Regularized Locality Preserving Learning of Pre-Image Problem in Kernel Principal Component Analysis

In this paper, we address the pre-image problem in kernel principal component analysis (KPCA). The pre-image problem finds a pattern as the pre-image of a feature vector defined in the nonlinear principal component space produced by KPCA. Since the pre-image typically seldom exists in general, an approximate solution is appreciated. By posing a novel perspective, we find the pre-image with regularized locality preserving learning. Our approach achieves a unique solution, avoiding iteration and numerical instability. Significant superiority of the proposed novel algorithm is demonstrated by driving two applications, namely face denoising and occluded face reconstruction, as comparing with some existing well-known methods on pre-image learning