Domain adaptation methods are designed to extract shared domain-invariant features by projecting data on a common subspace in order to align their domain distributions. However, these methods do not usually consider domain-specific features, and therefore their distributions may not be well aligned. To address this problem, we introduce a novel model that learns domain-invariant and domain-specific representations to extract both their general and specific features. We also propose progressive weighting to accurately transfer the source domain knowledge and to mitigate negative knowledge transfer from the source to the target domain and to employ low-rank coding for aligning the source and target distributions. We evaluated the model based on several real-world datasets and showed that our method significantly improved the accuracy for forecasting and diagnosis of glaucoma disease from fundus photographs.