Event-based cameras record asynchronous streamof per-pixel brightness changes. As such, they have numerous advantages over the common frame-based cameras, including high temporal resolution, high dynamic range, and no motion blur. Due to the asynchronous nature, efficient learning of compact representation for event data is challenging. While the extend to which the spatial and temporal event "information" is useful for pattern recognition tasks is not fully explored. In this paper, we focus on single layer architectures. We analyze the performance of two general problem formulations,i.e., the direct and the inverse, for unsupervised feature learning from local event data,i.e., local volumes of events that are described in space and time. We identify and show the main advantages of each approach. Theoretically, we analyze guarantees for local optimal solution, possibility for asynchronous and parallel parameter update as well as the computational complexity. We present numerical experiments for the task of object recognition, where we evaluate the solution under the direct and the inverse problem.We give a comparison with the state-of-the-art methods. Our empirical results highlight the advantages of the both approaches for representation learning from event data. Moreover, we show improvements of up to 9% in the recognition accuracy compared to the state-of-the-art methods from the same class of methods.