Before revision: A principal component analysis of the TCGA data for 15 cancer localizations leads to the following results: The effective dimensionality of the region spanned by normal tissues and tumors in the gene expression state space is around 10 (out of a huge initial space with more than 60000 genes). Gene expression profiles uniquely distinguish between normal and cancer states. For any given tissue, the cancer state is a kind of attractor in the gene expression state space with at least 2500 highly differentially-expressed genes and a power-like tail in the expression distribution function.
After revision: A principal component analysis of the TCGA data for 15 cancer localizations unveils the following qualitative facts about tumors: 1) The state of a tissue in gene expression space may be described by a few variables. In particular, there is a single variable describing the progression from a normal tissue to a tumor. 2) Each cancer localization is characterized by a gene expression profile, in which genes have specific weights in the definition of the cancer state. There are no less than 2500 highly differentially-expressed genes and a power-like tail in the expression distribution function.