Robust Locality Preserving Projection Based on Kernel Risk-Sensitive Loss

Lei Xing, Yunqi Mi, Yuanhao Li, Badong Chen

Abstract: Traditional locality preserving projection (LPP) is an excellent linear dimensionality reduction method that can preserve the local structure of the data. The objective function of LPP is based on L2-norm criterion, which results in obvious sensitivity to the outliers. In order to solve this problem, researchers proposed some LPP variants based on the L1-norm (LPP-L1) and the maximum correntropy criterion (LPP-MCC). In this paper, we propose a more robust version of LPP, called LPP-KRSL, whose objective function is based on the kernel risk-sensitive loss (KRSL). The objective function can be efficiently solved via a half-quadratic optimization procedure. The experimental results on both synthetic and real-world data demonstrate that LPP-KRSL is more robust and effective than other LPP methods.