Model for Gene Expression Profiling

The variables, parameters, mathematical models, and the genetic algorithm (GA) approach to model the gene expression profiling are discussed in this section. The various variables are discussed first. 

Xjk= expression ratio of / gene in experiment (one entry of the gene expression matrix (nxm) from cDNA microarray experiments) yik = expression ratio of cluster in k experiment (cluster locations calculated/predicted by GA) 

Zik = expression ratio of i cluster in experiment (cluster locations based on input gene expression data and specific association rule at each iteration/generation) 

An objective function is proposed where the error between z and y, is minimized, y are randondy generated in GA while zik are calculated using gene expression data and gene associations (described in detail in the next section (model implementation)). Ideally, y should be equal to Zik to obtain inherent clusters present in the dataset. Minimizing this difference, indirectly results in optimum number of clusters. Mathematically, it is represented as, 

This may result in each gene acting as an independent cluster to give zero error. Thus, another objective function is defined that minimizes number of clusters in gene expression data. This is especially useful for diagnostic purposes where lesser numbers of gene clusters are useful for quick diagnostics. Mathematically, it is represented as, 

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