  The three-dimensional data-driven Allen Gene Expression Atlas of the adult
mouse brain consists of numerized in-situ hybridization data for thousands of
genes, co-registered to the Allen Reference Atlas. We propose quantitative
criteria to rank genes as markers of a brain region, based on the localization
of the gene expression and on its functional fitting to the shape of the
region. These criteria lead to natural generalizations to sets of genes. We
find sets of genes weighted with coefficients of both signs with almost perfect
localization in all major regions of the left hemisphere of the brain, except
the pallidum. Generalization of the fitting criterion with positivity
constraint provides a lesser improvement of the markers, but requires sparser
sets of genes.
