Heterogeneous domain adaptation (HDA) is a challenging problem because of the different feature representations in the source and target domains. Most HDA methods search for mapping matrices from the source and target domains to discover latent features for learning. However, these methods barely consider the reconstruction error to measure the information loss during the mapping procedure. In this paper, we propose to jointly capture the information and match the source and target domain distributions in the latent feature space. In the learning model, we propose to minimize the reconstruction loss between the original and reconstructed representations to preserve information during transformation and reduce the Maximum Mean Discrepancy between the source and target domains to align their distributions. The resulting minimization problem involves two projection variables with orthogonal constraints that can be solved by the generalized gradient flow method, which can preserve orthogonal constraints in the computational procedure. We conduct extensive experiments on several image classification datasets to demonstrate that the effectiveness and efficiency of the proposed method are better than those of state-of-the-art HDA methods.