Nearest Prime Simplicial Complex for Object Recognition

TL;DR

This paper introduces a novel method called Nearest Prime Simplicial Complex (NSC) that uses persistent homology to model data structures for improved object recognition, demonstrating promising results on various datasets.

Contribution

The paper presents a new approach employing prime simplicial complexes and persistent homology for data structure modeling in object recognition tasks.

Findings

NSC achieves competitive accuracy on simulated datasets.

NSC maintains structure representation without performance loss.

Extension with projection constraint improves extrapolation ability.

Abstract

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.