Abstract: We present an expectation-maximization (EM) algorithm that yields topology preserving maps of data based on probabilistic mixture models. Our approach is applicable to any mixture model for which we have a normal EM algorithm. Compared to other mixture model approaches to self-organizing maps (SOMs), the function our algorithm maximizes has a clear interpretation: it sums data log-likelihood and a penalty term that enforces self-organization. Our approach allows principled handling of missing data and learning of mixtures of SOMs. We present example applications illustrating our approach for continuous, discrete, and mixed discrete and continuous data.