Boundary Detection Algorithm Inspired by Locally Linear Embedding

arXiv:2406.18456v1 Announce Type: new
Abstract: In the study of high-dimensional data, it is often assumed that the data set possesses an underlying lower-dimensional structure. A practical model for this structure is an embedded compact manifold with boundary. Since the underlying manifold structure is typically unknown, identifying boundary points from the data distributed on the manifold is crucial for various applications. In this work, we propose a method for detecting boundary points inspired by the widely used locally linear embedding algorithm. …

abstract algorithm arxiv compact data data set detection distributed embedded embedding linear manifold math.dg practical set stat.ml study type