  While we once thought of cancer as single monolithic diseases affecting a
specific organ site, we now understand that there are many subtypes of cancer
defined by unique patterns of gene mutations. These gene mutational data, which
can be more reliably obtained than gene expression data, help to determine how
the subtypes develop, evolve, and respond to therapies. Different from dense
continuous-value gene expression data, which most existing cancer subtype
discovery algorithms use, somatic mutational data are extremely sparse and
heterogeneous, because there are less than 0.5\% mutated genes in discrete
value 1/0 out of 20,000 human protein-coding genes, and identical mutated genes
are rarely shared by cancer patients.
  Our focus is to search for cancer subtypes from extremely sparse and high
dimensional gene mutational data in discrete 1 and 0 values using unsupervised
learning. We propose a new network-based distance metric. We project cancer
patients' mutational profile into their gene network structure and measure the
distance between two patients using the similarity between genes and between
the gene vertexes of the patients in the network. Experimental results in
synthetic data and real-world data show that our approach outperforms the top
competitors in cancer subtype discovery. Furthermore, our approach can identify
cancer subtypes that cannot be detected by other clustering algorithms in real
cancer data.
