Global optimization of clusters in gene expression data of DNA microarrays by deterministic annealing

The analysis of DNA microarry data is one of the most important things for functional genomics research. The matrix representation of microarray data and its successive optimal incisional hyperplanes is a useful platform for developing optimization algorithms to determine the optimal partitioning of pairwise proximity matrix representing completely connected and weighted graph. We developed Deterministic Annealing (DA) approach to determine the successive optimal binary partitioning. DA algorithm demonstrated good performance with the ability to find the globally optimal binary partitions. In addition, the objects that have not been clustered at small non-zero temperature, are considered to be very sensitive to even small randomness, and can be used to estimate the reliability of the clustering.