The purpose of our study was to develop a completely automated method for detecting abdominal tumors in given FDG-PET/CT images. The purpose of this article is to report on a classifier that distinguishes malignant tumors from false positives. For constructing the classifier, we employed the kernel Fisher discriminant analysis (KFDA), and experimentally evaluated the relationship between the dimensionality of training data, the leave-one-out (LOOCV) error of the classifier, and the stability of the classifier. The results showed that, as the dimensionality increased, the LOOCV error decreased but the classifier became unstable. Our method firstly binarizes a given PET image to extract candidates of malignant tumors. From a set of the images of the extracted candidates, we constructed the classifier. For computing the classification function, we normalize the size of the extracted images of the candidates and incorporate them into training data. When we change the size of the normalized images, the dimensionality of the training data changes and we obtain different classification function. For each classification function obtained at different dimensionality, we approximately evaluated its uniform stability and computed the upper bound of the difference between the LOOCV error of the classifier and the generalization error. In this article, we show that it is needed to evaluate the stability of the classifier to determine the size of the normalized images.