UODV: Improved algorithm and generalized theory. Uncorrelated Optimal Discrimination Vectors (UODV) is an effective linear discrimination approach. However, this approach has the disadvantages in both the algorithm and the theory. In light of this, we propose an improved UODV algorithm based on the typical principal component analysis, which can satisfy the statistical uncorrelation and utilize the total scatter information of the training samples. Then, a new and generalized theorem on UODV is presented. This generalized theorem reveals the essential relationship between UODV and the well-known Fisherface method, and proves that our improved UODV algorithm is theoretically superior to the Fisherface method. Experimental results on both 1-D and 2-D data prove that our algorithm outperforms the original UODV approach and the Fisherface method.