Molecular simulation is one example where large amounts of high-dimensional (high-d) data are generated. To extract useful information, e.g., about relevant states and important conformational transitions, a form of dimensionality reduction is required. Dimensionality reduction algorithms differ in their ability to efficiently project large amounts of data to an informative low-dimensional (low-d) representation and the way the low and high-d representations are linked. We propose a dimensionality reduction algorithm called EncoderMap that is based on a neural network autoencoder in combination with a nonlinear distance metric. A key advantage of this method is that it establishes a functional link from the high-d to the low-d representation and vice versa. This allows us not only to efficiently project data points to the low-d representation but also to generate high-d representatives for any point in the low-d map. The potential of the algorithm is demonstrated for molecular simulation data of a small, highly flexible peptide as well as for folding simulations of the 20-residue Trp-cage protein. We demonstrate that the algorithm is able to efficiently project the ensemble of high-d structures to a low-d map where major states can be identified and important conformational transitions are revealed. We also show that molecular conformations can be generated for any point or any connecting line between points on the low-d map. This ability of inverse mapping from the low-d to the high-d representation is particularly relevant for the use in algorithms that enhance the exploration of conformational space or the sampling of transitions between conformational states.