Fig. 12

Discriminating between two expression phenotypes based on the PET kinetic parameter \( {\boldsymbol{K}}_1/{\boldsymbol{k}}_2 \). Points in scatter plots represent output of Generalized Regression Neural Networks (GRNNs) trained to discriminate between two expression phenotypes denoted by \( {\boldsymbol{\Gamma}}^{\left(-\right)} \) and \( {\boldsymbol{\Gamma}}^{\left(+\right)} \) identified by the \( {\boldsymbol{\omega}}_{\boldsymbol{mRNA}}^{\left({\boldsymbol{K}}_1/{\boldsymbol{k}}_2\right)} \) expression signature. Expression phenotype \( {\boldsymbol{\Gamma}}^{\left(-\right)} \) contains 7 HCC, 6 ICC and 2 sarcomas while phenotype \( {\boldsymbol{\Gamma}}^{\left(+\right)} \) contains 20 normals and 25 HCC. In each panel, columns 1–20 represent normals and columns 21–50 represent liver tumors (15 HCC, 6 ICC, 2 sarcomas, 7 CL-HCC). Horizontal line (magenta) represents a threshold \( \boldsymbol{\tau} \) on the GRNN output where samples with GRNN values greater than \( \boldsymbol{\tau} \) are assigned to \( {\boldsymbol{\Gamma}}^{\left(-\right)} \), otherwise the sample is assigned to \( {\boldsymbol{\Gamma}}^{\left(+\right)} \). a GRNN output based on \( {\boldsymbol{K}}_1/{\boldsymbol{k}}_2 \) parameter vector aligned with sample grouping described above. Note that all members of \( {\boldsymbol{\Gamma}}^{\left(-\right)} \) and all but one of the normal samples are correctly classified with some confusion on the HCC samples with a correct classification rate of 87 %. b GRNN output on a random permutation of the \( {\boldsymbol{K}}_1/{\boldsymbol{k}}_2 \) parameter vector showing poor overall classification performance. Only 1 out of 1000 permutations of the \( {\boldsymbol{K}}_1/{\boldsymbol{k}}_2 \) parameter vector had a correct classification rate greater than 86 %, which resulted in an empirical p-value of 0.001 for the observed classification pattern shown in panel A