Functional graphical model classification

Abstract

The functional magnetic resonance imaging (fMRI) records signals coming from human brains, which show activities and states of brains. This measurements result in a high-dimensional time series, and each dimension represents a region of brains. In this paper, we propose a functional Gaussian graphical model to describe the distribution and the correlation structure for this type of high-dimensional time series data, and we find a quadratic discriminant analysis can be effective on functional graphical model. There are two kernel estimators introduced in our work to estimate the node set and the edge set of the functional graphical model, and they are used in our discriminant functions. The simulation study showed that this classification method outperforms other existing methods, and it demonstrated the idea of choosing tuning parameters with different simulated data set. In addition, we present two real data applications. One is an alcoholic condition detection with Electroencephalography (EEG) data collected from electrodes placed on subject’s scalps, and the other is a resting state detection using resting state fMRI data from the OpenfMRI database. In both applications, our proposed methodology performs better than other competitive methodologies.