Matrix factorization methods are widely exploited in order to reduce dimensionality of transcriptomic datasets to the action of few hidden factors (metagenes). Applying such methods to similar independent datasets should yield reproducible inter-series outputs, though it was never demonstrated yet. Here we systematically test state-of-art methods of matrix factorization on several transcriptomic datasets of the same cancer type. Inspired by concepts of evolutionary bioinformatics, we design a new framework based on Reciprocally Best Hit (RBH) graphs in order to benchmark reproducibility. We show that a particular protocol of application of Independent Component Analysis (ICA), accompanied by a stabilisation procedure, leads to a significant increase in the inter-series output reproducibility. Moreover, we show that the signals detected through this method are systematically more interpretable than those of other state-of-art methods. We developed a user-friendly tool BIODICA for performing the Stabilized ICA-based RBH meta-analysis. We apply this methodology to the study of colorectal cancer (CRC) for which 14 independent publicly available transcriptomic datasets can be collected. The resulting RBH graph maps the landscape of interconnected factors that can be associated to biological processes or to technological artefacts. These factors can be used as clinical biomarkers or robust and tumor-type specific transcriptomic signatures of tumoral cells or tumoral microenvironment. Their intensities in different samples shed light on the mechanistic basis of CRC molecular subtyping.