  Cancer subtyping is crucial for understanding the nature of tumors and
providing suitable therapy. However, existing labelling methods are medically
controversial, and have driven the process of subtyping away from teaching
signals. Moreover, cancer genetic expression profiles are high-dimensional,
scarce, and have complicated dependence, thereby posing a serious challenge to
existing subtyping models for outputting sensible clustering. In this study, we
propose a novel clustering method for exploiting genetic expression profiles
and distinguishing subtypes in an unsupervised manner. The proposed method
adaptively learns categorical correspondence from latent representations of
expression profiles to the subtypes output by the model. By maximizing the
problem -- agnostic mutual information between input expression profiles and
output subtypes, our method can automatically decide a suitable number of
subtypes. Through experiments, we demonstrate that our proposed method can
refine existing controversial labels, and, by further medical analysis, this
refinement is proven to have a high correlation with cancer survival rates.
