A pattern-association method is described that is based on a mixture of local PCA, which approximates a data distribution (chapter 3). We call the pattern association together with the approximation of the data distribution an abstract recurrent neural network. Analogue to a recall in a recurrent neural network, input and output components can be chosen arbitrarily after training. The output is said to be associated with the input. In the new model, the input is the offset of a constrained space whose span is the output space. The intersection of the constrained space with the mixture of ellipsoids gives the completed pattern. The algorithm was applied to function approximation, image completion, and the kinematics of a redundant robot arm in simulation. In the latter, a trained abstract recurrent neural network could be used both for the forward and the inverse kinematics. Experiments showed that the recall error increased with the number of input dimensions for a given trained network. To explain this increase, a simplified stochastic version of the mixture of local PCA is analyzed.