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In this contribution, the clustering procedure based on K-Means algorithm isstudied as an inverse problem, which is a special case of the illposedproblems. The attempts to improve the quality of the clustering inverse problemdrive to reduce the input data via Principal Component Analysis (PCA). Sincethere exists a theorem by Ding and He that links the cardinality of the optimalclusters found with K-Means and the cardinality of the selected informative PCAcomponents, the computational experiments tested the theorem between twoquantitative features selection methods: Kaiser criteria (based on imperativedecision) versus Wishart criteria (based on random matrix theory). The resultssuggested that PCA reduction with features selection by Wishart criteria leadsto a low matrix condition number and satisfies the relation between clustersand components predicts by the theorem. The data used for the computations arefrom a neuroscientific repository: it regards healthy and young subjects thatperformed a task-oriented functional Magnetic Resonance Imaging (fMRI)paradigm.

Solving clustering as ill-posed problem: experiments with K-Means algorithm