M-Normal against M-Metastases for the samples in Lapointe et al. [<b>44</b>].

We have seen in Figure 1, that the Normalized Shannon Entropy and the MPR-Statistical Complexity differentiate the metastatic samples from the normal samples, but that these two measures can not help to discriminate the primary tumors from the normals. We show here the results of two statistical complexity measures which are in some sense supervised (i.e. dependent on the dataset being interrogated). We call these two stastical mesured M-Normal and M-Metastases. They have the same functional form of the MPR-Statistical Complexity, but they use the average normal and average metastatic profile as probability distribution functions of reference. As a consequence, the M-normal and M-metastases are directly proportional to the Jensen-Shannon divergences with the normal (and respectively with the metastatic) gene expression profile. It is remarkable that, although we are using these end processes only (from Lapointe et al's, dataset of 5,153 probes×112 samples), most of the primary tumor samples appear as a transitional state between the normal and metastatic group. This is remarkable since the primary tumor samples were not used to define the M-normal and M-metastases measures and, in principle, the samples could have been located anywhere in the (M-normal, M-metastases)-plane. Computation of correlations of the probe expressions values can help us identify genes which are highly correlated with a divergence from the normal expression profile and, at the same time, converge towards the average metastatic profile.