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.

METHOD: This study included a total of 44 participants without subjective olfactory disturbances. Lavender and normal saline were used as the olfactory stimulant and control. Electroencephalogram was recorded and power spectra were analysed by the spectral analysis for each alpha, beta, delta, theta and gamma bandwidth frequency upon exposure to lavender and normal saline independently.

RESULTS: The oscillatory brain activities in response to the olfactory stimulant indicated that the lavender smell decreased the beta activity in the left frontal (F7 electrode) and central region (C3 electrode) with a reduction in the gamma activity in the right parietal region (P4 electrode) (p < 0.05).