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    PublicationOpen Access
    Classification of imbalanced data with a geometric digraph family
    (Journal of Machine Learning Research (JMLR), 2016) Department of Mathematics; Manukyan, Artur; Ceyhan, Elvan; PhD Student; Undergraduate Student; Faculty Member; Department of Mathematics; Graduate School of Sciences and Engineering; College of Sciences
    We use a geometric digraph family called class cover catch digraphs (CCCDs) to tackle the class imbalance problem in statistical classification. CCCDs provide graph theoretic solutions to the class cover problem and have been employed in classification. We assess the classification performance of CCCD classifiers by extensive Monte Carlo simulations, comparing them with other classifiers commonly used in the literature. In particular, we show that CCCD classifiers perform relatively well when one class is more frequent than the other in a two-class setting, an example of the cl ass imbalance problem. We also point out the relationship between class imbalance and class overlapping problems, and their influence on the performance of CCCD classifiers and other classification methods as well as some state-of-the-art algorithms which are robust to class imbalance by construction. Experiments on both simulated and real data sets indicate that CCCD classifiers are robust to the class imbalance problem. CCCDs substantially undersample from the majority class while preserving the information on the discarded points during the undersampling process. Many state-of-the-art methods, however, keep this information by means of ensemble classifiers, but CCCDs yield only a single classifier with the same property, making it both appealing and fast.
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    Publication
    Exact performance measures for peer-to-peer epidemic information diffusion
    (Springer-Verlag Berlin, 2006) N/A; Department of Computer Engineering; Department of Mathematics; Department of Mathematics; Department of Mathematics; Özkasap, Öznur; Yazıcı, Emine Şule; Küçükçifçi, Selda; Çağlar, Mine; Faculty Member; Faculty Member; Faculty Member; Faculty Member; Department of Computer Engineering; Department of Mathematics; College of Engineering; College of Sciences; College of Sciences; College of Sciences; 113507; 27432; 105252; 105131
    We consider peer-to-peer anti-entropy paradigms for epidemic information diffusion, namely pull, push and hybrid cases, and provide exact performance measures for them. Major benefits of the proposed epidemic algorithms are that they are fully distributed, utilize local information only via pair-wise interactions, and provide eventual consistency, scalability and communication topology-independence. Our contribution is the derivation of exact expressions for infection probabilities through elaborated counting techniques on a digraph. Considering the first passage times of a Markov chain based on these probabilities, we find the expected message delay experienced by each peer and its overall mean as a function of initial number of infectious peers. In terms of these criteria, the hybrid approach outperforms pull and push paradigms, and push is better than the pull case. Such theoretical results would be beneficial when integrating the models in several peer-to-peer distributed application scenarios.
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    Publication
    Statistical analysis of cortical morphometrics using pooled distances based on labeled cortical distance maps
    (Springer, 2011) Hosakere, M.; Nishino, T.; Alexopoulos, J.; Todd, R. D.; Botteron, K. N.; Miller, M. I.; Ratnanather, J. Tilak; Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/A
    Neuropsychiatric disorders have been demonstrated to manifest shape differences in cortical structures. Labeled Cortical Distance Mapping (LCDM) is a powerful tool in quantifying such morphometric differences and characterizes the morphometry of the laminar cortical mantle of cortical structures. Specifically, LCDM data are distances of labeled gray matter (GM) voxels with respect to the gray/white matter cortical surface. Volumes and descriptive measures (such as means and variances for each subject) based on LCDM distances provide descriptive summary information on some of the shape characteristics. However, additional morphometrics are contained in the data and their analysis may provide additional clues to underlying differences in cortical characteristics. To use more of this information, we pool (merge) LCDM distances from subjects in the same group. These pooled distances can help detect morphometric differences between groups, but do not provide information about the locations of such differences in the tissue in question. In this article, we check for the influence of the assumption violations on the analysis of pooled LCDM distances. We demonstrate that the classical parametric tests are robust to the non-normality and within sample dependence of LCDM distances and nonparametric tests are robust to within sample dependence of LCDM distances. We specify the types of alternatives for which the tests are more sensitive. We also show that the pooled LCDM distances provide powerful results for group differences in distribution of LCDM distances. As an illustrative example, we use GM in the ventral medial prefrontal cortex (VMPFC) in subjects with major depressive disorder (MDD), subjects at high risk (HR) of MDD, and healthy subjects. Significant morphometric differences were found in VMPFC due to MDD or being at HR. In particular, the analysis indicated that distances in left and right VMPFCs tend to decrease due to MDD or being at HR, possibly as a result of thinning. The methodology can also be applied to other cortical structures.
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    Publication
    Type-speciric analysis of morphometry of dendrite spines of mice
    (Institute of Electrical and Electronics Engineers (IEEE), 2007) Fong, L.; Tasky, T. N.; Hurdal, M. K.; Beg, M. F.; Martone, M. E.; Ratnanather, J. T.; Department of Mathematics; Ceyhan, Elvan; Faculty Member; Department of Mathematics; College of Sciences; N/A
    In this article, we analyze the morphometric measures of dendrite spines of mice derived from electron tomography images for different spine types based on pre-assigned categories. The morphometric measures we consider include the metric distance, volume, surface area, and length of dendrite spines of mice. The question of interest is how these morphometric measures differ by condition of mice; and how the metric distance relates to volume, surface area, length, and condition of mice. The Large Deformation Diffeomorphic Metric Mapping algorithm is the tool we use to obtain the metric distances that quantize the morphometry of binary images of dendrite spines with respect to a template spine. We demonstrate that for the values not adjusted for scale metric distances and other morphometric measures are significantly different between the conditions. The morphometric measures (rather than the mice condition) explain almost all the variation in metric distances. Since size (or scale) dominates the other variables in variation, we adjust metric distances and other morphometric measures for scale. We demonstrate that the scaled metric distances and other scaled morphometric variables still differ for condition, and scaled metric distances depend most significantly on scaled morphometric measures. The methodology used is also valid for morphometric measures of other organs or tissues and metric distances other than LDDMM.