2012/06/18 by Byron Boots, Boots, Byron, Geoff Gordon +1
Computer Science · #Blind Source Separation Techniques #FOS: Computer and information sciences #Machine Learning (cs.LG) #Neural Networks and Applications #Target Tracking and Data Fusion in Sensor Networks #cs.LG
paper · pdf · doi:10.48550/arxiv.1206.4648
ICML2012. arXiv admin note: text overlap with arXiv:1112.6399
arxiv created 2012/06/18 · openalex publication_date 2012/06/18 · arxiv updated 2012/06/22 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
Recently, there has been much interest in spectral approaches to learning\nmanifolds---so-called kernel eigenmap methods. These methods have had some\nsuccesses, but their applicability is limited because they are not robust to\nnoise. To address this limitation, we look at two-manifold problems, in which\nwe simultaneously reconstruct two related manifolds, each representing a\ndifferent view of the same data. By solving these interconnected learning\nproblems together, two-manifold algorithms are able to succeed where a\nnon-integrated approach would fail: each view allows us to suppress noise in\nthe other, reducing bias. We propose a class of algorithms for two-manifold\nproblems, based on spectral decomposition of cross-covariance operators in\nHilbert space, and discuss when two-manifold problems are useful. Finally, we\ndemonstrate that solving a two-manifold problem can aid in learning a nonlinear\ndynamical system from limited data.\n