Tutorial on PCA and approximate PCA and approximate kernel PCA

Abstract Principal Component Analysis (PCA) is one of the most widely used data analysis methods in machine learning and AI. This manuscript focuses on mathematical foundation classical PCA its application to a small-sample-size scenario large dataset high-dimensional space scenario. In particular, we discuss simple method that can be approximate latter case. also help kernel or (KPCA) for large-scale dataset. We hope this will give readers solid PCA, KPCA.