Unsupervised feature learning with deep networks has been widely studied in recent years. Among these networks, deep autoencoders have shown a decent performance in discovering hidden geometric structure of the original data. Both nonnegativity and graph constraints show the effectiveness in representing intrinsic structures in the high dimensional ambient space. This paper combines the nonnegativity and graph constraints to find the original geometrical information intrinsic to high dimensional data, keeping it in a dimensionality reduced space. In the experiments, we test the proposed networks on several standard image data sets. The results demonstrate that they outperform existing methods.