In this paper, we study zero-shot learning in audio classification through factored linear and nonlinear acoustic-semantic projections between audio instances and sound classes. Zero-shot learning in audio classification refers to classification problems that aim at recognizing audio instances of sound classes, which have no available training data but only semantic side information. In this paper, we address zero-shot learning by employing factored linear and nonlinear acoustic-semantic projections. We develop factored linear projections by applying rank decomposition to a bilinear model, and use nonlinear activation functions, such as tanh, to model the non-linearity between acoustic embeddings and semantic embeddings. Compared with the prior bilinear model, experimental results show that the proposed projection methods are effective for improving classification performance of zero-shot learning in audio classification.