The Multi-Frequency Decomposition Entropy Learning for Nonlinear fMRI Data Analysis

Functional magnetic resonance imaging (fMRI) have been widely adopted to explore the underlying neural mechanisms between psychiatric disorders which share common neurobiology and clinical manifestations. However, the existing studies mainly focus on linear relationships and ignore nonlinear contributions. To address the above issues, we propose a new method named multi-frequency decomposition entropy (MDE) learning for inferring nonlinear functional connectivity between brain regions. Firstly, the variational mode decomposition was used to divide fMRI data into five groups of frequency. Next, the copula entropy was used to calculate the nonlinear relationship between brain regions in each frequency group, and then the best important nonlinear relationships were screen out by using statistical t-test. Lastly, a gyrus importance index was proposed to reflect the distribution trend of gyri in different frequency groups. The results of applying MDE for the fMRI data analysis of schizophrenia, bipolar disorder, and attention-deficit hyperactivity disorder showed that the difference between the three groups of patient and healthy control is large at the hub nodes, and the nonlinear relationship between the patient groups is weak when they are at the same hub node. In addition, each disease exhibits unique characteristics compared with other diseases and healthy control. In a word, the nonlinear functional connectivity of different frequency groups reflect the differences and commonalities between diseases and reveal possible discriminating biomarkers among mental diseases.