2012/12/25 by Alexander Bernstein, Alexander V. Bernstein, Bernstein, Alexander V. +3
Computer Science · Engineering · #68T05 #Domain Adaptation and Few-Shot Learning #FOS: Computer and information sciences #Face and Expression Recognition #Machine Learning (cs.LG) #Sparse and Compressive Sensing Techniques #cs.LG #msc:68T05
paper · pdf · doi:10.48550/arxiv.1212.6031
25 pages, 6 figures
arxiv created 2012/12/25 · openalex publication_date 2012/12/25 · arxiv updated 2012/12/27 · openalex created_date 2022/10/06 · openalex updated_date 2026/07/28
One of the ultimate goals of Manifold Learning (ML) is to reconstruct an unknown nonlinear low-dimensional manifold embedded in a high-dimensional observation space by a given set of data points from the manifold. We derive a local lower bound for the maximum reconstruction error in a small neighborhood of an arbitrary point. The lower bound is defined in terms of the distance between tangent spaces to the original manifold and the estimated manifold at the considered point and reconstructed point, respectively. We propose an amplification of the ML, called Tangent Bundle ML, in which the proximity not only between the original manifold and its estimator but also between their tangent spaces is required. We present a new algorithm that solves this problem and gives a new solution for the ML also.