Dietmar Cordes^{1,2}, Muhammad Kaleem^{3}, Xiaowei Zhuang^{1}, Karthik Sreenivasan^{1}, Zhengshi Yang^{1}, Tim Curran^{2}, and Virendra Mishra^{1}

In this project, we have studied resting-state networks using Empirical Mode Decomposition (EMD) to obtain time-frequency-energy information. Intrinsic Mode Functions (IMFs) and associated spatial maps provide a data-driven decomposition of resting-state networks. We investigated the average energy-period relationship of IMFs of group independent components analysis (ICA) networks to better characterize temporal properties of networks and found that the IMFs of BOLD data provide inverted V-shaped energy-period signatures that allow a natural ranking of all resting-state networks when compared to signatures of pure noise.

[1] Huang NE, et al. The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. Proc. R. Soc. Lond. 1998, A 454, 903-995.

[2] Flandrin P. et al. Empirical mode decomposition as a filter bank, IEEE Sig. Proc. Letters 2004, 11(2), 112-114.

[3] Niazy RK, et al. Spectral characteristics of resting-state networks. Prog. Brain Res. 2011, 193:259-276.

[4] Hyvärinen A. Fast and Robust Fixed-Point Algorithms for Independent Component Analysis. IEEE Transactions on Neural Networks 1999, 10(3):626-634.

Fig.1: Energy-period
relationship for the first 9 IMFs of different noise processes for 1000
simulated time series data (TR 0.765 s, 2367 time frames): Gaussian
anticorrelated AR(1) noise (left), Gaussian white noise (middle), Gaussian correlated
AR(1) noise (right). All energy-period data points belonging to a specific IMF
form an oval-shaped cluster of points. Note that with increasing AR(1)
coefficient, the energy-period spectrum is shifted upwards for IMFs 2-9 whereas
for IMF 1 the shift is downwards towards the diagonal line. The blue dotted
lines represents the 5% and 95% of the energy-period distribution for all IMFs.

Fig.2: (A) Decomposition of the
DMN time course into 9 IMF components. (B,C) Average energy-period relationship
of the IMF components (colored dots) overlaid on IMFs for Gaussian white noise
using different sampling times, namely TR=0.765s (B) and TR=2.4s (C). Note,
that a large TR (C) does not lead to much separation of the signal components
from Gaussian noise components.

Fig.3: K-means clustering of the energy-period signatures for all 30 ICA
components. The K-means cross
validation error (CVE) is shown in
(A). Note that the minimum CVE(k)
occurs for k=5 clusters. The
clustering of the 30 ICA components are shown in 2D by using a PCA
decomposition of the energy-period feature vectors of all ICA data points. The
5 clusters obtained are color-coded. (B) shows the clusters obtained in PCA
space. Each point corresponds to an ICA component. The corresponding 5 feature
vectors for the energy-period relationship of the first 9 IMFs are shown in
(C).