We applied two state-of-the-art, knowledge independent data-mining methods - Dynamic Quantum Clustering (DQC) and t-Distributed Stochastic Neighbor Embedding (t-SNE) - to data from The Cancer Genome Atlas (TCGA). We showed that the RNA expression patterns for a mixture of 2,016 samples from five tumor types can sort the tumors into groups enriched for relevant annotations including tumor type, gender, tumor stage, and ethnicity. DQC feature selection analysis discovered 48 core biomarker transcripts that clustered tumors by tumor type. When these transcripts were removed, the geometry of tumor relationships changed, but it was still possible to classify the tumors using the RNA expression profiles of the remaining transcripts. We continued to remove the top biomarkers for several iterations and performed cluster analysis. Even though the most informative transcripts were removed from the cluster analysis, the sorting ability of remaining transcripts remained strong after each iteration. Further, in some iterations we detected a repeating pattern of biological function that wasn't detectable with the core biomarker transcripts present. This suggests the existence of a "background classification" potential in which the pattern of gene expression after continued removal of "biomarker" transcripts could still classify tumors in agreement with the tumor type.