# Factorized Orthogonal Latent Spaces

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Mathieu Salzmann,
Carl Henrik Ek,
Raquel Urtasun,
Trevor Darrell
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Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, PMLR 9:701-708, 2010.

#### Abstract

Existing approaches to multi-view learning are particularly effective when the views are either independent (i.e, multi-kernel approaches) or fully dependent (i.e., shared latent spaces). However, in real scenarios, these assumptions are almost never truly satisfied. Recently, two methods have attempted to tackle this problem by factorizing the information and learn separate latent spaces for modeling the shared (i.e., correlated) and private (i.e., independent) parts of the data. However, these approaches are very sensitive to parameters setting or initialization. In this paper we propose a robust approach to factorizing the latent space into shared and private spaces by introducing orthogonality constraints, which penalize redundant latent representations. Furthermore, unlike previous approaches, we simultaneously learn the structure and dimensionality of the latent spaces by relying on a regularizer that encourages the latent space of each data stream to be low dimensional. To demonstrate the benefits of our approach, we apply it to two existing shared latent space models that assume full dependence of the views, the sGPLVM and the sKIE, and show that our constraints improve the performance of these models on the task of pose estimation from monocular images.

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