Robots operating in home environments must be able to interact with articulated objects such as doors or drawers.  Ideally, robots are able to autonomously infer articulation models by observation.  In this paper, we present an approach to learn kinematic models by inferring the connectivity of rigid parts and the articulation models for the corresponding links.  Our method uses a mixture of parameterized and parameter-free (Gaussian process) representations and finds low-dimensional manifolds that provide the best explanation of the given observations.  Our approach has been implemented and evaluated using real data obtained in various realistic home environment settings.