Bounded manifold completion
نویسندگان
چکیده
Nonlinear dimensionality reduction is an active area of research. In this paper, we present a thematically different approach to detect low-dimensional manifold that lies within set bounds derived from given point cloud. A matrix representing distances on low-rank, and our method based current low-rank Matrix Completion (MC) techniques for recovering partially observed fully entries. MC methods are currently used solve challenging real-world problems such as image inpainting recommender systems. Our scheme utilizes efficient optimization employ nuclear norm convex relaxation surrogate non-convex discontinuous rank minimization. The theoretically guarantees detection embeddings robust non-uniformity in the sampling manifold. We validate performance using both theoretical analysis well synthetic benchmark datasets.
منابع مشابه
Enhanced Matrix Completion with Manifold Learning
We study the problem of matrix completion when information about row or column proximities is available, in the form of weighted graphs. The problem can be formulated as the optimization of a convex function that can be solved efficiently using the alternating direction multipliers method. Experiments show that our model offers better reconstruction than the standard method that only uses a low...
متن کاملThe Information Manifold for Relatively Bounded Potentials
We construct a Banach manifold of states, which are Gibbs states for potentials that are form-bounded relative to the free Hamiltonian. We construct the (+1)-affine structure and the (+1)−connection. keywords Information manifold, Fisher metric, quantum geometry, Bogoliubov metric, Kubo theory, statistical manifold.
متن کاملThe Completion of the Manifold of Riemannian Metrics
We give a description of the completion of the manifold of all smooth Riemannian metrics on a fixed smooth, closed, finite-dimensional, orientable manifold with respect to a natural metric called the L metric. The primary motivation for studying this problem comes from Teichmüller theory, where similar considerations lead to a completion of the well-knownWeil-Petersson metric. We give an applic...
متن کاملTensor Completion with Side Information: A Riemannian Manifold Approach
By restricting the iterate on a nonlinear manifold, the recently proposed Riemannian optimization methods prove to be both efficient and effective in low rank tensor completion problems. However, existing methods fail to exploit the easily accessible side information, due to their format mismatch. Consequently, there is still room for improvement. To fill the gap, in this paper, a novel Riemann...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Pattern Recognition
سال: 2021
ISSN: ['1873-5142', '0031-3203']
DOI: https://doi.org/10.1016/j.patcog.2020.107661