By the late 2020s or early 2030s, the next generation of telescopes will be able to directly observe the reflected starlight of Earth-like exoplanets. Because of the huge distance to other stars, such exoplanets will appear as single unresolved pixels. A single pixel can, however, provide information about what the planet looks like because its brightness varies in time as it rotates about its axis and orbits its star. Several researchers have shown that these changes in brightness can, indeed, be used to retrieve a map of the planet. Their methods use the Lambertian model of diffuse reflection to retrieve albedo maps of the planet's surface. We aim to develop new algorithms that can retrieve maps of non-Lambertian planets with a Rayleigh scattering atmosphere, clouds with water droplets that cause rainbows and oceans that exhibit a glint feature. We also aim to evaluate the validity of the Lambertian assumption for such non-Lambertian planets. We numerically compute reflected light curves with the previously mentioned non-Lambertian effects, including the polarization of the reflected light. Instead of retrieving albedo maps, we classify facets by their surface type and cloud coverage, using convolutional neural networks. We show that a convolutional neural network can classify facets on a non-Lambertian planet with an accuracy of 87% for an ideal geometry and no noise, when the rotation axis is known. Using another neural network architecture, we show that the rotation axis can be constrained with a mean squared error as low as 0.006 for our training data and similar results are seen for a model Earth. Including polarization in the retrieval improves the rotation axis retrieval's mean squared error (MSE) by roughly 15% and the classification accuracies of ocean facets and cloudy facets by 2% and 1%, respectively. We show that a retrieval algorithm that relies on the Lambertian assumption causes concentric artefacts about the poles when applied to light curves of a non-Lambertian planet for all inclinations besides face-on. The MSE of the rotation axis retrievals increases by roughly one order of magnitude for these inclination when making the Lambertian assumption.