  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 capture 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.
