The study of human brain functions has dramatically increased in recent years greatly due to the advent of Functional Magnetic Resonance Imaging. In this paper we apply and compare different machine learning techniques to the problem of classifying the instantaneous cognitive state of a person based on her functional Magnetic Resonance Imaging data. In particular, we present successful case studies of induced classifiers which accurately discriminate between cognitive states produced by listening to different auditory stimuli. The problem investigated in this paper provides a very interesting case study of training classifiers with extremely high dimensional, sparse and noisy data. We present and discuss the results obtained in the case studies.