As one of the most prevalent branches of transfer learning, domain adaptation is dedicated to generalizing the knowledge of a source domain to a target domain to perform machine learning tasks. In domain adaptation, the key strategy is to overcome the shift between different domains and learn shared features with domain invariance. However, most existing methods focus on extracting the common features of the source and target domains, and do not consider the shift problem of class center in the target domain caused by this process. Specifically, when we align the domain distributions, we often ignore the inherent feature attributes of the data, or under the guidance of false pseudo-labels, cause the target domain data to be far away from the class center after projection. This is not conducive to classification task. To address these problems, in this study, we propose a novel domain adaptation method, referred to as discriminative invariant alignment (DIA), for image representation. DIA enriches the knowledge matrix by combining the class discriminative information of the source domain and local data structure information of the target domain into a new framework. By introducing the maximum margin criterion of the source domain, the classification boundaries are expanded. To verify the performance of the proposed method, we compared DIA with several state-of-the-art methods on five benchmark databases. The experimental results show that DIA is superior to the state-of-the-art methods. IEEE