In this paper, we technically propose an enriched prior guided framework, called Dual-constrained Deep Semi-Supervised Coupled Factorization Network (DS2CF-Net), for discovering hierarchical coupled data representation. To extract hidden deep features, DS2CF-Net is formulated as a partial-label and geometrical structure-constrained framework. Specifically, DS2CF-Net designs a deep factorization architecture using multilayers of linear transformations, which can coupled update both the basis vectors and new representations in each layer. To enable learned deep representations and coefficients to be discriminative, we also consider enriching the supervised prior by joint deep coefficients-based label prediction and then incorporate the enriched prior information as additional label and structure constraints. The label constraint can enable the intra-class samples to have same coordinate in feature space, and the structure constraint forces the coefficients in each layer to be block-diagonal so that the enriched prior using the self-expressive label propagation are more accurate. Our network also integrates the adaptive dual-graph learning to retain the local structures of both data and feature manifolds in each layer. Extensive experiments on image datasets demonstrate the effectiveness of DS2CF-Net for representation learning and clustering.