NNNPE: non-neighbourhood and neighbourhood preserving embedding. Issue 1 (31st December 2022) - Chen, Kaizhi; Le, Chengpei; Zhong, Shangping; Guo, Longkun; Xu, Ge
ABSTRACT: Manifold learning is an important class of methods for nonlinear dimensionality reduction. Among them, the LLE optimisation goal is to maintain the relationship between local neighbourhoods in the original embedding manifold to reduce dimensionality, and NPE is a linear approximation to LLE. However, these two algorithms only consider maintaining the neighbour relationship of samples in low-dimensional space and ignore the global features between non-neighbour samples, such as the face shooting angle. Therefore, in order to simultaneously consider the nearest neighbour structure and global features of samples in nonlinear dimensionality reduction, it can be linearly calculated. This work provides a novel linear dimensionality reduction approach named non-neighbour and neighbour preserving embedding (NNNPE). First, we rewrite the objective function of the algorithm LLE based on the principle of our novel algorithm. Second, we introduce the linear mapping to the objective function. Finally, the mapping matrix is calculated by the method of the fast learning Mahalanobis metric. The experimental results show that the method proposed in this paper is effective.