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In many real-world applications, the same object may have different observations (or descriptions) from multiview observation spaces, which are highly related but sometimes look different from each other. Conventional metric-learning methods achieve satisfactory performance on distance metric computation of data in a single-view observation space, but fail to handle well data sampled from multiview observation spaces, especially those with highly nonlinear structure. To tackle this problem, we propose a new method called Multiview Metric Learning with Global consistency and Local smoothness (MVML-GL) under a semisupervised learning setting, which jointly considers global consistency and local smoothness. The basic idea is to reveal the shared latent feature space of the multiview observations by embodying global consistency constraints and preserving local geometric structures. Specifically, this framework is composed of two main steps. In the first step, we seek a global consistent shared latent feature space, which not only preserves the local geometric structure in each space but also makes those labeled corresponding instances as close as possible. In the second step, the explicit mapping functions between the input spaces and the shared latent space are learned via regularized locally linear regression. Furthermore, these two steps both can be solved by convex optimizations in closed form. Experimental results with application to manifold alignment on real-world datasets of pose and facial expression demonstrate the effectiveness of the proposed method.

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In this paper, we propose a novel manifold alignment method by learning the underlying common manifold with supervision of corresponding data pairs from different observation sets. Different from the previous algorithms of semi-supervised manifold alignment, our method learns the explicit corresponding projections from each original observation space to the common embedding space everywhere. Benefiting from this property, our method could process new test data directly rather than re-alignment. Furthermore, our approach doesn't have any assumption on the data structures, thus it could handle more complex cases and get better results compared with previous work. In the proposed algorithm, manifold alignment is formulated as a minimization problem with proper constraints, which could be solved in an analytical manner with closed-form solution. Experimental results on pose manifold alignment of different objects and faces demonstrate the effectiveness of our proposed method.

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