-0009.

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Abstract We propose new approximate alternating projection methods, based on randomized sketching, for the low-rank nonnegative matrix approximation problem: find a low-rank approximation of a nonnegative matrix that is nonnegative, but whose factors can be arbitrary. We calculate the computational complexities of the proposed methods and evaluate their performance in numerical experiments. The comparison with the known deterministic alternating projection methods shows that the randomized approaches are faster and exhibit similar convergence properties.

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35

Li, Chi-Kwong, and Gilbert Strang. "An elementary proof of Mirsky's low rank approximation theorem." Electronic Journal of Linear Algebra 36, no. 36 (October 14, 2020): 694–97. http://dx.doi.org/10.13001/ela.2020.5551.

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36

Shi, Chengfei, Zhengdong Huang, Li Wan, and Tifan Xiong. "Low-Rank Tensor Completion Based on Log-Det Rank Approximation and Matrix Factorization." Journal of Scientific Computing 80, no. 3 (July 15, 2019): 1888–912. http://dx.doi.org/10.1007/s10915-019-01009-x.

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37

Lebedeva, O. S., A. I. Osinsky, and S. V. Petrov. "Low-Rank Approximation Algorithms for Matrix Completion with Random Sampling." Computational Mathematics and Mathematical Physics 61, no. 5 (May 2021): 799–815. http://dx.doi.org/10.1134/s0965542521050122.

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38

Huang, Zhi-Long, and Hsu-Feng Hsiao. "Inter-frame Prediction with Fast Weighted Low-rank Matrix Approximation." International Journal of Electronics and Telecommunications 59, no. 1 (March 1, 2013): 9–16. http://dx.doi.org/10.2478/eletel-2013-0001.

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Abstract In the field of video coding, inter-frame prediction plays an important role in improving compression efficiency. The improved efficiency is achieved by finding predictors for video blocks such that the residual data can be close to zero as much as possible. For recent video coding standards, motion vectors are required for a decoder to locate the predictors during video reconstruction. Block matching algorithms are usually utilized in the stage of motion estimation to find such motion vectors. For decoder-side motion derivation, proper templates are defined and template matching algorithms are used to produce a predictor for each block such that the overhead of embedding coded motion vectors in bit-stream can be avoided. However, the conventional criteria of either block matching or template matching algorithms may lead to the generation of worse predictors. To enhance coding efficiency, a fast weighted low-rank matrix approximation approach to deriving decoder-side motion vectors for inter frame video coding is proposed in this paper. The proposed method first finds the dominating block candidates and their corresponding importance factors. Then, finding a predictor for each block is treated as a weighted low-rank matrix approximation problem, which is solved by the proposed column-repetition approach. Together with mode decision, the coder can switch to a better mode between the motion compensation by using either block matching or the proposed template matching scheme.

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39

Kirsteins, I. P., and D. W. Tufts. "Adaptive detection using low rank approximation to a data matrix." IEEE Transactions on Aerospace and Electronic Systems 30, no. 1 (1994): 55–67. http://dx.doi.org/10.1109/7.250406.

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40

Xu, Fei, Jingqi Han, Yongli Wang, Ming Chen, Yongyong Chen, Guoping He, and Yunhong Hu. "Dynamic Magnetic Resonance Imaging via Nonconvex Low-Rank Matrix Approximation." IEEE Access 5 (2017): 1958–66. http://dx.doi.org/10.1109/access.2017.2657645.

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41

Zhou, Guoxu, Andrzej Cichocki, and Shengli Xie. "Fast Nonnegative Matrix/Tensor Factorization Based on Low-Rank Approximation." IEEE Transactions on Signal Processing 60, no. 6 (June 2012): 2928–40. http://dx.doi.org/10.1109/tsp.2012.2190410.

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42

Nechepurenko, Yuri M., and Miloud Sadkane. "A Low-Rank Approximation for Computing the Matrix Exponential Norm." SIAM Journal on Matrix Analysis and Applications 32, no. 2 (April 2011): 349–63. http://dx.doi.org/10.1137/100789774.

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43

Shen, Haipeng, and Jianhua Z. Huang. "Sparse principal component analysis via regularized low rank matrix approximation." Journal of Multivariate Analysis 99, no. 6 (July 2008): 1015–34. http://dx.doi.org/10.1016/j.jmva.2007.06.007.

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44

Feng, Xingdong, and Xuming He. "Statistical inference based on robust low-rank data matrix approximation." Annals of Statistics 42, no. 1 (February 2014): 190–210. http://dx.doi.org/10.1214/13-aos1186.

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45

Gillard, J. W., and A. A. Zhigljavsky. "Stochastic algorithms for solving structured low-rank matrix approximation problems." Communications in Nonlinear Science and Numerical Simulation 21, no. 1-3 (April 2015): 70–88. http://dx.doi.org/10.1016/j.cnsns.2014.08.023.

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46

Chang, Haixia. "Constrained Low Rank Approximation of the Hermitian Nonnegative-Definite Matrix." Advances in Linear Algebra & Matrix Theory 10, no. 02 (2020): 22–33. http://dx.doi.org/10.4236/alamt.2020.102003.

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47

Chen, Yongyong, Yanwen Guo, Yongli Wang, Dong Wang, Chong Peng, and Guoping He. "Denoising of Hyperspectral Images Using Nonconvex Low Rank Matrix Approximation." IEEE Transactions on Geoscience and Remote Sensing 55, no. 9 (September 2017): 5366–80. http://dx.doi.org/10.1109/tgrs.2017.2706326.

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48

Inoue, Kohei, and Kiichi Urahama. "Dimensionality reduction by simultaneous low-rank approximation of matrix data." Electronics and Communications in Japan (Part II: Electronics) 90, no. 9 (2007): 42–49. http://dx.doi.org/10.1002/ecjb.20379.

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49

Hutchings, Matthew, and Bertrand Gauthier. "Energy-Based Sequential Sampling for Low-Rank PSD-Matrix Approximation." SIAM Journal on Mathematics of Data Science 6, no. 4 (October 28, 2024): 1055–77. http://dx.doi.org/10.1137/23m162449x.

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50

Brick, Yaniv, and Ali E. Yilmaz. "Rapid Rank Estimation and Low-Rank Approximation of Impedance Matrix Blocks Using Proxy Grids." IEEE Transactions on Antennas and Propagation 66, no. 10 (October 2018): 5359–69. http://dx.doi.org/10.1109/tap.2018.2854361.

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