NMF in Screening Some Spirometric Data, an Insight into 12-Dimensional Data Space

  • Anna M. Bartkowiak
  • Jerzy Liebhart
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10244)


We present the usage of the Non-negative Matrix Factorization (NMF), an unsupervised machine learning method, which learns normal and abnormal state of patient’s ventilatory systems. This is done using samples of patients having defects of obturative and restrictive kind and a control group.

We show that the NMF method can identify patients being in the normal state and screen them off from the remaining patients; however the kind of the ventilatory disorder for the remaining patients is not recognized. This is confronted with clustering provided by the k-means method and visualization of the 12-dimensional data using heatmaps and Kohonen’s self-organizing maps.

The data set can be reconstructed with a 0.9746 accuracy (fraction of explained variance) from 6 base vectors provided by the NMF and using appropriate encoders provided also by the NMF; while 3 factors yield an 0.8573 fraction of explained variance.


Healthy state Abnormal state Non-negative matrix factorization (NMF) Heatmap Self-organizing map (SOM) Inner factors Reconstruction of data 


  1. 1.
    Bartkowiak, A.M.: Classic and convex non-negative matrix visualization in clustering two benchmark data. Przeglad Elektrotechniczny R93(1), 53–59 (2017)Google Scholar
  2. 2.
    Bartkowiak, A.M., Zimroz, R.: NMF and PCA as applied to gearbox fault data. In: Jackowski, K., Burduk, R., Walkowiak, K., Woźniak, M., Yin, H. (eds.) IDEAL 2015. LNCS, vol. 9375, pp. 199–206. Springer, Cham (2015). doi: 10.1007/978-3-319-24834-9_24 CrossRefGoogle Scholar
  3. 3.
    Bartkowiak, A., Liebhart, E.: Estimation of the spirometric residual volume (RV) by a regression built from Gower distances. Biometrical J. 37(2), 131–149 (1995)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Cichocki, A., Zdunek, R., Phan, A.H., Amari, S.: Nonnegative Matrix and Tensor Factorizations. Applications to Exploratory Multi-way Data Analysis and Blind Source Separation. Wiley, Chichester (2009)Google Scholar
  5. 5.
    Ding, C., Li, T., Jordan, M.: Convex and semi-nonnegative matrix factorizations. IEEE Trans. Pattern Anal. Mach. Intell. (TPAMI) 32, 45–55 (2010)CrossRefGoogle Scholar
  6. 6.
    Jolliffe, I.T.: Principal Component Analysis, 2nd edn. Springer, New York (2002)zbMATHGoogle Scholar
  7. 7.
    Kasim, A., Shkedy, Z., Kaiser, S., Hochreiter, S., Talloen, S. (eds.): Applied Biclustering Methods for Big and High-Dimensional Data Using R. CRC Press, Taylor & Francis Group, A Chapman & Hall Book, Boca Raton (2017)Google Scholar
  8. 8.
    Kohonen, T.: Self-Organizing Maps, Third Extended Edition. Springer, Heidelberg (2001)CrossRefzbMATHGoogle Scholar
  9. 9.
    Lee, D.D., Seung, H.S.: Learning the parts of objects by nonnegative matrix factorization. Nature 401, 788–791 (1999)CrossRefGoogle Scholar
  10. 10.
    Li, Y., Ngom, A.: The non-negative matrix factorization toolbox for biological data mining. BMC Source Code Biol. Med. 8(10), 1–15 (2013)Google Scholar
  11. 11.
    Liebhart, J., Bartkowiak, A., Liebhart, E.: The impact of outliers in in the regression estimating TLC from age and some spirometric observations. Model. Simul. Control C 15, 1–19 (1989). AMSE PresszbMATHGoogle Scholar
  12. 12.
    Schmidt, M.N., Larsen, J., Hsiao, F.-T.: Wind noise reduction using non-negative sparse coding. In: IEEE International Workshop on Machine Learning for Signal Processing, (MLSP), pp. 431–436, August 2007Google Scholar
  13. 13.
    Vesanto, J., et al.: SOM Toolbox for Matlab 5, Som Toolbox Team, HUT, Finland. Libella Oy, Espoo, Version 0beta 2.0, pp. 1–54, November 2001Google Scholar
  14. 14.
    Zdunek, R.: Extraction of nonnegative features from multidimensional nonstationary signals. In: Tan, Y., Shi, Y. (eds.) DMBD 2016. LNCS, pp. 557–566. Springer, Heidelberg (2016)Google Scholar
  15. 15.
    Zdunek, R.: Convex nonnegative matrix factorization with Rank-1 update for clustering. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2015. LNCS, vol. 9120, pp. 59–68. Springer, Cham (2015). doi: 10.1007/978-3-319-19369-4_6 CrossRefGoogle Scholar
  16. 16.
    Zdunek, R.: Data clustering with semi-binary nonnegative matrix factorization. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2008. LNCS, vol. 5097, pp. 705–716. Springer, Heidelberg (2008). doi: 10.1007/978-3-540-69731-2_68 CrossRefGoogle Scholar
  17. 17.
    Zurada, J.M., Ensari, T., Asi, E.H., Chorowski, J.: Nonnegative matrix factorization and its application to pattern recognition and text mining. In: Proceedings of the 13th Federated Conference on Computer Science and Information Systems, Cracow, pp. 11–16 (2013)Google Scholar

Copyright information

© IFIP International Federation for Information Processing 2017

Authors and Affiliations

  1. 1.Institute of Computer ScienceWroclaw UniversityWroclawPoland
  2. 2.Department and Clinic of Internal Diseases and AllergologyWroclaw Medical UniversityWroclawPoland

Personalised recommendations