<reponame>luosichengx/myplace<filename>src/main/resources/static/mas_json/2012_icml_-774569001277181472.json
{"title": "Two Manifold Problems with Applications to Nonlinear System Identification.", "fields": ["operator", "kernel", "nonlinear system identification", "manifold", "matrix decomposition"], "abstract": "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.", "citation": "Citations (29)", "departments": ["Carnegie Mellon University", "Carnegie Mellon University"], "authors": ["<NAME>.....http://dblp.org/pers/hd/b/Boots:Byron", "<NAME>.....http://dblp.org/pers/hd/g/Gordon:Geoffrey_J="], "conf": "icml", "year": "2012", "pages": -1}