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Abstract:
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Analyzing functional magnetic resonance imaging (fMRI) signals is challenging because of its complicated spatio-temporal correlation structures and its massive amount of data. One of interest in fMRI analysis is to provide brain parcellation based on its functional connectivity, because researchers observe that fMRI signals are not coherent even within the same area in the currently available brain atlases. Therefore, providing parcellation of a brain, especially based on its functional connectivity, is necessary to understand brain activities. One of the well-used techniques in a brain parcellation is spectral clustering. However, its asymptotic behavior is not fully clarified. In addition, there has previously been no available mathematical justification of the large-sample properties of spectral clustering when the data are dependent. Von Luxburg et al (2008) showed the consistency of spectral clustering under the assumption that data are independent and identically distributed. We extended von Luxburg's work to 3-dimensional spatially dependent data satisfying strong mixing conditions, which will be the case for fMRI data.
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