In this paper, we introduce a training and compensation algorithm of the class-conditioned basis vectors in the non-negative matrix factorization (NMF) model for single-channel speech enhancement. The main goal is to estimate the basis vectors of different signal sources in a way that prevents them from representing other sources, in order to reduce the residual noise components that have features similar to the speech signal. During the proposed training stage, the basis matrices for the clean speech and noises are estimated jointly by constraining them to belong to different classes. To this end, we employ the probabilistic generative model (PGM) of classification, specified by class-conditional densities, as an a priori distribution for the basis vectors. The update rules of the NMF and the PGM parameters of classification are jointly obtained by using the variational Bayesian expectation-maximization (VBEM) algorithm, which guarantees convergence to a stationary point. Another goal of the proposed algorithm is to handle a mismatch between the characteristics of the training and test data. This is accomplished during the proposed enhancement stage, where we implement a basis compensation scheme. Specifically, we use extra free basis vectors to capture the features which are not included in the training data. Objective experimental results for different combination of speaker and noise types show that the proposed algorithm can provide better speech enhancement performance than the benchmark algorithms under various conditions.