Data-based Manifold Reconstruction via Tangent Bundle Manifold Learning
نویسندگان
چکیده
The goal of Manifold Learning (ML) is to find a description of low-dimensional structure of an unknown q-dimensional manifold embedded in high-dimensional ambient Euclidean space R p , q < p, from their finite samples. There are a variety of formulations of the problem. The methods of Manifold Approximation (MA) reconstruct (estimate) the manifold but don’t find a low-dimensional parameterization on the manifold. The most of Manifold Embedding (ME) methods find a low-dimensional parameterization but don’t reconstruct the manifold from a sample. In the paper, the ML is considered as Tangent Bundle Manifold Learning (TBML) problem in which the manifold, its tangent spaces and lowdimensional representation accurately reconstructed from a sample. A new geometrically motivated method for the TBML solution is presented, it also gives a new solution for the MA and ME.
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