Total Bregman Divergence, a Robust Divergence Measure and its Applications; Information-geometric Learning for Lesion Classification and Retrieval.
A robust divergence measure is fundamental in both theoretical and practical aspects. In my thesis, I proposed a new class of divergences, termed by total Bregman divergence (tBD). For a prescribed convex function, tBD measures the orthogonal distance between the convex function at the first argument and the tangent at the second. This is in contrast to the ordinate distance used in the regular Bregman class of divergences. A series of theoretical results for this new divergence are established. In particular, the L1-norm tBD induces a novel center for a set of samples. This center is called t-center. I prove that the t-center is a weighted mean of samples, and the weights are automatically adjusted for noisy data and outliers. Hence, 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 was 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.
In addition, I will briefly talk about classification strategies for computer-aided diagnosis. These strategies include classification using metric learning, sparse classification using learned dictionaries, and coarse to fine classification (feature selection, dimension reduction, template matching) approach using heterogeneous features.
Dr. Meizhu Liu is a Research Scientist at the Siemens Corporate Research (SCR). She got her Ph.D. degree in Department of Computer Information Science and Engineering from University of Florida in 2011. She received her B.S. degree from University of Science and Technology of China in 2007. Her research focuses on exploring computer vision and machine learning techniques for medical image analysis. She worked at Siemens Medical Solutions USA, and INRIA in France. She also had collaborations with RIKEN Brain Science Institute in Japan, INRIA in France, Universidad de Alicante in Spain, University of York in UK, Ecole Polytechnique in France, Sony CSL in Japan, and many other research institutes.