Skip to main content
SpringerLink
Log in

Graph Regularized Non-negative Matrix with L0-Constraints for Selecting Characteristic Genes

  • 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:

  • 1534 Accesses

Abstract

Non-negative Matrix Factorization (NMF) has been widely concerned in computer vision and data representation. However, the penalized and restriction L0-norm measure are imposed on the NMF model in traditional NMF methods. In this paper, we propose a novel graph regularized non-negative matrix with L0-constraints (GL0NMF) method which comprises the geometrical structure and a more interpretation sparseness measure. In order to extract the characteristic gene effectively, the steps are shown as follows. Firstly, the original data \( {\mathbf{Q}} \) is decomposed into two non-negative matrices \( {\mathbf{F}} \) and \( {\mathbf{P}} \) by utilizing GL0NMF method. Secondly, characteristic genes are extracted by the sparse matrix \( {\mathbf{F}} \). Finally, the extracted characteristic genes are validated by using Gene Ontology. In conclusion, the results demonstrate that our method can extract more genes than other conventional gene selection 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. Alter, O., Brown, P.O., Botstein, D.: Singular value decomposition for genome-wide expression data processing and modeling. Proc. Natl. Acad. Sci. 97, 10101–10106 (2000)

    Article  Google Scholar 

  2. 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  Google Scholar 

  3. Bartlett, M.S., Movellan, J.R., Sejnowski, T.J.: Face recognition by independent component analysis. IEEE Trans. Neural Netw. 13, 1450–1464 (2002)

    Article  Google Scholar 

  4. Huang, D.-S., Zheng, C.-H.: Independent component analysis-based penalized discriminant method for tumor classification using gene expression data. Bioinformatics 22, 1855–1862 (2006)

    Article  Google Scholar 

  5. Witten, D.M., Tibshirani, R., Hastie, T.: A penalized matrix decomposition, with applications to sparse principal components and canonical correlation analysis. Biostatistics 10, 515–534 (2009)

    Article  Google Scholar 

  6. 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 

  7. Liu, J., Zheng, C., Xu, Y.: Lasso logistic regression based approach for extracting plants coregenes responding to abiotic stresses. In: 2011 Fourth International Workshop on Advanced Computational Intelligence (IWACI), pp. 461–464 (2011)

    Google Scholar 

  8. Liu, J.-X., Xu, Y., Zheng, C.-H., Wang, Y., Yang, J.-Y.: Characteristic gene selection via weighting principal components by singular values. PLoS ONE 7, e38873 (2012)

    Article  Google Scholar 

  9. Liu, J.-X., Wang, Y.-T., Zheng, C.-H., Sha, W., Mi, J.-X., Xu, Y.: Robust PCA based method for discovering differentially expressed genes. BMC Bioinformatics 14, 1–10 (2013)

    Article  Google Scholar 

  10. Aradhya, V.N.M., Masulli, F., Rovetta, S.: A novel approach for biclustering gene expression data using modular singular value decomposition. In: Masulli, F., Peterson, L.E., Tagliaferri, R. (eds.) CIBB 2009. LNCS, vol. 6160, pp. 254–265. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  11. Lee, D.D., Seung, H.S.: Learning the parts of objects by non-negative matrix factorization. Nature 401, 788–791 (1999)

    Article  Google Scholar 

  12. Li, Y., Ngom, A.: The non-negative matrix factorization toolbox for biological data mining. Source Code Biol. Med. 8, 1–15 (2013)

    Article  Google Scholar 

  13. Yang, S., Ye, M.: Global minima analysis of Lee and Seung’s NMF algorithms. Neural Process. Lett. 38, 29–51 (2013)

    Article  MATH  Google Scholar 

  14. Lee, D.D., Seung, H.S.: Algorithms for non-negative matrix factorization. In: Advances in Neural Information Processing Systems, pp. 556–562 (2000)

    Google Scholar 

  15. Gao, Y., Church, G.: Improving molecular cancer class discovery through sparse non-negative matrix factorization. Bioinformatics 21, 3970–3975 (2005)

    Article  Google Scholar 

  16. Wang, Y., Jia, Y.: Fisher non-negative matrix factorization for learning local features. In: Proceedings of Asian Conference on Computer Vision. Citeseer (2004)

    Google Scholar 

  17. Hoyer, P.O.: Non-negative matrix factorization with sparseness constraints. J. Mach. Learn. Res. 5, 1457–1469 (2004)

    MathSciNet  Google Scholar 

  18. 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 

  19. Zheng, C.-H., Ng, T.-Y., Zhang, D., Shiu, C.-K., Wang, H.-Q.: Tumor classification based on non-negative matrix factorization using gene expression data. IEEE Trans. Nanobiosci. 10, 86–93 (2011)

    Article  Google Scholar 

  20. Du, J.-X., Zhai, C.-M., Ye, Y.-Q.: Face aging simulation based on NMF algorithm with sparseness constraints. In: Huang, D.-S., Gan, Y., Gupta, P., Gromiha, M.M. (eds.) ICIC 2011. LNCS, vol. 6839, pp. 516–522. Springer, Heidelberg (2012)

    Google Scholar 

  21. Kong, X., Zheng, C.-H., Wu, Y., Shang, L.: Molecular cancer class discovery using non-negative matrix factorization with sparseness constraint. In: Huang, D.-S., Heutte, L., Loog, M. (eds.) ICIC 2007. LNCS, vol. 4681, pp. 792–802. Springer, Heidelberg (2007)

    Google Scholar 

  22. Tang, Z., Ding, S.: Nonnegative dictionary learning by nonnegative matrix factorization with a sparsity constraint. In: Wang, J., Yen, G.G., Polycarpou, M.M. (eds.) ISNN 2012, Part II. LNCS, vol. 7368, pp. 92–101. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  23. Peharz, R., Stark, M., Pernkopf, F.: Sparse nonnegative matrix factorization with ℓ0-constraints. Neurocomputing 80, 38–46 (2010)

    Article  Google Scholar 

  24. Morup, M., Madsen, K.H., Hansen, L.K.: Approximate L0 constrained non-negative matrix and tensor factorization. In: IEEE International Symposium on Circuits and Systems, ISCAS 2008, pp. 1328–1331 (2008)

    Google Scholar 

  25. Long, X., Lu, H., Peng, Y., Li, W.: Graph regularized discriminative non-negative matrix factorization for face recognition. Multimedia Tools Appl. 72, 2679–2699 (2014)

    Article  Google Scholar 

  26. 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 

  27. 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 

  28. Wu, Z., Irizarry, R.A., Gentleman, R., Murillo, F.M., Spencer, F.: A model based background adjustment for oligonucleotide expression arrays (2004)

    Google Scholar 

  29. Consortium, G.O.: The gene ontology in 2010: extensions and refinements. Nucleic Acids Res. 38, D331–D335 (2010)

    Article  MATH  Google Scholar 

Download references

Acknowledgements

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

    Chun-Xia Ma, Dong Wang & Jin-Xing Liu

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

    Ying-Lian Gao

  3. School of Communication, Qufu Normal University, Rizhao, China

    Jian Liu

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

    Jin-Xing Liu

Authors
  1. Chun-Xia Ma
    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. Dong Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jian Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Jin-Xing Liu
    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

Ma, CX., Gao, YL., Wang, D., Liu, J., Liu, JX. (2015). Graph Regularized Non-negative Matrix with L0-Constraints for Selecting Characteristic Genes. 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_61

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-22186-1_61

  • 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