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Principal component analysis (PCA) is a popular tool for lineardimensionality reduction and feature extraction. Kernel PCA is the nonlinearform of PCA, which better exploits the complicated spatial structure ofhigh-dimensional features. In this paper, we first review the basic ideas ofPCA and kernel PCA. Then we focus on the reconstruction of pre-images forkernel PCA. We also give an introduction on how PCA is used in active shapemodels (ASMs), and discuss how kernel PCA can be applied to improve traditionalASMs. Then we show some experimental results to compare the performance ofkernel PCA and standard PCA for classification problems. We also implement thekernel PCA-based ASMs, and use it to construct human face models.

Kernel Principal Component Analysis and its Applications in Face Recognition and Active Shape Models