Low-cost orthogonal basis-core extraction for classification and reconstruction using tensor ring overlay panel

S. Akhter; M. M. Alam; M. S. Islam; M. A. Momen; M. S. Islam; M. Shoyaib

doi:10.1016/j.patcog.2024.110548

Journal Article2024Cited by 1

Low-cost orthogonal basis-core extraction for classification and reconstruction using tensor ring overlay panel

S. Akhter, M. M. Alam, M. S. Islam, M. A. Momen, M. S. Islam, M. Shoyaib

Pattern Recognition

Elsevier BV, Vol. 154, pp. 110548, ISBN: 0031-3203

DOI: 10.1016/j.patcog.2024.110548 URL

Keywords

Tensor (intrinsic definition)Benchmark (surveying)Basis (linear algebra)Computer scienceOrthogonal basisRing (chemistry)AlgorithmPattern recognition (psychology)Tensor productCore (optical fiber)Artificial intelligenceMathematics

CCDS Authors

Prof. M Shoyaib, PhD

Collaborator, AI/ML Wing

Professor

Institute of Information Technology

University of Dhaka

Research Interests

Image Processing

References

1.Ash A. Alizadeh, Michael B. Eisen, R. Eric Davis, Chi Ma, Izidore S. Lossos, Andreas Rosenwald, Jennifer C. Boldrick, Hajeer Sabet, Truc Tran, Xin Yu, John I. Powell, Liming Yang, Gerald E. Marti, Troy Moore, James Hudson, Lisheng Lu, David B. Lewis, Robert Tibshirani, Gavin Sherlock, Wing C. Chan, Timothy C. Greiner, Dennis D. Weisenburger, James O. Armitage, Roger Warnke, Ronald Levy, Wyndham Wilson, Michael R. Grever, John C. Byrd, David Botstein, Patrick O. Brown, Louis M. Staudt. (2000). Distinct types of diffuse large B-cell lymphoma identified by gene expression profiling. Nature, 403(6769), 503–511[10.1038/35000501]
2.Ledyard R Tucker. (1966). Some Mathematical Notes on Three-Mode Factor Analysis. Psychometrika, 31(3), 279–311[10.1007/bf02289464]
3.U. Alon, N. Barkai, D. A. Notterman, K. Gish, S. Ybarra, D. Mack, A. J. Levine. (1999). Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proceedings of the National Academy of Sciences, 96(12), 6745–6750[10.1073/pnas.96.12.6745]
4.Lieven De Lathauwer, Bart De Moor, Joos Vandewalle. (2000). A Multilinear Singular Value Decomposition. SIAM Journal on Matrix Analysis and Applications, 21(4), 1253–1278[10.1137/s0895479896305696]
5.Emanuel F Petricoin, Ali M Ardekani, Ben A Hitt, Peter J Levine, Vincent A Fusaro, Seth M Steinberg, Gordon B Mills, Charles Simone, David A Fishman, Elise C Kohn, Lance A Liotta. (2002). Use of proteomic patterns in serum to identify ovarian cancer. The Lancet, 359(9306), 572–577[10.1016/s0140-6736(02)07746-2]
6.I. V. Oseledets. (2011). Tensor-Train Decomposition. SIAM Journal on Scientific Computing, 33(5), 2295–2317[10.1137/090752286]
7.Javed Khan, Jun S. Wei, Markus Ringnér, Lao H. Saal, Marc Ladanyi, Frank Westermann, Frank Berthold, Manfred Schwab, Cristina R. Antonescu, Carsten Peterson, Paul S. Meltzer. (2001). Classification and diagnostic prediction of cancers using gene expression profiling and artificial neural networks. Nature Medicine, 7(6), 673–679[10.1038/89044]
8.Arindam Bhattacharjee, William G. Richards, Jane Staunton, Cheng Li, Stefano Monti, Priya Vasa, Christine Ladd, Javad Beheshti, Raphael Bueno, Michael Gillette, Massimo Loda, Griffin Weber, Eugene J. Mark, Eric S. Lander, Wing Wong, Bruce E. Johnson, Todd R. Golub, David J. Sugarbaker, Matthew Meyerson. (2001). Classification of human lung carcinomas by mRNA expression profiling reveals distinct adenocarcinoma subclasses. Proceedings of the National Academy of Sciences, 98(24), 13790–13795[10.1073/pnas.191502998]
9.Lieven De Lathauwer, Bart De Moor, Joos Vandewalle. (2000). On the Best Rank-1 and Rank-(R1 ,R2 ,. . .,RN) Approximation of Higher-Order Tensors. SIAM Journal on Matrix Analysis and Applications, 21(4), 1324–1342[10.1137/s0895479898346995]
10.Jonathan R. Pollack, Charles M. Perou, Ash A. Alizadeh, Michael B. Eisen, Alexander Pergamenschikov, Cheryl F. Williams, Stefanie S. Jeffrey, David Botstein, Patrick O. Brown. (1999). Genome-wide analysis of DNA copy-number changes using cDNA microarrays. Nature Genetics, 23(1), 41–46[10.1038/12640]
11.Sanjoy Dasgupta, Anupam Gupta. (2002). An elementary proof of a theorem of Johnson and Lindenstrauss. Random Structures and Algorithms, 22(1), 60–65[10.1002/rsa.10073]
12.(2003). Principal Component Analysis. Technometrics, 45(3), 276[10.1198/tech.2003.s783]
13.Haiping Lu, K.N. Plataniotis, A.N. Venetsanopoulos. (2008). MPCA: Multilinear Principal Component Analysis of Tensor Objects. IEEE Transactions on Neural Networks, 19(1), 18–39[10.1109/tnn.2007.901277]
14.Kurniabudi, Deris Stiawan, Darmawijoyo, Mohd Yazid Bin Idris, Alwi M. Bamhdi, Rahmat Budiarto. (2020). CICIDS-2017 Dataset Feature Analysis With Information Gain for Anomaly Detection. IEEE Access, 8, 132911–132921[10.1109/access.2020.3009843]
15.Anh Huy Phan, Andrzej Cichocki. (2010). Tensor decompositions for feature extraction and classification of high dimensional datasets. Nonlinear Theory and Its Applications IEICE, 1(1), 37–68[10.1587/nolta.1.37]
16.Madeleine Udell, Alex Townsend. (2019). Why Are Big Data Matrices Approximately Low Rank?. SIAM Journal on Mathematics of Data Science, 1(1), 144–160[10.1137/18m1183480]
17.Sadia Sharmin, Mohammad Shoyaib, Amin Ahsan Ali, Muhammad Asif Hossain Khan, Oksam Chae. (2019). Simultaneous feature selection and discretization based on mutual information. Pattern Recognition, 91, 162–174[10.1016/j.patcog.2019.02.016]
18.Wei He, Yong Chen, Naoto Yokoya, Chao Li, Qibin Zhao. (2021). Hyperspectral super-resolution via coupled tensor ring factorization. Pattern Recognition, 122, 108280[10.1016/j.patcog.2021.108280]
19.Miguel A. Veganzones, Jeremy E. Cohen, Rodrigo Cabral Farias, Jocelyn Chanussot, Pierre Comon. (2015). Nonnegative Tensor CP Decomposition of Hyperspectral Data. IEEE Transactions on Geoscience and Remote Sensing, 54(5), 2577–2588[10.1109/tgrs.2015.2503737]
20.Evgin Goceri. (2022). Evaluation of denoising techniques to remove speckle and Gaussian noise from dermoscopy images. Computers in Biology and Medicine, 152, 106474[10.1016/j.compbiomed.2022.106474]
21.Wei Zhou, Peng Dou, Tao Su, Haifeng Hu, Zhijie Zheng. (2022). Feature learning network with transformer for multi-label image classification. Pattern Recognition, 136, 109203[10.1016/j.patcog.2022.109203]
22.Ming Yang, Qilun Luo, Wen Li, Mingqing Xiao. (2021). Nonconvex 3D array image data recovery and pattern recognition under tensor framework. Pattern Recognition, 122, 108311[10.1016/j.patcog.2021.108311]
23.Qiquan Shi, Yiu-Ming Cheung, Qibin Zhao, Haiping Lu. (2018). Feature Extraction for Incomplete Data Via Low-Rank Tensor Decomposition With Feature Regularization. IEEE Transactions on Neural Networks and Learning Systems, 30(6), 1803–1817[10.1109/tnnls.2018.2873655]
24.Longhao Yuan, Chao Li, Jianting Cao, Qibin Zhao. (2019). Rank minimization on tensor ring: an efficient approach for tensor decomposition and completion. Machine Learning, 109(3), 603–622[10.1007/s10994-019-05846-7]
25.Yuyuan Yu, Guoxu Zhou, Ning Zheng, Yuning Qiu, Shengli Xie, Qibin Zhao. (2022). Graph-Regularized Non-Negative Tensor-Ring Decomposition for Multiway Representation Learning. IEEE Transactions on Cybernetics, 53(5), 3114–3127[10.1109/tcyb.2022.3157133]
26.Le Xu, Lei Cheng, Ngai Wong, Yik-Chung Wu. (2023). Tensor train factorization under noisy and incomplete data with automatic rank estimation. Pattern Recognition, 141, 109650[10.1016/j.patcog.2023.109650]
27.Maksim E. Eren, Juston S. Moore, Erik Skau, Elisabeth Moore, Manish Bhattarai, Gopinath Chennupati, Boian S. Alexandrov. (2022). General-purpose Unsupervised Cyber Anomaly Detection via Non-negative Tensor Factorization. Digital Threats Research and Practice, 4(1), 1–28[10.1145/3519602]
28.Tianchi Liao, Zhebin Wu, Chuan Chen, Zibin Zheng, Xiongjun Zhang. (2023). Tensor completion via convolutional sparse coding with small samples-based training. Pattern Recognition, 141, 109624[10.1016/j.patcog.2023.109624]
29.Johann A. Bengua, Phien N. Ho, Hoang Duong Tuan, Minh N. Do. (2017). Matrix Product State for Higher-Order Tensor Compression and Classification. IEEE Transactions on Signal Processing, 65(15), 4019–4030[10.1109/tsp.2017.2703882]
30.A. Breger, J. I. Orlando, P. Harar, M. Dörfler, S. Klimscha, C. Grechenig, B. S. Gerendas, U. Schmidt-Erfurth, M. Ehler. (2019). On Orthogonal Projections for Dimension Reduction and Applications in Augmented Target Loss Functions for Learning Problems. Journal of Mathematical Imaging and Vision, 62(3), 376–394[10.1007/s10851-019-00902-2]
31.Chang Liu, Tao Yan, WeiDong Zhao, YongHong Liu, Dan Li, Feng Lin, JiLiu Zhou. (2014). Incremental Tensor Principal Component Analysis for Handwritten Digit Recognition. Mathematical Problems in Engineering, 2014(1)[10.1155/2014/819758]
32.Zhao, Qibin, Zhou, Guoxu, Xie, Shengli, Zhang, Liqing, Cichocki, Andrzej. (2016). Tensor Ring Decomposition. arXiv (Cornell University)[10.48550/arxiv.1606.05535]

Cited By

1.Shartaz Sajid Nahid, Md. Shariful Islam, Md. Arman Hossain, Muhammad Mahbub Alam, Mohammad Shoyaib. (2025). OCMTL: Transfer learning by orthogonal core-extraction of a matrix and its application in cross-project defect prediction. Alexandria Engineering Journal, 133, 498–516[10.1016/j.aej.2025.11.039]

← All publications

References

1.Ash A. Alizadeh, Michael B. Eisen, R. Eric Davis, Chi Ma, Izidore S. Lossos, Andreas Rosenwald, Jennifer C. Boldrick, Hajeer Sabet, Truc Tran, Xin Yu, John I. Powell, Liming Yang, Gerald E. Marti, Troy Moore, James Hudson, Lisheng Lu, David B. Lewis, Robert Tibshirani, Gavin Sherlock, Wing C. Chan, Timothy C. Greiner, Dennis D. Weisenburger, James O. Armitage, Roger Warnke, Ronald Levy, Wyndham Wilson, Michael R. Grever, John C. Byrd, David Botstein, Patrick O. Brown, Louis M. Staudt. (2000). Distinct types of diffuse large B-cell lymphoma identified by gene expression profiling. Nature, 403(6769), 503–511[10.1038/35000501]

2.Ledyard R Tucker. (1966). Some Mathematical Notes on Three-Mode Factor Analysis. Psychometrika, 31(3), 279–311[10.1007/bf02289464]

3.U. Alon, N. Barkai, D. A. Notterman, K. Gish, S. Ybarra, D. Mack, A. J. Levine. (1999). Broad patterns of gene expression revealed by clustering analysis of tumor and normal colon tissues probed by oligonucleotide arrays. Proceedings of the National Academy of Sciences, 96(12), 6745–6750[10.1073/pnas.96.12.6745]

4.Lieven De Lathauwer, Bart De Moor, Joos Vandewalle. (2000). A Multilinear Singular Value Decomposition. SIAM Journal on Matrix Analysis and Applications, 21(4), 1253–1278[10.1137/s0895479896305696]

5.Emanuel F Petricoin, Ali M Ardekani, Ben A Hitt, Peter J Levine, Vincent A Fusaro, Seth M Steinberg, Gordon B Mills, Charles Simone, David A Fishman, Elise C Kohn, Lance A Liotta. (2002). Use of proteomic patterns in serum to identify ovarian cancer. The Lancet, 359(9306), 572–577[10.1016/s0140-6736(02)07746-2]

6.I. V. Oseledets. (2011). Tensor-Train Decomposition. SIAM Journal on Scientific Computing, 33(5), 2295–2317[10.1137/090752286]

7.Javed Khan, Jun S. Wei, Markus Ringnér, Lao H. Saal, Marc Ladanyi, Frank Westermann, Frank Berthold, Manfred Schwab, Cristina R. Antonescu, Carsten Peterson, Paul S. Meltzer. (2001). Classification and diagnostic prediction of cancers using gene expression profiling and artificial neural networks. Nature Medicine, 7(6), 673–679[10.1038/89044]

8.Arindam Bhattacharjee, William G. Richards, Jane Staunton, Cheng Li, Stefano Monti, Priya Vasa, Christine Ladd, Javad Beheshti, Raphael Bueno, Michael Gillette, Massimo Loda, Griffin Weber, Eugene J. Mark, Eric S. Lander, Wing Wong, Bruce E. Johnson, Todd R. Golub, David J. Sugarbaker, Matthew Meyerson. (2001). Classification of human lung carcinomas by mRNA expression profiling reveals distinct adenocarcinoma subclasses. Proceedings of the National Academy of Sciences, 98(24), 13790–13795[10.1073/pnas.191502998]

9.Lieven De Lathauwer, Bart De Moor, Joos Vandewalle. (2000). On the Best Rank-1 and Rank-(R1 ,R2 ,. . .,RN) Approximation of Higher-Order Tensors. SIAM Journal on Matrix Analysis and Applications, 21(4), 1324–1342[10.1137/s0895479898346995]

10.Jonathan R. Pollack, Charles M. Perou, Ash A. Alizadeh, Michael B. Eisen, Alexander Pergamenschikov, Cheryl F. Williams, Stefanie S. Jeffrey, David Botstein, Patrick O. Brown. (1999). Genome-wide analysis of DNA copy-number changes using cDNA microarrays. Nature Genetics, 23(1), 41–46[10.1038/12640]

11.Sanjoy Dasgupta, Anupam Gupta. (2002). An elementary proof of a theorem of Johnson and Lindenstrauss. Random Structures and Algorithms, 22(1), 60–65[10.1002/rsa.10073]

12.(2003). Principal Component Analysis. Technometrics, 45(3), 276[10.1198/tech.2003.s783]

13.Haiping Lu, K.N. Plataniotis, A.N. Venetsanopoulos. (2008). MPCA: Multilinear Principal Component Analysis of Tensor Objects. IEEE Transactions on Neural Networks, 19(1), 18–39[10.1109/tnn.2007.901277]

14.Kurniabudi, Deris Stiawan, Darmawijoyo, Mohd Yazid Bin Idris, Alwi M. Bamhdi, Rahmat Budiarto. (2020). CICIDS-2017 Dataset Feature Analysis With Information Gain for Anomaly Detection. IEEE Access, 8, 132911–132921[10.1109/access.2020.3009843]

15.Anh Huy Phan, Andrzej Cichocki. (2010). Tensor decompositions for feature extraction and classification of high dimensional datasets. Nonlinear Theory and Its Applications IEICE, 1(1), 37–68[10.1587/nolta.1.37]

16.Madeleine Udell, Alex Townsend. (2019). Why Are Big Data Matrices Approximately Low Rank?. SIAM Journal on Mathematics of Data Science, 1(1), 144–160[10.1137/18m1183480]

17.Sadia Sharmin, Mohammad Shoyaib, Amin Ahsan Ali, Muhammad Asif Hossain Khan, Oksam Chae. (2019). Simultaneous feature selection and discretization based on mutual information. Pattern Recognition, 91, 162–174[10.1016/j.patcog.2019.02.016]

18.Wei He, Yong Chen, Naoto Yokoya, Chao Li, Qibin Zhao. (2021). Hyperspectral super-resolution via coupled tensor ring factorization. Pattern Recognition, 122, 108280[10.1016/j.patcog.2021.108280]

19.Miguel A. Veganzones, Jeremy E. Cohen, Rodrigo Cabral Farias, Jocelyn Chanussot, Pierre Comon. (2015). Nonnegative Tensor CP Decomposition of Hyperspectral Data. IEEE Transactions on Geoscience and Remote Sensing, 54(5), 2577–2588[10.1109/tgrs.2015.2503737]

20.Evgin Goceri. (2022). Evaluation of denoising techniques to remove speckle and Gaussian noise from dermoscopy images. Computers in Biology and Medicine, 152, 106474[10.1016/j.compbiomed.2022.106474]

21.Wei Zhou, Peng Dou, Tao Su, Haifeng Hu, Zhijie Zheng. (2022). Feature learning network with transformer for multi-label image classification. Pattern Recognition, 136, 109203[10.1016/j.patcog.2022.109203]

22.Ming Yang, Qilun Luo, Wen Li, Mingqing Xiao. (2021). Nonconvex 3D array image data recovery and pattern recognition under tensor framework. Pattern Recognition, 122, 108311[10.1016/j.patcog.2021.108311]

23.Qiquan Shi, Yiu-Ming Cheung, Qibin Zhao, Haiping Lu. (2018). Feature Extraction for Incomplete Data Via Low-Rank Tensor Decomposition With Feature Regularization. IEEE Transactions on Neural Networks and Learning Systems, 30(6), 1803–1817[10.1109/tnnls.2018.2873655]

24.Longhao Yuan, Chao Li, Jianting Cao, Qibin Zhao. (2019). Rank minimization on tensor ring: an efficient approach for tensor decomposition and completion. Machine Learning, 109(3), 603–622[10.1007/s10994-019-05846-7]

25.Yuyuan Yu, Guoxu Zhou, Ning Zheng, Yuning Qiu, Shengli Xie, Qibin Zhao. (2022). Graph-Regularized Non-Negative Tensor-Ring Decomposition for Multiway Representation Learning. IEEE Transactions on Cybernetics, 53(5), 3114–3127[10.1109/tcyb.2022.3157133]

26.Le Xu, Lei Cheng, Ngai Wong, Yik-Chung Wu. (2023). Tensor train factorization under noisy and incomplete data with automatic rank estimation. Pattern Recognition, 141, 109650[10.1016/j.patcog.2023.109650]

27.Maksim E. Eren, Juston S. Moore, Erik Skau, Elisabeth Moore, Manish Bhattarai, Gopinath Chennupati, Boian S. Alexandrov. (2022). General-purpose Unsupervised Cyber Anomaly Detection via Non-negative Tensor Factorization. Digital Threats Research and Practice, 4(1), 1–28[10.1145/3519602]

28.Tianchi Liao, Zhebin Wu, Chuan Chen, Zibin Zheng, Xiongjun Zhang. (2023). Tensor completion via convolutional sparse coding with small samples-based training. Pattern Recognition, 141, 109624[10.1016/j.patcog.2023.109624]

29.Johann A. Bengua, Phien N. Ho, Hoang Duong Tuan, Minh N. Do. (2017). Matrix Product State for Higher-Order Tensor Compression and Classification. IEEE Transactions on Signal Processing, 65(15), 4019–4030[10.1109/tsp.2017.2703882]

30.A. Breger, J. I. Orlando, P. Harar, M. Dörfler, S. Klimscha, C. Grechenig, B. S. Gerendas, U. Schmidt-Erfurth, M. Ehler. (2019). On Orthogonal Projections for Dimension Reduction and Applications in Augmented Target Loss Functions for Learning Problems. Journal of Mathematical Imaging and Vision, 62(3), 376–394[10.1007/s10851-019-00902-2]

31.Chang Liu, Tao Yan, WeiDong Zhao, YongHong Liu, Dan Li, Feng Lin, JiLiu Zhou. (2014). Incremental Tensor Principal Component Analysis for Handwritten Digit Recognition. Mathematical Problems in Engineering, 2014(1)[10.1155/2014/819758]

32.Zhao, Qibin, Zhou, Guoxu, Xie, Shengli, Zhang, Liqing, Cichocki, Andrzej. (2016). Tensor Ring Decomposition. arXiv (Cornell University)[10.48550/arxiv.1606.05535]

Cited By

1.Shartaz Sajid Nahid, Md. Shariful Islam, Md. Arman Hossain, Muhammad Mahbub Alam, Mohammad Shoyaib. (2025). OCMTL: Transfer learning by orthogonal core-extraction of a matrix and its application in cross-project defect prediction. Alexandria Engineering Journal, 133, 498–516[10.1016/j.aej.2025.11.039]