A review of decomposition methods for brain states estimation.

In the rapidly advancing field of neuroscience, sophisticated imaging techniques such as functional magnetic resonance imaging (fMRI) enable detailed analysis of brain activity. Researchers increasingly seek to disentangle distinct brain states, recognizing that fMRI data typically comprise a mixture of these states. To enable independent analysis of individual brain states, numerous methodologies have been proposed, each requiring careful consideration in practical application. This review provides a comprehensive survey of decomposition methods, covering classical, probabilistic, and tensor-based approaches and their applications. Furthermore, the review discusses additional methodological considerations essential for the effective use of these techniques. By comparing decomposition algorithms with other widely used techniques in fMRI data analysis, this review highlights their methodological strengths and limitations, and further demonstrates their broad applicability for extracting brain states from fMRI data.