Robust locality preserving projection based on maximum correntropy criterion

• LPP-MCC utilizes the maximum correntropy as the distance metric.
• The objective problem of LPP-MCC is solved via a half-quadratic optimization procedure.
• LPP-MCC is more robust to large outliers than LPP-L2 and LPP-L1.
• LPP-MCC avoids the small sample size (SSS) problem.

Conventional local preserving projection (LPP) is sensitive to outliers because its objective function is based on the L2-norm distance criterion and suffers from the small sample size (SSS) problem. To improve the robustness of LPP against outliers, LPP-L1 uses L1-norm distance metric. However, LPP-L1 does not work ideally when there are larger outliers. We propose a more robust version of LPP, called LPP-MCC, which formulates the objective problem based on maximum correntropy criterion (MCC). The objective problem is efficiently solved via a half-quadratic optimization procedure and the complicated non-linear optimization procedure can thereby be reduced to a simple quadratic optimization at each iteration. Moreover, LPP-MCC avoids the SSS problem because the generalized eigenvalues computation is not involved in the optimization procedure. The experimental results on both synthetic and real-world databases demonstrate that the proposed method can outperform LPP and LPP-L1 when there are large outliers in the training data.