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Robust Locality Preserving Projection Based on Kernel Risk-Sensitive Loss

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.