NNNPE: non-neighbourhood and neighbourhood preserving embedding

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.

KEYWORDS:

• Machine learning
• manifold learning
• dimensionality reduction
• neighborhood preserving embedding

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is supported by the National Natural Science Foundation of China (NSFC) [grant number 61972187], Natural Science Foundation of Fujian Province, China [grant number 2022J01119], and Fujian Province Young and Middle-aged Teacher Education Research Project [grant number JAT200004]. Open Project of Fujian Provincial Key Laboratory of Information Processing and Intelligent Control (Minjiang University) [grant number MJUKF-IPIC202202].