We present a probabilistic generative approach for constructing topographic maps of light curves of eclipsing binary stars. The model defines a low-dimensional manifold of local noise models induced by a smooth non-linear mapping from a low-dimensional latent space to the space of probabilistic models of the observed light curves. Once the model has been trained, each light curve is projected to a point in the latent space, obtained from the mean of posterior probabilities over the local noise models, given the data. The smooth nature of the mapping between the latent space and the model manifold enables us to analytically calculate magnification factors that reveal local contractions or expansions in the projections, resulting from the non-linearity in the topographic mapping of the light curves. We demonstrate our approach on a dataset of artificially generated light curves and on a dataset comprised of real light curves from a variety of eclipsing binaries, and show that this is an efficient way of searching for transiting extrasolar planets in large datasets.