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.
Ek, C. H., Rihan, J., Torr, P. H. S., Rogez, G., & Lawrence, N. D. (2008). Ambiguity modeling in latent spaces. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5237 LNCS, pp. 62–73). https://doi.org/10.1007/978-3-540-85853-9-6