Feature selection for clustering of functional magnetic resonance imaging data

Functional magnetic resonance imaging (fMRI) is widely used for non-invasively studying human brain functions. The detection of activation using fMRI relies on the complex coupling between neuroactivity, brain hemodynamics, and magnetic proper ties of oxyhemoglobin and deoxyhemoglobin. In this thesis, an analysis of fMRI data is proposed. We explore a new paradigm for the analysis of fMRI data. We regard the fMRI data as a very large set of time series x_i(t), indexed by the position i of a voxel inside the brain. The decision that a voxel i₀ is activated is based not solely on the value of the fMRI signal at i₀, but rather on the comparison of all time series x_i(t) in a small neighborhood V(i₀) around i₀. We construct basis functions on which the projections of fMRI data reveal the organization of the time series x_i( t) into “activated” and “non-activated” clusters. These “clustering basis waveforms” are selected from a large dictionary of wavelet packets according to their ability to separate the fMRI time series into an activated cluster and a non-activated cluster. This principle exploits the intrinsic spatial correlation that is present in the data, and does not assume any particular model of the hemodynamic response. Once the best “clustering basis waveforms” are found, the coefficients are obtained by projecting the time series x_i(t) onto the waveforms. These coefficients are partitioned into two clusters. Several clustering results obtained with the time series $xi0t$ and its different neighborhoods V(i ₀) are combined to obtain a more robust and reliable result.