Advertisement

Semi-supervised Learning of Sparse Linear Models in Mass Spectral Imaging

  • Fabian Ojeda
  • Marco Signoretto
  • Raf Van de Plas
  • Etienne Waelkens
  • Bart De Moor
  • Johan A. K. Suykens
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6282)

Abstract

We present an approach to learn predictive models and perform variable selection by incorporating structural information from Mass Spectral Imaging (MSI) data. We explore the use of a smooth quadratic penalty to model the natural ordering of the physical variables, that is the mass-to-charge (m/z) ratios. Thereby, estimated model parameters for nearby variables are enforced to smoothly vary. Similarly, to overcome the lack of labeled data we model the spatial proximity among spectra by means of a connectivity graph over the set of predicted labels. We explore the usefulness of this approach in a mouse brain MSI data set.

Keywords

MSI sparsity ordered variables spatial information smoothing penalty graph Laplacian convex optimization regularization 

References

  1. 1.
    Stoeckli, M., Chaurand, P., Hallahan, D.E., Caprioli, R.M.: Imaging mass spectrometry: A new technology for the analysis of protein expression in mammalian tissues. Nature Medicine 7(4), 493–496 (2001)CrossRefPubMedGoogle Scholar
  2. 2.
    McDonnell, L.A., Heeren, R.M.A.: Imaging mass spectrometry. Mass Spectrometry Reviews 26(4), 606–643 (2007)CrossRefPubMedGoogle Scholar
  3. 3.
    Van de Plas, R., Ojeda, F., Dewil, M., Van Den Bosch, L., De Moor, B., Waelkens, E.: Prospective exploration of biochemical tissue composition via imaging mass spectrometry guided by principal component analysis. In: Proceedings of the Pacific Symposium on Biocomputing, Maui, vol. 12, pp. 458–469 (2007)Google Scholar
  4. 4.
    McCombie, G., Staab, D., Stoeckli, M., Knochenmuss, R.: Spatial and spectral correlations in MALDI mass spectrometry images by clustering and multivariate analysis. Analytical Chemistry (19), 6118–6124 (2005)Google Scholar
  5. 5.
    Hanselmann, M., Köthe, U., Kirchner, M., Renard, B.Y., Amstalden, E.R., Glunde, K., Heeren, R.M.A., Hamprecht, F.A.: Toward digital staining using imaging mass spectrometry and random forests. Journal of Proteome Research 8(7), 3558–3567 (2009)CrossRefPubMedPubMedCentralGoogle Scholar
  6. 6.
    Luts, J., Ojeda, F., Van de Plas, R., De Moor, B., Van Huffel, S., Suykens, J.A.K.: A tutorial on support vector machine-based methods for classification problems in chemometrics. Analytica Chimica Acta 665(2), 129–145 (2010)CrossRefPubMedGoogle Scholar
  7. 7.
    Tibshirani, R., Saunders, M., Rosset, S., Zhu, J., Knight, K.: Sparsity and smoothness via the fused lasso. Journal of The Royal Statistical Society Series B 67(1), 91–108 (2005)CrossRefGoogle Scholar
  8. 8.
    Efron, B., Hastie, T., Johnstone, I., Tibshirani, R.: Least angle regression. The Annals of Statistics 32(2), 407–451 (2004)CrossRefGoogle Scholar
  9. 9.
    Chung, F.R.K.: Spectral Graph Theory (CBMS Regional Conference Series in Mathematics, vol. 92. American Mathematical Society, Providence (February 1997)Google Scholar
  10. 10.
    Li, C., Li, H.: Network-constrained regularization and variable selection for analysis of genomic data. Bioinformatics 24(9), 1175–1182 (2008)CrossRefPubMedGoogle Scholar
  11. 11.
    Signoretto, M., Daemen, A., Savorgnan, C., Suykens, J.A.K.: Variable selection and grouping with multiple graph priors. In: 2nd Neural Information Processing Systmes (NIPS) Workshop on Optimization for Machine Learning (2009)Google Scholar
  12. 12.
    Zou, H., Hastie, T.: Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society, Series B 67, 301–320 (2005)CrossRefGoogle Scholar
  13. 13.
    Belkin, M., Niyogi, P., Sindhwani, V.: Manifold regularization: A geometric framework for learning from labeled and unlabeled examples. Journal of Machine Learning Research 7, 2399–2434 (2006)Google Scholar
  14. 14.
    Yuan, M., Lin, Y.: Model selection and estimation in regression with grouped variables. Journal of the Royal Statistical Society, Series B 68, 49–67 (2006)CrossRefGoogle Scholar
  15. 15.
    Van de Plas, R., Pelckmans, K., De Moor, B., Waelkens, E.: Spatial querying of imaging mass spectrometry data: A nonnegative least squares approach. In: Neural Information Processing Systems Workshop on Machine Learning in Computational Biology (2007)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Fabian Ojeda
    • 1
  • Marco Signoretto
    • 1
  • Raf Van de Plas
    • 1
    • 3
  • Etienne Waelkens
    • 2
    • 3
  • Bart De Moor
    • 1
    • 3
  • Johan A. K. Suykens
    • 1
  1. 1.ESAT-SCD-SISTA, Department of Electrical EngineeringKatholieke Universiteit LeuvenLeuvenBelgium
  2. 2.Laboratory for PhosphoproteomicsKatholieke Universiteit Leuven, O & NLeuvenBelgium
  3. 3.ProMeta, Interfaculty Centre for Proteomics and MetabolomicsKatholieke Universiteit LeuvenLeuvenBelgium

Personalised recommendations