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 paper, we present a novel divergence dubbed the Total Bregman divergence (TBD), which is intrinsically robust to outliers, a very desirable property in many applications. Further, we derive the TBD center, called the t-center (using the ℓ1-norm), for a population of positive definite matrices in closed form and show that it is invariant to transformation from the special linear group. This t-center, which is also robust to outliers, is then used in tensor interpolation as well as in an active contour based piecewise constant segmentation of a diffusion tensor magnetic resonance image (DT-MRI). Additionally, we derive the piecewise smooth active contour model for segmentation of DT-MRI using the TBD and present several comparative results on real data.

Nationality identi cation unlocks important demographic information, with many applications in biomedical and sociological research. Existing name-based nationality classi ers use name substrings as features and are trained on small, unrepresentative sets of labeled names, typically extracted from Wikipedia. As a result, these methods achieve limited performance and cannot support ne-grained classi cation. We exploit the phenomena of homophily in communication patterns to learn name embeddings, a new representation that encodes gender, ethnicity, and nationality which is readily applicable to building classi ers and other systems. rough our analysis of 57M contact lists from a major Internet company, we are able to design a ne-grained nationality classi er covering 39 groups representing over 90% of the world population. In an evaluation against other published systems over 13 common classes, our F1 score (0.795) is substantial be er than our closest competitor Ethnea (0.580). To the best of our knowledge, this is the most accurate, ne-grained nationality classi er available.As a social media application, we apply our classi ers to the followers of major Twi er celebrities over six di erent domains. We demonstrate stark di erences in the ethnicities of the followers of Trump and Obama, and in the sports and entertainments favored by di erent groups. Finally, we identify an anomalous political gure whose presumably in ated following appears largely incapable of reading the language he posts in.

Multivariate time series (MTS) datasets broadly exist in numerous fields, including health care, multimedia, finance, and biometrics. How to classify MTS accurately has become a hot research topic since it is an important element in many computer vision and pattern recognition applications. In this paper, we propose a Mahalanobis distance-based dynamic time warping (DTW) measure for MTS classification. The Mahalanobis distance builds an accurate relationship between each variable and its corresponding category. It is utilized to calculate the local distance between vectors in MTS. Then we use DTW to align those MTS which are out of synchronization or with different lengths. After that, how to learn an accurate Mahalanobis distance function becomes another key problem. This paper establishes a LogDet divergence-based metric learning with triplet constraint model which can learn Mahalanobis matrix with high precision and robustness. Furthermore, the proposed method is applied on nine MTS datasets selected from the University of California, Irvine machine learning repository and Robert T. Olszewski's homepage, and the results demonstrate the improved performance of the proposed approach.

Shape database search is ubiquitous in the world of biometric systems, CAD systems etc. Shape data in these domains is experiencing an explosive growth and usually requires search of whole shape databases to retrieve the best matches with accuracy and efficiency for a variety of tasks. In this paper, we present a novel divergence measure between any two given points in double-struckRn or two distribution functions. This divergence measures the orthogonal distance between the tangent to the convex function (used in the definition of the divergence) at one of its input arguments and its second argument. This is in contrast to the ordinate distance taken in the usual definition of the Bregman class of divergences [4]. We use this orthogonal distance to redefine the Bregman class of divergences and develop a new theory for estimating the center of a set of vectors as well as probability distribution functions. The new class of divergences are dubbed the total Bregman divergence (TBD). We present the l1-norm based TBD center that is dubbed the t-center which is then used as a cluster center of a class of shapes The t-center is weighted mean and this weight is small for noise and outliers. We present a shape retrieval scheme using TBD and the t-center for representing the classes of shapes from the MPEG-7 database and compare the results with other state-of-the-art methods in literature.