High-Dimensional Dataset Simplification by Laplace-Beltrami Operator

With the development of Internet and other digital technologies, speed data generation has become considerably faster than processing. Because big typically contain massive redundant information, it is possible to significantly simplify a dataset while maintaining key information. In this paper, we develop high-dimensional (HD) simplification method based on eigenvalues eigenfunctions Laplace-Beltrami operator (LBO). Specifically, given that can be considered as an unorganized point set in HD space, discrete LBO defined constructed, its eigenvectors are calculated. Then, local extremum saddle points proposed feature dataset, constituting simplified dataset. Moreover, detection methods for functions devise metrics measuring fidelity original set. Finally, examples applications demonstrated validate efficiency effectiveness methods, demonstrating developed feasible processing maximum-sized using limited capability.