Applications of the SDL Global Optimization Method in DNA Microarray Data Analysis - DNA Microarray Technology and Data Analysis in Cancer Research - page 69

of interdependent variables has been proposed in this study. Although
many optimization algorithms may be appropriate for the gene classifica-
tion problem, SDL global optimization was proposed and applied to
cancer classification in this study for its superb performance in theory and
applications.
It is a challenge to discover the optimum gene subset solutions from a
microarray gene expression system with a large number of interacting
gene variables. It is also well known that orthogonal arrays (OAs) have
a number of advantages when they are used in designs of experiments
(Dey and Mukerjee, 1999; Hedayat et al ., 1999). With the help of an
established objective function based on k -nearest neighbors (KNN), SDL
global optimization combines an OA sampling procedure with some search
space reduction strategies for constructing a multi-subset class predictor
with a pyramidal hierarchy in order to predict the types of tumor tissues
correctly.
With the SDL global optimization algorithms proposed in this
research, one knows that the solution gene subsets found are optimized
within the criteria set — there is no need to try other starting conditions
for the same gene subset structure at a given length, because there are no
starting guesses. The algorithms inexorably must find the optimum solu-
tion that exists within the boundary conditions. This efficiency has pow-
erful economic consequences. For example, previous solutions needing
excessive numbers of genes can now be replaced with fewer genes to get
the same classification performance and better confidence. One can
improve classification performance as well as offer previously unavail-
able and undetectable gene subsets as class predictors.
Some strategies of SDL global optimization were first successfully
applied to the optical thin film design problem (Li and Nathan, 1996). It
was also a candidate for the real function testbed of the First International
Contest on Evolutionary Optimization in order to solve ten hard mathe-
matical multivariable optimization problems (Alon et al ., 1999; Golub
et al ., 1999). It is of great interest to develop techniques for extracting use-
ful information from the microarray datasets. In this chapter, we report the
application of the SDL global optimization approach for classifying and
validating two well-known datasets (Alon et al ., 1999; Golub et al ., 1999)
consisting of the expression patterns of different cell types.