Total bregman divergence, a robust divergence measure, and its applications
Baba C. Vemuri, Meizhu Liu · 2011
Divergence measures provide a means to measure the pairwise dissimilarity between “objects”, e.g., vectors and probability density functions (pdfs). Kullback-Leibler (KL) divergence and the square loss (SL) function are two examples of commonly used dissimilarity measures which along with others belong to the family of Bregman divergences (BD). In this thesis, we present a novel divergence dubbed the Total Bregman divergence (TBD), which is inherently very robust to outliers, a very desirable property in many applications. Further, we derive the TBD center, called the t-center (using the e1-norm), for a population of positive definite matrices is in closed form and show that it is invariant to transformations from the special linear group. This t-center, which is also robust to outliers, is then used in shape retrieval, diffusion tensor imaging (DTI) estimation, interpolation and segmentation. Furthermore, TBD is used to regularize the conventional boosting algorithms, which have been applied to applications in pattern classification. (Full text of this dissertation may be available via the University of Florida Libraries web site. Please check http://www.uflib.ufl.edu/etd.html)