Skip to main content
SpringerLink
Log in

Application of Graph Regularized Non-negative Matrix Factorization in Characteristic Gene Selection

  • Conference paper
  • First Online:
Intelligent Computing Theories and Methodologies (ICIC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 9226))

Included in the following conference series:

Abstract

Nonnegative matrix factorization (NMF) has become a popular method and widely used in many fields, for the reason that NMF algorithm can deal with many high dimension, non-negative problems. However, in real gene expression data applications, we often have to deal with the geometric structure problems. Thus a Graph Regularized version of NMF is needed. In this paper, we propose a Graph Regularized Non-negative Matrix Factorization (GRNMF) with emphasizing graph regularized on error function to extract characteristic gene set. This method considers the samples in low-dimensional manifold which embedded in a high-dimensional ambient space, and reveals the data geometric structure embedded in the original data. Experiment results on tumor datasets and plants gene expression data demonstrate that our GRNMF model can extract more differential genes than other existing state-of-the-art methods.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Liu, J.-X., Zheng, C.-H., Xu, Y.: Extracting plants core genes responding to abiotic stresses by penalized matrix decomposition. Comput. Biol. Med. 42, 582–589 (2012)

    Article  Google Scholar 

  2. Liu, J.-X., Liu, J., Gao, Y.-L., Mi, J.-X., Ma, C.-X., Wang, D.: A class-information-based penalized matrix decomposition for identifying plants core genes responding to abiotic stresses. PloS one 9, e106097 (2014)

    Article  Google Scholar 

  3. Livak, K.J., Schmittgen, T.D.: Analysis of relative gene expression data using real-time quantitative pcr and the 2−ΔΔCT method. Methods 25, 402–408 (2001)

    Article  Google Scholar 

  4. Journée, M., Nesterov, Y., Richtárik, P., Sepulchre, R.: Generalized power method for sparse principal component analysis. J. Mach. Learn. Res. 11, 517–553 (2010)

    MathSciNet  MATH  Google Scholar 

  5. Liu, J.-X., Gao, Y.-L., Xu, Y., Zheng, C.-H., You, J.: Differential expression analysis on RNA-Seq count data based on penalized matrix decomposition. IEEE Trans. Nanobiosci. 13, 12–18 (2014)

    Article  Google Scholar 

  6. Yalavarthy, P.K., Pogue, B.W., Dehghani, H., Paulsen, K.D.: Weight-matrix structured regularization provides optimal generalized least-squares estimate in diffuse optical tomography. Med. Phys. 34, 2085–2098 (2007)

    Article  Google Scholar 

  7. Chen, D., Cao, X., Wen, F., Sun, J.: Blessing of dimensionality: high-dimensional feature and its efficient compression for face verification. In: 2013 IEEE Conference on Computer Vision and Pattern Recognition (CVPR), pp. 3025–3032. IEEE (2013)

    Google Scholar 

  8. Hall, P., Marron, J., Neeman, A.: Geometric representation of high dimension, low sample size data. J. R. Stat. Soc. Ser. B (Stat. Method.) 67, 427–444 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  9. Geng, B., Tao, D., Xu, C., Yang, Y., Hua, X.-S.: Ensemble manifold regularization. IEEE Trans. Pattern Anal. Mach. Intell. 34, 1227–1233 (2012)

    Article  Google Scholar 

  10. Lee, D.-C., Wuest, M., McEwan, A., Jans, H.-S.: Dynamic FDG PET images of mice analyzed with a novel non-negative matrix factorization (NMF) technique. In: Society of Nuclear Medicine Annual Meeting Abstracts, p. 1422. Soc Nuclear Med (2008)

    Google Scholar 

  11. Li, S.Z., Hou, X., Zhang, H., Cheng, Q.: Learning spatially localized, parts-based representation. In: Proceedings of the 2001 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR 2001), vol. 201, pp. I-207–I-212. IEEE (2001)

    Google Scholar 

  12. Huang, Y., Pei, J., Yang, J., Wang, T., Yang, H., Wang, B.: Kernel generalized neighbor discriminant embedding for SAR automatic target recognition. EURASIP J. Adv. Signal Process. 2014, 72 (2014)

    Article  Google Scholar 

  13. Hammond, D.K., Vandergheynst, P., Gribonval, R.: Wavelets on graphs via spectral graph theory. Appl. Comput. Harmonic Anal. 30, 129–150 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. Carr, J.: Applications of Centre Manifold Theory. Springer, Berlin (1981)

    Book  MATH  Google Scholar 

  15. Deng, C., Xiaofei, H., Jiawei, H., Huang, T.S.: Graph regularized nonnegative matrix factorization for data representation. IEEE Trans. Pattern Anal. Mach. Intell. 33, 1548–1560 (2011)

    Article  Google Scholar 

  16. Izenman, A.J.: Modern Multivariate Statistical Techniques: Regression, Classification, and Manifold Learning. Springer, New York (2009)

    Google Scholar 

  17. Liu, J., Wu, Z., Sun, L., Wei, Z., Xiao, L.: Hyperspectral image classification using kernel sparse representation and semilocal spatial graph regularization. IEEE Geosci. Remote Sens. Lett. 11, 1320–1324 (2014)

    Article  Google Scholar 

  18. Roughgarden, T., Schoppmann, F.: Local smoothness and the price of anarchy in splittable congestion games. J. Econ. Theory 156, 317–342 (2014)

    Article  Google Scholar 

  19. Liu, X., Zhai, D., Zhao, D., Zhai, G., Gao, W.: Progressive image denoising through hybrid graph laplacian regularization: a unified framework. IEEE Trans. Image Process. Publ. IEEE Signal Process. Soc. 23, 1491–1503 (2014)

    MathSciNet  Google Scholar 

  20. Wu, G.-C., Baleanu, D.: Variational iteration method for the burgers’ flow with fractional derivatives—new lagrange multipliers. Appl. Math. Model. 37, 6183–6190 (2013)

    Article  MathSciNet  Google Scholar 

  21. Facchinei, F., Kanzow, C., Sagratella, S.: Solving quasi-variational inequalities via their KKT conditions. Math. Program. 144, 369–412 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  22. Witten, D.M., Tibshirani, R., Hastie, T.: A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis. Biostatistics (2009). doi:10.1093/biostatistics/kxp008

  23. Nyamundanda, G., Gormley, I.C., Brennan, L.: A dynamic probabilistic principal components model for the analysis of longitudinal metabolomics data. J. R. Stat. Soc. Ser. C (Appl. Stat.) 63(5), 763–782 (2014)

    Article  MathSciNet  Google Scholar 

  24. Craigon, D.J., James, N., Okyere, J., Higgins, J., Jotham, J., May, S.: NASCArrays: a repository for microarray data generated by NASC’s transcriptomics service. Nucleic Acids Res. 32, D575–D577 (2004)

    Article  Google Scholar 

  25. Shen, H., Huang, J.Z.: Sparse principal component analysis via regularized low rank matrix approximation. J. Multivar. Anal. 99, 1015–1034 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  26. Jenks, M.A., Hasegawa, P.M.: Plant Abiotic Stress. Wiley, Hoboken (2008)

    Google Scholar 

  27. Feigelman, J., Theis, F.J., Marr, C.: MCA: multiresolution correlation analysis, a graphical tool for subpopulation identification in single-cell gene expression data. arXiv preprint. arXiv:1407.2112 (2014)

    Google Scholar 

  28. Dinkla, K., El-Kebir, M., Bucur, C.-I., Siderius, M., Smit, M.J., Westenberg, M.A., Klau, G.W.: eXamine: exploring annotated modules in networks. BMC Bioinformatics 15, 201 (2014)

    Article  Google Scholar 

  29. Tembhare, P.R., Subramanian, P.G., Sehgal, K., Yajamanam, B., Kumar, A., Gujral, S.: Hypergranular precursor B-cell acute lymphoblastic leukemia in a 16-year-old boy. Indian J. Pathol. Microbiol. 52(3), 421 (2009)

    Article  Google Scholar 

Download references

Acknowledgement

This work was supported in part by the NSFC under grant Nos. 61370163, 61373027 and 61272339; China Postdoctoral Science Foundation funded project, No. 2014M560264; Shandong Provincial Natural Science Foundation, under grant Nos. ZR2013FL016 and ZR2012FM023; Shenzhen Municipal Science and Technology Innovation Council (Nos. JCYJ20140417172417174, CXZZ20140904154910774 and JCYJ20140904154645958); the Scientific Research Reward Foundation for Excellent Young and Middle-age Scientists of Shandong Province (BS2014DX004).

Author information

Authors and Affiliations

  1. School of Information Science and Engineering, Qufu Normal University, Rizhao, China

    Dong Wang, Jin-Xing Liu, Ji-Guo Yu & Chang-Gang Wen

  2. Library of Qufu Normal University, Qufu Normal University, Rizhao, China

    Ying-Lian Gao

  3. Bio-Computing Research Center, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, Guangdong, China

    Jin-Xing Liu

Authors
  1. Dong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ying-Lian Gao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Jin-Xing Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Ji-Guo Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Chang-Gang Wen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Jin-Xing Liu .

Editor information

Editors and Affiliations

  1. Tongji University, Shanghai, China

    De-Shuang Huang

  2. University of Ulsan, Ulsan, Korea (Republic of)

    Kang-Hyun Jo

  3. Liverpool John Moores University, Liverpool, United Kingdom

    Abir Hussain

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Wang, D., Gao, YL., Liu, JX., Yu, JG., Wen, CG. (2015). Application of Graph Regularized Non-negative Matrix Factorization in Characteristic Gene Selection. In: Huang, DS., Jo, KH., Hussain, A. (eds) Intelligent Computing Theories and Methodologies. ICIC 2015. Lecture Notes in Computer Science(), vol 9226. Springer, Cham. https://doi.org/10.1007/978-3-319-22186-1_60

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-22186-1_60

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22185-4

  • Online ISBN: 978-3-319-22186-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation