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Two-Manifold Problems with Applications to Nonlinear System Identification

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journal contribution
posted on 01.06.2012 by Byron Boots, Geoffrey J. Gordon

Recently, there has been much interest in spectral approaches to learning manifolds— so-called kernel eigenmap methods. These methods have had some successes, but their applicability is limited because they are not robust to noise. To address this limitation, we look at two-manifold problems, in which we simultaneously reconstruct two related manifolds, each representing a different view of the same data. By solving these interconnected learning problems together, two-manifold algorithms are able to succeed where a non-integrated approach would fail: each view allows us to suppress noise in the other, reducing bias. We propose a class of algorithms for two-manifold problems, based on spectral decomposition of cross-covariance operators in Hilbert space, and discuss when two-manifold problems are useful. Finally, we demonstrate that solving a two-manifold problem can aid in learning a nonlinear dynamical system from limited data.


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Copyright 2012 by the author(s)/owner(s)