Locality preserving projection based on Euler representation

Abstract

Locality preserving projection (LPP) is a widely used linear dimensionality reduction method, which preserves the locality structure of the original data. Motivated by the fact that kernel technique can capture nonlinear similarity of features and help to improve separability between nearby data points, this paper proposes locality preserving projection model based on Euler representation (named as ELPP). This model first projects the data into a complex space with Euler representation, then learns the dimensionality reduction projection with preserving locality structure in this complex space. We also extend ELPP to F-ELPP by replacing the squared F-norm with F-norm, which will weaken the exaggerated errors and be more robustness to outliers. The optimization algorithms of the two models are given, and the convergence of F-ELPP is proved. A large number of experiments on several public databases have demonstrated that the two proposed models have good robustness and feature extraction ability.