Before revision:  We demonstrate that the proposed method is useful for identifying distinct state spacesin the resting-state connectivities of males and females through the transition matrices of the common states .
After revision:  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 through the transition matrices of the common states .