Complex Function Sets Improve Symbolic Discriminant Analysis of Microarray Data

Our ability to simultaneously measure the expression levels of thousands of genes in biological samples is providing important new opportunities for improving the diagnosis, prevention, and treatment of common diseases. However, new technologies such as DNA microarrays are generating new challenges for variable selection and statistical modeling. In response to these challenges, a genetic programming-based strategy called symbolic discriminant analysis (SDA) for the automatic selection of gene expression variables and mathematical functions for statistical modeling of clinical endpoints has been developed. The initial development and evaluation of SDA has focused on a function set consisting of only the four basic arithmetic operators. The goal of the present study is to evaluate whether adding more complex operators such as square root to the function set improves SDA modeling of microarray data. The results presented in this paper demonstrate that adding complex functions to the terminal set significantly improves SDA modeling by reducing model size and, in some cases, reducing classification error and runtime. We anticipate SDA will be an important new evolutionary computation tool to be added to the repertoire of methods for the analysis of microarray data.