iPGA: Incremental Principal Geodesic Analysis with Applications to Movement Disorder Classification

  • Hesamoddin Salehian
  • David Vaillancourt
  • Baba C. Vemuri
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8674)


The nonlinear version of the well known PCA called the Principal Geodesic Analysis (PGA) was introduced in the past decade for statistical analysis of shapes as well as diffusion tensors. PGA of diffusion tensor fields or any other manifold-valued fields can be a computationally demanding task due to the dimensionality of the problem and thus establishing motivation for an incremental PGA (iPGA) algorithm. In this paper, we present a novel iPGA algorithm that incrementally updates the current Karcher mean and the principal sub-manifolds with any newly introduced data into the pool without having to recompute the PGA from scratch. We demonstrate substantial computational and memory savings of iPGA over the batch mode PGA for diffusion tensor fields via synthetic and real data examples. Further, we use the iPGA derived representation in an NN classifier to automatically discriminate between controls, Parkinson’s Disease and Essential Tremor patients, given their HARDI brain scans.


Tangent Space Diffusion Tensor Essential Tremor Geodesic Distance High Angular Resolution Diffusion Imaging 
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.


  1. 1.
    Cheng, G., Salehian, H., Vemuri, B.C.: Efficient recursive algorithms for computing the mean diffusion tensor and applications to DTI segmentation. In: Fitzgibbon, A., Lazebnik, S., Perona, P., Sato, Y., Schmid, C. (eds.) ECCV 2012, Part VII. LNCS, vol. 7578, pp. 390–401. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  2. 2.
    Cheng, G., Vemuri, B.C., Hwang, M.-S., Howland, D., Forder, J.R.: Atlas construction from high angular resolution diffusion imaging data represented by gaussian mixture fields. In: ISBI 2011, pp. 549–552. IEEE (2011)Google Scholar
  3. 3.
    Fletcher, P.T., Joshi, S.: Riemannian geometry for the statistical analysis of diffusion tensor data. Signal Processing 87(2), 250–262 (2007)CrossRefGoogle Scholar
  4. 4.
    Fletcher, P.T., Lu, C., Pizer, S.M., Joshi, S.: Principal geodesic analysis for the study of nonlinear statistics of shape. TMI 23(8), 995–1005 (2004)Google Scholar
  5. 5.
    Golub, G.H., Reinsch, C.: Singular value decomposition and least squares solutions. Numerische Mathematik 14(5), 403–420 (1970)zbMATHMathSciNetCrossRefGoogle Scholar
  6. 6.
    Ho, J., Cheng, G., Salehian, H., Vemuri, B.: Recursive karcher expectation estimators and geometric law of large numbers. In: AISTATS 2013, pp. 325–332 (2013)Google Scholar
  7. 7.
    Jian, B., Vemuri, B.C.: A unified computational framework for deconvolution to reconstruct multiple fibers from diffusion weighted mri. TMI 26(11), 1464–1471 (2007)zbMATHGoogle Scholar
  8. 8.
    Pennec, X.: Intrinsic statistics on riemannian manifolds: Basic tools for geometric measurements. J. of Math. Imaging and Vision 25(1), 127–154 (2006)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Sommer, S., Lauze, F., Hauberg, S., Nielsen, M.: Manifold valued statistics, exact principal geodesic analysis and the effect of linear approximations. In: Daniilidis, K., Maragos, P., Paragios, N. (eds.) ECCV 2010, Part VI. LNCS, vol. 6316, pp. 43–56. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  10. 10.
    Vaillancourt, D.E., Spraker, M.B., Prodoehl, J., Abraham, I., Corcos, D.M., Zhou, X.J., Comella, C.L., Little, D.M.: High-resolution diffusion tensor imaging in the substantia nigra of de novo parkinson disease. Neurology 72(16), 1378–1384 (2009)CrossRefGoogle Scholar
  11. 11.
    Xie, Y., Vemuri, B.C., Ho, J.: Statistical analysis of tensor fields. In: Jiang, T., Navab, N., Pluim, J.P.W., Viergever, M.A. (eds.) MICCAI 2010, Part I. LNCS, vol. 6361, pp. 682–689. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  12. 12.
    Zhao, H., Yuen, P.C., Kwok, J.T.: A novel incremental principal component analysis and its application for face recognition. IEEE Trans. on SMC 36(4), 873–886 (2006)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Hesamoddin Salehian
    • 1
  • David Vaillancourt
    • 2
  • Baba C. Vemuri
    • 1
  1. 1.Department of CISEUniversity of FloridaGainesvilleUSA
  2. 2.Department of Applied Physiology and KinesiologyUniversity of FloridaGainesvilleUSA

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