Gene signatures are more and more used to interpret results of omics data analyses but suffer from compositional (large overlap) and functional (correlated read-outs) redundancy. Moreover, many gene signatures rarely come out as significant in statistical tests. Based on pan-cancer data analysis, we construct a restricted set of 962 signatures defined as informative and demonstrate that they have a higher probability to appear enriched in comparative cancer studies. We show that the majority of informative signatures conserve their weights for the genes composing the signature (eigengenes) from one cancer type to another. We finally construct InfoSigMap, an interactive online map of these signatures and their cross-correlations. This map highlights the structure of compositional and functional redundancies between informative signatures, and it charts the territories of biological functions. InfoSigMap can be used to visualize the results of omics data analyses and suggests a rearrangement of existing gene sets.