The structure representation of data distribution plays an important role in understanding the underlying mechanism of generating data. In this paper, we propose nearest prime simplicial complex approaches (NSC) by utilizing persistent homology to ca
pture such structures. Assuming that each class is represented with a prime simplicial complex, we classify unlabeled samples based on the nearest projection distances from the samples to the simplicial complexes. We also extend the extrapolation ability of these complexes with a projection constraint term. Experiments in simulated and practical datasets indicate that compared with several published algorithms, the proposed NSC approaches achieve promising performance without losing the structure representation.
