Abstract Zero-shot learning (ZSL) aims to build models to recognize novel visual categories that have no associated labelled training samples. The basic framework is to transfer knowledge from seen classes to unseen classes by learning the visual-semantic embedding. However, most of approaches do not preserve the underlying sub-manifold of samples in the embedding space. In addition, whether the mapping can precisely reconstruct the original visual feature is not investigated in-depth. In order to solve these problems, we formulate a novel framework named Graph and Autoencoder Based Feature Extraction (GAFE) to seek a low-rank mapping to preserve the sub-manifold of samples. Taking the encoder-decoder paradigm, the encoder part learns a mapping from the visual feature to the semantic space, while decoder part reconstructs the original features with the learned mapping. In addition, a graph is constructed to guarantee the learned mapping can preserve the local intrinsic structure of the data. To this end, an L21 norm sparsity constraint is imposed on the mapping to identify features relevant to the target domain. Extensive experiments on five attribute datasets demonstrate the effectiveness of the proposed model