Biology Reference
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5.6. Conclusion
DNA microarrays make it practical, for the first time, to survey the
expression of thousands of genes under thousands of conditions. This
technology makes it possible to study the expression of all of the genes at
once. Large-scale expression profiling has emerged as a leading technol-
ogy in the systematic analysis of cellular physiology. However, method
development for analyzing gene expression data is still in its infancy. SDL
optimization uses a mathematical method based on orthogonal sets of
numbers. By slicing the multi-dimensional parameter space with a hori-
zontal plane of the objective function, with each parameter independent of
the others, a peak is always surrounded by a slope. By finding all regions
in which the objective function has values above that of the plane, one can
narrow the search region. After finding the boundary of all the isolated
regions where this occurs, the plane is raised again, and the process
repeated.
Orthogonal arrays (OAs) are immensely important in all areas of
human investigation. In statistics, they are primarily used in designing
experiments. An OA is an array of numbers constructed by utilizing
orthogonal Latin squares. One can form an array of several dimensions
that are orthogonal to each other, and therefore allow the calculation of a
resultant using many interdependent variables. Combining OA sampling
with function domain contraction techniques results in an optimization
with two desirable properties. Firstly, the number of function evaluations
can be greatly reduced. Secondly, there is a guarantee of finding the global
optimum solution. In this study, a carefully selected OA was successfully
used for conducting an orthogonal search space sampling.
By using OA and other mathematical techniques, it is practical to
develop a global optimization program for cancer classification and vali-
dation on a desktop computer. The primary advantages of this technique
are that the global optimum is always found, excellent solutions can be
found with little prior knowledge, and the new objective functions can be
created according to whatever combination of parameters is required.
The mathematical procedures used in this form of global optimization are
possible to apply to a variety of other previously unsolved problems relat-
ing to the resultant of dependent variables, including experimental design
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