Ambiguity Modeling in Latent Spaces
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.
KeywordsManifold Covariance Rounded
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- 3.Harmeling, S.: Exploring model selection techniques for nonlinear dimensionality reduction. Technical Report EDI-INF-RR-0960, University of Edinburgh (2007)Google Scholar
- 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
- 7.Navaratnam, R., Fitzgibbon, A., Cipolla, R.: The joint manifold model. In: IEEE International Conference on Computer Vision (ICCV) (2007)Google Scholar
- 8.Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning (Adaptive Computation and Machine Learning). MIT Press, Cambridge (2005)Google Scholar
- 10.Scholkopf, B., Smola, A.J.: Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. MIT Press, Cambridge (2001)Google Scholar
- 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.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.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.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.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