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A novel approach to describe the variability of the statistics of intracranial EEG (icEEG) data is proposed that is an adaptation of the diffusion map framework. Diffusion maps, which extend principal components analysis and provide a nonlinear approach, provide dimensionality reduction of the data as well as pattern recognition that can be used to distinguish different states of a patient, for example, interictal and preseizure. A new algorithm, which is an extension of diffusion maps, is developed to construct coordinates that generate efficient geometric representations of the complex structures in the icEEG data. This method is adapted to the icEEG data and enables the extraction of the underlying brain activity to identify preseizure states. The algorithm is tested on icEEG data recorded from several electrode contacts from a patient being evaluated for possible epilepsy surgery at the Yale-New Haven Hospital. Numerical results show that the proposed approach provides a distinction between interictal and preseizure states. In addition, the icEEG are used to test the existence of a relationship between distant parts of the default mode network (DMN), a resting state network defined by fMRI studies. Magnitude squared coherence, mutual information, and cross-approximate entropy are estimated to evaluate the relationship between two test areas within the DMN. The results obtained underscore the considerable difference between electrophysiological and hemodynamic measurements of brain activity and possibly suggest a lack of neuronal involvement in the DMN.