  Background: Recent studies have indicated that functional connectivity is
dynamic even during rest. A common approach to modeling the dynamic functional
connectivity in whole-brain resting-state fMRI is to compute the correlation
between anatomical regions via sliding time windows. However, the direct use of
the sample correlation matrices is not reliable due to the image acquisition
and processing noises in resting-sate fMRI.
  New method: To overcome these limitations, we propose a new statistical model
that smooths out the noise by exploiting the geometric structure of correlation
matrices. The dynamic correlation matrix is modeled as a linear combination of
symmetric positive-definite matrices combined with cosine series
representation. The resulting smoothed dynamic correlation matrices are
clustered into disjoint brain connectivity states using the k-means clustering
algorithm.
  Results: The proposed model preserves the geometric structure of underlying
physiological dynamic correlation, eliminates unwanted noise in connectivity
and obtains more accurate state spaces. The difference in the estimated dynamic
connectivity states between males and females is identified.
  Comparison with existing methods: We demonstrate that the proposed
statistical model has less rapid state changes caused by noise and improves the
accuracy in identifying and discriminating different states.
  Conclusions: We propose a new regression model on dynamically changing
correlation matrices that provides better performance over existing windowed
correlation and is more reliable for the modeling of dynamic connectivity.
