  Gene expression profiles are essential in identifying different cancer
phenotypes. Clustering gene expression datasets can provide accurate
identification of cancerous cell lines, but this task is challenging due to the
small sample size and high dimensionality. Using the $K$-means clustering
algorithm we determine the organisation of the solution space for a variety of
gene expression datasets using energy landscape theory. The solution space
landscapes allow us to understand $K$-means performance, and guide more
effective use when varying common dataset properties; number of features,
number of clusters, and cluster distribution. We find that the landscapes have
a single-funnelled structure for the appropriate number of clusters, which is
lost when the number of clusters deviates from this. We quantify this landscape
structure using a frustration metric and show that it may provide a novel
diagnostic tool for the appropriate number of cancer subtypes.
