Anatomical Regularization on Statistical Manifolds for the Classification of Patients with Alzheimer’s Disease

  • Rémi Cuingnet
  • Joan Alexis Glaunès
  • Marie Chupin
  • Habib Benali
  • Olivier Colliot
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7009)


This paper introduces a continuous framework to spatially regularize support vector machines (SVM) for brain image analysis based on the Fisher metric. We show that, by considering the images as elements of a statistical manifold, one can define a metric that integrates various types of information. Based on this metric, replacing the standard SVM regularization with a Laplace-Beltrami regularization operator allows integrating to the classifier various types of constraints based on spatial and anatomical information. The proposed framework is applied to the classification of magnetic resonance (MR) images based on gray matter concentration maps from 137 patients with Alzheimer’s disease and 162 elderly controls. The results demonstrate that the proposed classifier generates less-noisy and consequently more interpretable feature maps with no loss of classification performance.


Support Vector Machine Compact Riemannian Manifold Linear Support Vector Machine Statistical Manifold Spatial Regularization 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Ashburner, J., Friston, K.J.: Voxel-based morphometry–the methods. NeuroImage 11(6), 805–821 (2000)CrossRefGoogle Scholar
  2. 2.
    Davatzikos, C.: Why voxel-based morphometric analysis should be used with great caution when characterizing group differences. NeuroImage 23(1), 17–20 (2004)CrossRefGoogle Scholar
  3. 3.
    Vapnik, V.N.: The Nature of Statistical Learning Theory. Springer, Heidelberg (1995)CrossRefzbMATHGoogle Scholar
  4. 4.
    Schölkopf, B., Smola, A.J.: Learning with Kernels. MIT Press, Cambridge (2001)zbMATHGoogle Scholar
  5. 5.
    Davatzikos, C., et al.: Individual patient diagnosis of AD and FTD via high-dimensional pattern classification of MRI. NeuroImage 41(4), 1220–1227 (2008)CrossRefGoogle Scholar
  6. 6.
    Klöppel, S., et al.: Automatic classification of MR scans in Alzheimer’s disease. Brain 131(3), 681–689 (2008)CrossRefGoogle Scholar
  7. 7.
    Vemuri, P., et al.: Alzheimer’s disease diagnosis in individual subjects using structural mr images: Validation studies. NeuroImage 39(3), 1186–1197 (2008)CrossRefGoogle Scholar
  8. 8.
    Gerardin, É., et al.: Multidimensional classification of hippocampal shape features discriminates Alzheimer’s disease and mild cognitive impairment from normal aging. NeuroImage 47(4), 1476–1486 (2009)CrossRefGoogle Scholar
  9. 9.
    Cuingnet, R., et al.: Automatic classification of patients with Alzheimer’s disease from structural MRI: A comparison of ten methods using the ADNI database. NeuroImage 56(2), 766–781 (2011)CrossRefGoogle Scholar
  10. 10.
    Fan, Y., et al.: COMPARE: classification of morphological patterns using adaptive regional elements. IEEE Transactions on Medical Imaging 26(1), 93–105 (2007)CrossRefGoogle Scholar
  11. 11.
    Duchesne, S., et al.: Automated computer differential classification in Parkinsonian syndromes via pattern analysis on MRI. Academic Radiology 16(1), 61–70 (2009)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Cuingnet, R., Rosso, C., Lehéricy, S., Dormont, D., Benali, H., Samson, Y., Colliot, O.: Spatially regularized SVM for the detection of brain areas associated with stroke outcome. In: Jiang, T., Navab, N., Pluim, J.P.W., Viergever, M.A. (eds.) MICCAI 2010. LNCS, vol. 6361, pp. 316–323. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  13. 13.
    Querbes, O., et al.: Early diagnosis of Alzheimer’s disease using cortical thickness: impact of cognitive reserve. Brain 132(8), 2036–2047 (2009)CrossRefGoogle Scholar
  14. 14.
    Jost, J.: Riemannian geometry and geometric analysis. Springer, Heidelberg (2008)zbMATHGoogle Scholar
  15. 15.
    Lafferty, J., Lebanon, G.: Diffusion kernels on statistical manifolds. JMLR 6, 129–163 (2005)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Hebey, E.: Sobolev spaces on Riemannian manifolds. Springer, Heidelberg (1996)CrossRefzbMATHGoogle Scholar
  17. 17.
    Amari, S.I., et al.: Differential Geometry in Statistical Inference, vol. 10. Institute of Mathematical Statistics (1987)Google Scholar
  18. 18.
    Druet, O., Hebey, E., Robert, F.: Blow-up theory for elliptic PDEs in Riemannian geometry. Princeton Univ. Press, Princeton (2004)zbMATHGoogle Scholar
  19. 19.
    Jack, C.R., et al.: The Alzheimer’s disease neuroimaging initiative (ADNI): MRI methods. Journal of Magnetic Resonance Imaging 27(4) (2008)Google Scholar
  20. 20.
    Ashburner, J., Friston, K.J.: Unified segmentation. NeuroImage 26(3), 839–851 (2005)CrossRefGoogle Scholar
  21. 21.
    Ashburner, J.: A fast diffeomorphic image registration algorithm. NeuroImage 38(1), 95–113 (2007)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Rémi Cuingnet
    • 1
    • 2
  • Joan Alexis Glaunès
    • 1
    • 3
  • Marie Chupin
    • 1
  • Habib Benali
    • 2
  • Olivier Colliot
    • 1
  1. 1.CNRS UMR 7225, Inserm UMR_S 975, Centre de Recherche de l’Institut Cerveau-Moelle (CRICM)Université Pierre et Marie Curie-Paris 6ParisFrance
  2. 2.UMR_S 678, LIFInsermParisFrance
  3. 3.MAP5Université Paris 5 - René DescartesParisFrance

Personalised recommendations