Estimating intrinsic dimensionality of fMRI dataset incorporating an AR(1) noise model with cubic spline interpolation

Estimating the true dimensionality of the data to determine what is essential in the data is an important but a difficult problem in fMRI dataset. In this paper, cubic spline interpolation is introduced to detect the number of essential components in fMRI dataset. By constructing proper interpolation variable, more reasonable estimation of the coefficient of an autoregressive noise model of order 1 can be made. Simulation data and real fMRI dataset of resting-state in human brains are used to compare the performance of the new method incorporating an autoregressive noise model of order 1 with cubic spline interpolation (AR1CSI) with that of the method based only on an autoregressive noise model of order 1 (AR1). The results show the AR1CSI method leads to more accurate estimate of the model order at many circumstances, as illustrated in simulated datasets and real fMRI datasets of resting-state human brain.