A multi-spectral palm vein image acquisition device based on an open environment has been designed to achieve a highly secure and user-friendly biometric recognition system. Furthermore, we conducted a study on a supervised discriminative sparse principal component analysis algorithm that preserves the neighborhood structure for palm vein recognition. The algorithm incorporates label information, sparse constraints, and local information for effective supervised learning. By employing a robust neighborhood selection technique, it extracts discriminative and interpretable principal component features from non-uniformly distributed multi-spectral palm vein images. The algorithm addresses challenges posed by light scattering, as well as issues related to rotation, translation, scale variation, and illumination changes during non-contact image acquisition, which can increase intra-class distance. Experimental tests are conducted using databases from the CASIA, Tongji University, and Hong Kong Polytechnic University, as well as a self-built multi-spectral palm vein dataset. The results demonstrate that the algorithm achieves the lowest equal error rates of 0.50%, 0.19%, 0.16%, and 0.1%, respectively, using the optimal projection parameters. Compared to other typical methods, the algorithm exhibits distinct advantages and holds practical value.