Logical Analysis of Data: From Combinatorial Optimization to Medical Applications
Peter L. Hammer, Tibérius O. Bonates · 2005
After reviewing the basic concept of the Logical Analysis of Data (LAD), the paper presents a series of discrete optimization models associated to the implementation of various components of the general methodology of LAD, and concludes with an outline of applications of LAD to medical problems. The combinatorial optimization models described in the paper represent variations on the general theme of set covering, including some with nonlinear objective functions. The medical applications described include the development of diagnostic and prognostic systems in cancer research and pulmonology, risk assessment among cardiac patients, and the design of biomaterials. Acknowledgements: The first author gratefully acknowledges the partial support of the National Science Foundation (grant NSF-IIS-0312953), and the National Institutes of Health (award numbers HL-072771-01 and NIH-002748-001). The second author gratefully acknowledges the partial support of a DIMACS Graduate Student Award. We also acknowledge the assistance provided by Dash Optimization by allowing the use of its linear and integer programming solver Xpress-MP within its Academic Partnership Program. Page 2 RRR 10 2005