Simplicial nonlinear principal component analysis
Krener, Arthur J.
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We present a new manifold learning algorithm that takes a set of data points lying on or near a lower dimensional manifold as input, possibly with noise, and outputs a simplicial complex that ts the data and the man- ifold. We have implemented the algorithm in the case where the input data has arbitrary dimension, but can be triangulated. We provide triangulations of data sets that fall on the surface of a torus, sphere, swiss roll, and creased sheet embedded in R50. We also discuss the theoretical justi cation of our algorithm.