  In this contribution, the clustering procedure based on K-Means algorithm is
studied as an inverse problem, which is a special case of the illposed
problems. The attempts to improve the quality of the clustering inverse problem
drive to reduce the input data via Principal Component Analysis (PCA). Since
there exists a theorem by Ding and He that links the cardinality of the optimal
clusters found with K-Means and the cardinality of the selected informative PCA
components, the computational experiments tested the theorem between two
quantitative features selection methods: Kaiser criteria (based on imperative
decision) versus Wishart criteria (based on random matrix theory). The results
suggested that PCA reduction with features selection by Wishart criteria leads
to a low matrix condition number and satisfies the relation between clusters
and components predicts by the theorem. The data used for the computations are
from a neuroscientific repository: it regards healthy and young subjects that
performed a task-oriented functional Magnetic Resonance Imaging (fMRI)
paradigm.
