When Locally Linear Embedding Hits Boundary
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Based on the Riemannian manifold model, we study the asymptotical behavior of a widely applied unsupervised learning algorithm, locally linear embedding (LLE), when the point cloud is sampled from a compact, smooth manifold with boundary. We show several peculiar behaviors of LLE near the boundary that are different from those diffusion based algorithms. This study leads to an alternative boundary detection algorithm.
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