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There is a growing demand for detailed and accurate landslide maps and inventories around the globe, but particularly in hazard-prone regions such as the Himalayas. Most standard mapping methods require expert knowledge, supervision and fieldwork. In this study, we use optical data from the Rapid Eye satellite and topographic factors to analyze the potential of machine learning methods, i.e., artificial neural network (ANN), support vector machines (SVM) and random forest (RF), and different deep-learning convolution neural networks (CNNs) for landslide detection. We use two training zones and one test zone to independently evaluate the performance of different methods in the highly landslide-prone Rasuwa district in Nepal. Twenty different maps are created using ANN, SVM and RF and different CNN instantiations and are compared against the results of extensive fieldwork through a mean intersection-over-union (mIOU) and other common metrics. This accuracy assessment yields the best result of 78.26% mIOU for a small window size CNN, which uses spectral information only. The additional information from a 5 m digital elevation model helps to discriminate between human settlements and landslides but does not improve the overall classification accuracy. CNNs do not automatically outperform ANN, SVM and RF, although this is sometimes claimed. Rather, the performance of CNNs strongly depends on their design, i.e., layer depth, input window sizes and training strategies. Here, we conclude that the CNN method is still in its infancy as most researchers will either use predefined parameters in solutions like Google TensorFlow or will apply different settings in a trial-and-error manner. Nevertheless, deep-learning can improve landslide mapping in the future if the effects of the different designs are better understood, enough training samples exist, and the effects of augmentation strategies to artificially increase the number of existing samples are better understood.