Wierman, John and Xiang, Pengfei (2003), Asymptotic Theory for the Domination Number of Random Class Cover Catch Digraphs, Computing Science and Statistics, 35, I2003Proceedings/WiermanJohn/WiermanJohn.paper.pdf
The study of class cover catch digraphs (CCCDs) is motivated by applications in nonparametric classification and pattern recognition. Priebe, Marchette, and Devinney have developed classifiers based on CCCDs for supervised classification, and also applied CCCDs to clustering problems. For the special case of uniformly distributed data in one dimension, Priebe, Marchette, and Devinney studied the exact distribution of the domination number of the data-based random CCCD, and Devinney and Wierman proved the Strong Law of Large Numbers (SLLN). This talk will discuss progress toward the SLLN and the Central Limit Theorem (CLT) for general data distributions in one dimension. The long-term goal of this investigation is to establish SLLN and CLT results for data in higher dimensions.