An Orthogonal Semi-Nonnegative Matrix Factorization Method for Dynamic Functional Connectivity Analysis and Its Application to Schizophrenia.

Dynamic functional connectivity (dFC) analysis investigates how the functional interactions between brain regions change over time by identifying recurring connectivity patterns, known as dFC states, and tracking transitions between them. Non-negative matrix factorization (NMF) has been used in dFC analysis because it produces non-negative dFC states and coefficients, interpreting dFC states and their transitions straightforwardly. However, existing NMF-based methods are limited to processing dFC data with exclusively positive values, failing to align with the functional correlations and anti-correlations between brain regions. This paper proposes an orthogonal semi-nonnegative matrix factorization (OSemiNMF) method, extending NMF to directly handle mixed-sign dFC data. Furthermore, an orthogonality constraint on the bases (i.e., dFC states) is incorporated to enhance the uniqueness of dFC states. For 10 simulated datasets with varying properties, our method outperforms comparison methods, supporting its superior ability to capture dFC states and state transitions. Using four resting-state fMRI datasets consisting of 708 healthy controls (HCs) and 537 schizophrenia patients (SZs), our method identifies reproducible dFC states and state transitions across datasets. Further, our findings reveal that SZs spend less time in high-connectivity states compared to HCs. Our study identifies meaningful and reproducible biomarkers of schizophrenia, mainly involving the connectivity associated with the sub-cortical domain. In summary, the OSemiNMF method facilitates the dFC analysis for understanding brain dynamics.