Abstract
Cancer genomics data often contain multi-view resources of different data types, which provide rich complementary information. Analyzing multi-view cancer genomics data can effectively advance cancer research. The main process of analyzing multi-view cancer genomics data in this paper is to discover the relationship between cancers and genes by clustering cancer samples and identification of differentially expressed genes. To make full use of the consistency and complementarity between genomics data, we propose a new tensor robust model based on enhanced tensor nuclear norm and low-rank constraint (EPTR-TV). First, we define the concept of the enhanced partial sum of tensor nuclear norm (EPSTNN). It dramatically improves the flexibility of the tensor nuclear norm (TNN), effectively avoiding some errors brought by TNN when approximating tensor rank. Then, the anisotropic spatial-temporal total variation (TV) regularization is introduced, which enables the model to exploit the relationship between the structures of tensor data while focusing on the details of the tensor data features. In addition, EPSTNN and TV regularization are unified into the low-rank tensor framework for in-depth analysis of cancer genomics data. Finally, the iterative optimization problem of EPTR-TV is solved by alternating direction method of multipliers (ADMM). Experimental results from clustering and feature selection experiments performed on three multi-view cancer genomics datasets show that EPTR-TV outperforms other comparative models. These suggest that EPTR-TV plays an important role in identifying cancer subtypes and finding new carcinogenic information, thus providing important insights into cancer mechanisms.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Liu, J.X., Xu, Y., Zheng, C.H., Kong, H., Lai, Z.H.: RPCA-based tumor classification using gene expression data. IEEE/ACM Trans. Comput. Biol. Bioinform. 12(4), 1 (2014)
Lu, C., Feng, J., Chen, Y., Liu, W., Lin, Z., Yan, S.: Tensor robust principal component analysis: exact recovery of corrupted low-rank tensors via convex optimization. Comput. Vis. Pattern Recognit., 5249–5257 (2016)
Hu, Y., Liu, J.-X., Gao, Y.-L., Li, S.-J., Wang, J.: Differentially expressed genes extracted by the tensor robust principal component analysis (TRPCA) method. Complexity 2019, 1–13 (2019). https://doi.org/10.1155/2019/6136245
Zhao, Y.Y., Jiao, C.N., Wang, M.L., Liu, J.X., Zheng, C.H.: HTRPCA: hypergraph regularized tensor robust principal component analysis for sample clustering in tumor omics data. Interdiscip. Sci. Comput. Life Sci. (6) (2021)
Zhou, P., Feng J.: Outlier-robust tensor PCA. Comput. Vis. Pattern Recognit., 3938–3946 (2017)
Kilmer, M.E., Martin, C.D.: Factorization strategies for third-order tensors. Linear Algebra Appl. 435(3), 641–658 (2011). https://doi.org/10.1016/J.LAA.2010.09.020
Braman, K.: Third-order tensors as linear operators on a space of matrices. Linear Algebra Appl. 433(7), 1241–1253 (2010). https://doi.org/10.1016/J.LAA.2010.05.025
Liu, Y., Chen, L., Zhu, C.: Improved robust tensor principal component analysis via low-rank core matrix. IEEE J. Sel. Top. Signal Process. 12(6), 1378–1389 (2018). https://doi.org/10.1109/JSTSP.2018.2873142
Zhang, L., Peng, Z.: Infrared small target detection based on partial sum of the tensor nuclear norm. Remote Sens. 11(4) (2019). https://doi.org/10.3390/RS11040382
He, W., Zhang, H., Zhang, L., Shen, H.: Total-variation-regularized low-rank matrix factorization for hyperspectral image restoration. IEEE Trans. Geosci. Remote Sens. 54(1), 178–188 (2016). https://doi.org/10.1109/TGRS.2015.2452812
Lu, C., Feng, J., Chen, Y., Liu, W., Lin, Z., Yan, S.: Tensor robust principal component analysis with a new tensor nuclear norm. IEEE Trans. Pattern Anal. Mach. Intell. 42(4), 925–938 (2020). https://doi.org/10.1109/TPAMI.2019.2891760
Oh, T.-H., Tai, Y.-W., Bazin, J.-C., Kim, H., Kweon, I.S.: Partial sum minimization of singular values in robust PCA: algorithm and applications. IEEE Trans. Pattern Anal. Mach. Intell. 38(4), 744–758 (2016). https://doi.org/10.1109/TPAMI.2015.2465956
Tomczak, K., Czerwińska, P., Wiznerowicz, M.: Review The Cancer Genome Atlas (TCGA): an immeasurable source of knowledge. Contemp. Oncol. Współczesna Onkologia 2015(1), 68–77 (2015)
Safran, M., Dalah I., Alexander, J., Rosen, N., Iny Stein, T., Shmoish, M., et al.: GeneCards version 3: the human gene integrator. Database 2010 (2010)
Howe, J.R., Shellnut, J., Wagner, B., Ringold, J.C., Sayed, M.G., Ahmed, A.F., et al.: Common deletion of SMAD4 in juvenile polyposis is a mutational hotspot. Am. J. Hum. Genet. 70(5), 1357–1362 (2002)
Jiang, D., Wang, X., Wang, Y., Philips, D., Meng, W., Xiong, M., et al.: Mutation in BRAF and SMAD4 associated with resistance to neoadjuvant chemoradiation therapy in locally advanced rectal cancer. Virchows Arch. 475(1), 39–47 (2019)
Yu, M., Lin, Y., Zhou, Y., Jin, H., Hou, B., Wu, Z., et al.: MiR-144 suppresses cell proliferation, migration, and invasion in hepatocellular carcinoma by targeting SMAD4. OncoTargets Ther. 9, 4705 (2016)
Bian, C., Li, Z., Xu, Y., Wang, J., Xu, L., Shen, H.: Clinical outcome and expression of mutant P53, P16, and Smad4 in lung adenocarcinoma: a prospective study. World J. Surg. Oncol. 13(1), 1–8 (2015)
Acknowledgments
This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61872220 and 62172254.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Qiao, Q., Yuan, SS., Shang, J., Liu, JX. (2022). A Tensor Robust Model Based on Enhanced Tensor Nuclear Norm and Low-Rank Constraint for Multi-view Cancer Genomics Data. In: Bansal, M.S., Cai, Z., Mangul, S. (eds) Bioinformatics Research and Applications. ISBRA 2022. Lecture Notes in Computer Science(), vol 13760. Springer, Cham. https://doi.org/10.1007/978-3-031-23198-8_34
Download citation
DOI: https://doi.org/10.1007/978-3-031-23198-8_34
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-23197-1
Online ISBN: 978-3-031-23198-8
eBook Packages: Computer ScienceComputer Science (R0)