Ambiguity Modeling in Latent Spaces

  • Carl Henrik Ek
  • Jon Rihan
  • Philip H. S. Torr
  • Grégory Rogez
  • Neil D. Lawrence
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5237)


We are interested in the situation where we have two or more representations of an underlying phenomenon. In particular we are interested in the scenario where the representation are complementary. This implies that a single individual representation is not sufficient to fully discriminate a specific instance of the underlying phenomenon, it also means that each representation is an ambiguous representation of the other complementary spaces. In this paper we present a latent variable model capable of consolidating multiple complementary representations. Our method extends canonical correlation analysis by introducing additional latent spaces that are specific to the different representations, thereby explaining the full variance of the observations. These additional spaces, explaining representation specific variance, separately model the variance in a representation ambiguous to the other. We develop a spectral algorithm for fast computation of the embeddings and a probabilistic model (based on Gaussian processes) for validation and inference. The proposed model has several potential application areas, we demonstrate its use for multi-modal regression on a benchmark human pose estimation data set.


Latent Space Canonical Correlation Analysis Latent Variable Model Motion Capture Data Nonlinear Dimensionality Reduction 
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.
    Agarwal, A., Triggs, B.: Recovering 3 d human pose from monocular images. IEEE Transactions on Pattern Analysis and Machine Intelligence 28(1), 44–58 (2006)CrossRefGoogle Scholar
  2. 2.
    Ek, C.H., Torr, P.H.S., Lawrence, N.D.: Gaussian process latent variable models for human pose estimation. In: Popescu-Belis, A., Renals, S., Bourlard, H. (eds.) MLMI 2007. LNCS, vol. 4892, pp. 132–143. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  3. 3.
    Harmeling, S.: Exploring model selection techniques for nonlinear dimensionality reduction. Technical Report EDI-INF-RR-0960, University of Edinburgh (2007)Google Scholar
  4. 4.
    Kuss, M., Graepel, T.: The geometry of kernel canonical correlation analysis. Technical Report TR-108, Max Planck Institute for Biological Cybernetics, Tübingen, Germany (2003)Google Scholar
  5. 5.
    Lawrence, N.D.: Probabilistic non-linear principal component analysis with Gaussian Process latent variable models. J. Mach. Learn. Res. 6, 1783–1816 (2005)MathSciNetGoogle Scholar
  6. 6.
    Lawrence, N.D., Quionero-Candela, J.: Local distance preservation in the GP-LVM through back constraints. In: Greiner, R., Schuurmans, D. (eds.) ICML 2006, vol. 21, pp. 513–520. ACM, New York (2006)CrossRefGoogle Scholar
  7. 7.
    Navaratnam, R., Fitzgibbon, A., Cipolla, R.: The joint manifold model. In: IEEE International Conference on Computer Vision (ICCV) (2007)Google Scholar
  8. 8.
    Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning). MIT Press, Cambridge (2005)Google Scholar
  9. 9.
    Sanguinetti, G., Lawrence, N.D.: Missing data in kernel PCA. In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds.) ECML 2006. LNCS (LNAI), vol. 4212. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. 10.
    Scholkopf, B., Smola, A.J.: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, Cambridge (2001)Google Scholar
  11. 11.
    Shon, A.P., Grochow, K., Hertzmann, A., Rao, R.P.N.: Learning shared latent structure for image synthesis and robotic imitation. In: Proc. NIPS, pp. 1233–1240 (2006)Google Scholar
  12. 12.
    Sigal, L., Black, M.J.: Humaneva: Synchronized video and motion capture dataset for evaluation of articulated human motion. Brown Univertsity TR (2006)Google Scholar
  13. 13.
    Sminchisescu, C., Kanaujia, A., Li, Z., Metaxas, D.: Discriminative density propagation for 3d human motion estimation. In: Proc. Conf. Computer Vision and Pattern Recognition, pp. 217–323 (2005)Google Scholar
  14. 14.
    Weinberger, K.Q., Sha, F., Saul, L.K.: Learning a kernel matrix for nonlinear dimensionality reduction. In: ACM International Conference Proceeding Series (2004)Google Scholar
  15. 15.
    Zhu, Q., Avidan, S., Yeh, M.C., Cheng, K.T.: Fast Human Detection Using a Cascade of Histograms of Oriented Gradients. CVPR 1(2), 4 (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Carl Henrik Ek
    • 1
  • Jon Rihan
    • 1
  • Philip H. S. Torr
    • 1
  • Grégory Rogez
    • 2
  • Neil D. Lawrence
    • 3
  1. 1.Oxford Brookes UniversityUK
  2. 2.University of ZaragozaSpain
  3. 3.University of ManchesterUK

Personalised recommendations