Skip to main content

Group-Constrained Laplacian Eigenmaps: Longitudinal AD Biomarker Learning

  • 2848 Accesses

Part of the Lecture Notes in Computer Science book series (LNIP,volume 9352)


Longitudinal modeling of biomarkers to assess a subject’s risk of developing Alzheimers disease (AD) or determine the current state in the disease trajectory has recently received increased attention.Here, a new method to estimate the time-to-conversion (TTC) of mild cognitive impaired (MCI) subjects to AD from a low-dimensional representation of the data is proposed. This is achieved via a combination of multilevel feature selection followed by a novel formulation of the Laplacian Eigenmaps manifold learning algorithm that allows the incorporation of group constraints.Feature selection is performed using Magnetic Resonance (MR) images that have been aligned at different detail levels to a template. The suggested group constraints are added to the construction of the neighborhood matrix which is used to calculate the graph Laplacian in the Laplacian Eigenmaps algorithm.The proposed formulation yields relevant improvements for the prediction of the TTC and for the three-way classification (control/MCI/AD) on the ADNI database.

This is a preview of subscription content, access via your institution.

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Belkin, M., Niyogi, P.: Laplacian eigenmaps and spectral techniques for embedding and clustering. Advances in Neural Information Processing Systems 14, 585–591 (2002)

    Google Scholar 

  2. Tenenbaum, J.B., Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290(5500), 2319–2323 (2000)

    CrossRef  Google Scholar 

  3. Jenkins, O.C., Matarić, M.J.: A spatio-temporal extension to Isomap nonlinear dimension reduction. In: International Conference on Machine Learning, pp. 441–448 (2004)

    Google Scholar 

  4. Lewandowski, M., Martinez-del-Rincon, J., Makris, D., Nebel, J.: Temporal extension of laplacian eigenmaps for unsupervised dimensionality reduction of time series. In: International Conference on Pattern Recognition, pp. 161–164 (2010)

    Google Scholar 

  5. Misra, C., Fan, Y., Davatzikos, C.: Baseline and longitudinal patterns of brain atrophy in MCI patients, and their use in prediction of short-term conversion to AD: results from ADNI. NeuroImage 44(4), 141522 (2009)

    CrossRef  Google Scholar 

  6. Li, Y., Wang, Y., Wu, G., Shi, F., Zhou, L., Lin, W., Shen, D.: Discriminant analysis of longitudinal cortical thickness changes in Alzheimers disease using dynamic and network features. Neurobiology of Aging 33(2), 427.e1530 (2012)

    CrossRef  Google Scholar 

  7. Wolz, R., Aljabar, P., Hajnal, J.V., Rueckert, D.: Manifold learning for biomarker discovery in MR imaging. In: Wang, F., Yan, P., Suzuki, K., Shen, D. (eds.) MLMI 2010. LNCS, vol. 6357, pp. 116–123. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  8. Zou, H., Hastie, T.: Regularization and variable selection via the elastic net. Journal of the Royal Statistical Society, Series B 67, 301–320 (2005)

    MathSciNet  CrossRef  Google Scholar 

  9. Meinshausen, N., Bühlmann, P.: Stability selection. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72(4), 417–473 (2010)

    MathSciNet  CrossRef  Google Scholar 

  10. Guerrero, R., Wolz, R., Rao, A.W., Rueckert, D.: Manifold population modeling as a neuro-imaging biomarker: Application to ADNI and ADNI-GO. NeuroImage 94C, 275–286 (2014)

    CrossRef  Google Scholar 

  11. Ojala, T., Pietikäinen, M., Harwood, D.: A comparative study of texture measures with classification based on featured distributions. Pattern Recognition 29(1), 51–59 (1996)

    CrossRef  Google Scholar 

  12. Rueckert, D., Sonoda, L.I., Hayes, C., Hill, D.L.G., Leach, M.O., Hawkes, D.J.: Nonrigid registration using free-form deformations: Application to breast MR images. IEEE Transactions on Medical Imaging 18(8), 712–721 (1999)

    CrossRef  Google Scholar 

  13. Heckemann, R.A., Ledig, C., Aljabar, P., Gray, K.R., Rueckert, D., Hajnal, J.V., Hammers, A.: Label propagation using group agreement. In: MICCAI 2012 Grand Challenge and Workshop on Multi-Atlas Labeling, pp. 75–78 (2012)

    Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to R. Guerrero .

Editor information

Editors and Affiliations

Rights and permissions

Open Access This chapter is licensed under the terms of the Creative Commons Attribution-NonCommercial 2.5 International License (, which permits any noncommercial use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.

The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.

Reprints and Permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Guerrero, R., Ledig, C., Schmidt-Richberg, A., Rueckert, D. (2015). Group-Constrained Laplacian Eigenmaps: Longitudinal AD Biomarker Learning. In: Zhou, L., Wang, L., Wang, Q., Shi, Y. (eds) Machine Learning in Medical Imaging. MLMI 2015. Lecture Notes in Computer Science(), vol 9352. Springer, Cham.

Download citation

  • DOI:

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-24887-5

  • Online ISBN: 978-3-319-24888-2

  • eBook Packages: Computer ScienceComputer Science (R0)