A mixture of factor analyzer is a semiparametric density estimator that performs clustering and dimensionality reduction in each cluster (component) simultaneously. It performs nonlinear dimensionality reduction by modeling the density as a mixture of local linear models. The approach can be used for classification by modeling each class-conditional density using a mixture model and the complete data is then a mixture of mixtures. We propose an incremental mixture of factor analysis algorithm where the number of components (local models) in the mixture and the number of factors in each component (local dimensionality) are determined adaptively. Our results on different pattern classification tasks prove the utility of our approach and indicate that our algorithms find a good trade-off between model complexity and accuracy.