Second step: data generation

The second step concerns the generation of the artificial expression data and is ruled by the following parameters:

• $n :$ Number of rows of the matrix, i.e. number of artificial tissues;

• $n_1 :$ Number of tissues that have to be verified by the first EP;

• $r :$ Total number of considered artificial genes, i.e. number of columns of the matrix;

• A range $[-M,M]$ for the admitted data values (gene expression levels);

• A minimum $x_{\min}$ and a maximum level $x_{\max}$ that can be assumed by genes not belonging to the EPs.

Once the value for the parameters are fixed, the procedure generates data as follows:

• The expression levels of all the $r$ genes are generated according to a normal distribution with mean $(x_{\min}+x_{\max})/2$ and standard deviation $\min((x_{\max}-\mu),(\mu-x_{\min}))/3$.
• Then, the expression levels of genes belonging to the first EP are changed in the first $n_1$ rows and are chosen so that a sufficient number of genes is modulated to make the EP verified. Similarly, the expression levels of the genes that belong to the second EP are changed in the remaining $n-n_1$ tissues, so that the modulated genes are sufficient to verify the second EP. The expression level of a generic overexpressed gene $g_k$ is chosen according to a normal distribution with mean $(M+t_k)/2$ and variance $(M-t_k)/8$, where $t_k$ is the modulation threshold of $g_k$, while, if $g_k$ is an underexpressed gene, its level is chosen according to a normal distribution with mean $-(M+t_k)/2$ and same variance.