The paper presents a hybrid generative/discriminative classification method aimed at identifying abnormalities, such as cancer, in lung X-ray images. The proposed method involves a generative model that performs generative embedding in Probabilistic Component Analysis (PrCA). The primary goal of PrCA is to model co-existing information within a probabilistic framework, with the intent to locate the feature vector space for X-ray data based on a defined kernel structure. A kernel-based classifier, grounded in information-theoretic principles, was employed in this study. The performance of the proposed method is evaluated against nearest neighbour (NN) classifiers and support vector machine (SVM) classifiers, which use a diagonal covariance matrix and incorporate normal linear and non-linear kernels, respectively. The method is found to achieve superior accuracy, offering a viable solution to the class of problems presented. Accuracy rates achieved by the kernels in the NN and SVM models were 95.02% and 92.45%, respectively, suggesting the method's competitiveness with state-of-the-art approaches.