A robust divergence measure is fundamental in both theoretical and practical applications. Dr. Liu proposed a new robust class of divergences, termed by total Bregman divergence (tBD). A series of theoretical results for this new divergence are established. In particular, the L1-norm tBD induces a closed form center for a set of samples. This center is automatically adjusted for noisy data and outliers. Thus, tBD and the t-centers are statistically more robust than the conventional divergences and their induced centers.
The effectiveness of tBD has been validated in many real applications. For instance, a hierarchical shape retrieval scheme has been developed to integrate Gaussian mixture model based shape representation and tBD hard/soft clustering. tBD and t-center were also applied to clinical diffusion tensor imaging (DTI) problems for image analysis, including DTI signal estimation, interpolation and segmentation, and fiber clustering etc. In addition, tBD is used to regularize the conventional boosting and metric learning algorithms for classification. It has been shown that tBD can enhance the robustness and improve the accuracy of these algorithms, and reduce their computational complexity.