Over the last decades, finger vein biometric recognition has generated increasing attention because of its high security, accuracy, and natural anti-counterfeiting. However, most of the existing finger vein recognition approaches rely on image enhancement or require much prior knowledge, which limits their generalization ability to different databases and different scenarios. Additionally, these methods rarely take into account the interference of noise elements in feature representation, which is detrimental to the final recognition results. To tackle these problems, we propose a novel jointly embedding model, called Joint Discriminative Analysis with Low-Rank Projection (JDA-LRP), to simultaneously extract noise component and salient information from the raw image pixels. Specifically, JDA-LRP decomposes the input image into noise and clean components via low-rank representation and transforms the clean data into a subspace to adaptively learn salient features. To further extract the most representative features, the proposed JDA-LRP enforces the discriminative class-induced constraint of the training samples as well as the sparse constraint of the embedding matrix to aggregate the embedded data of each class in their respective subspace. In this way, the discriminant ability of the jointly embedding model is greatly improved, such that JDA-LRP can be adapted to multiple scenarios. Comprehensive experiments conducted on three commonly used finger vein databases and four palm-based biometric databases illustrate the superiority of our proposed model in recognition accuracy, computational efficiency, and domain adaptation.