A new family of proximity graphs: class cover catch digraphs

Authors:
Jason DeVinney;Carey E. Priebe
Affiliations:
Center for Computing Sciences, Bowie, MD;Applied Mathematics and Statistics, Johns Hopkins University, Baltimore, MD
Venue:
Discrete Applied Mathematics
Year:
2006

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Abstract

Motivated by issues in machine learning and statistical pattern classification, we investigate a class cover problem (CCP) with an associated family of directed graphs--class cover catch digraphs (CCCDs). CCCDs are a special case of catch digraphs. Solving the underlying CCP is equivalent to finding a smallest cardinality dominating set for the associated CCCD, which in turn provides regularization for statistical pattern classification. Some relevant properties of CCCDs are studied and a characterization of a family of CCCDs is given.