In this paper, new statistical learning algorithms with kernel function are presented. Recently, iterative learning algorithms for obtaining eigenvectors in the principal component analysis (PCA) have been presented in the field of pattern recognition and neural network. However, the Fisher linear discriminant analysis (FLDA) has been used in many fields, especially face image analysis. The drawback of FLDA is a long computational time based on a large-sized covariance matrix and the issue that the within-class covariance matrix is usually singular. In order to overcome this difficulty, we proposed the feature generation method Simple-FLDA which is approximately derived from geometrical interpretation of FLDA. This algorithm is similar to Simple-PCA and does not need matrix operation. In this paper, new statistical kernel based learning algorithms are presented. They are extended versions of Simple-PCA and Simple-FLDA to nonlinear space using the kernel function. Their preliminary simulation results are given for a simple face recognition problem.