  Due to advances in sensors, growing large and complex medical image data have
the ability to visualize the pathological change in the cellular or even the
molecular level or anatomical changes in tissues and organs. As a consequence,
the medical images have the potential to enhance diagnosis of disease,
prediction of clinical outcomes, characterization of disease progression,
management of health care and development of treatments, but also pose great
methodological and computational challenges for representation and selection of
features in image cluster analysis. To address these challenges, we first
extend one dimensional functional principal component analysis to the two
dimensional functional principle component analyses (2DFPCA) to fully capture
space variation of image signals. Image signals contain a large number of
redundant and irrelevant features which provide no additional or no useful
information for cluster analysis. Widely used methods for removing redundant
and irrelevant features are sparse clustering algorithms using a lasso-type
penalty to select the features. However, the accuracy of clustering using a
lasso-type penalty depends on how to select penalty parameters and a threshold
for selecting features. In practice, they are difficult to determine. Recently,
randomized algorithms have received a great deal of attention in big data
analysis. This paper presents a randomized algorithm for accurate feature
selection in image cluster analysis. The proposed method is applied to ovarian
and kidney cancer histology image data from the TCGA database. The results
demonstrate that the randomized feature selection method coupled with
functional principal component analysis substantially outperforms the current
sparse clustering algorithms in image cluster analysis.
