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Due to advances in sensors, growing large and complex medical image data havethe ability to visualize the pathological change in the cellular or even themolecular 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 greatmethodological and computational challenges for representation and selection offeatures in image cluster analysis. To address these challenges, we firstextend one dimensional functional principal component analysis to the twodimensional functional principle component analyses (2DFPCA) to fully capturespace variation of image signals. Image signals contain a large number ofredundant and irrelevant features which provide no additional or no usefulinformation for cluster analysis. Widely used methods for removing redundantand irrelevant features are sparse clustering algorithms using a lasso-typepenalty to select the features. However, the accuracy of clustering using alasso-type penalty depends on how to select penalty parameters and a thresholdfor selecting features. In practice, they are difficult to determine. Recently,randomized algorithms have received a great deal of attention in big dataanalysis. This paper presents a randomized algorithm for accurate featureselection in image cluster analysis. The proposed method is applied to ovarianand kidney cancer histology image data from the TCGA database. The resultsdemonstrate that the randomized feature selection method coupled withfunctional principal component analysis substantially outperforms the currentsparse clustering algorithms in image cluster analysis.

Functional Principal Component Analysis and Randomized Sparse Clustering Algorithm for Medical Image Analysis