Construction of low dimensional Functional connectivity networks from fMRI data using manifold learning algorithms

Neuroimaging techniques, especially fMRI analysis provide images that are contained in a high dimensional space. In a typical fMRI scan more than 100,000 voxels are recorded at each time instance, thus one gets tens of millions of data if one also considers groups of subjects. Hence, one confronts with issues, that of (a) noise/ artifact removal and, (b) dimensionality reduction (Siettos and Starke, 2016). In this work, we employ a data-driven approach to dimensionality reduction with the aim to construct brain functional connectivity networks (FCN) as emerged through fMRI images. For the construction of the FCN we exploit state-of-the-art nonlinear manifold learning algorithms, namely Isometric Feature Mapping (ISOMAP) (Tenenbaum et al., 2000) and Diffusion Maps (Coifman et al., 2005) to embed the high dimensional space to lower order manifolds. We illustrate the efficiency of the methods through fMRI recordings acquired before and after the implementation of the Integrated Psychological Therapy (IPT) to a relatively small size of patients suffering from schizophrenia. IPT is a group medication program integrating neurocognitive and psychosocial rehabilitation. We show that while linear standard techniques fail to identify significant differences in the FCNs of the patients before and after the treatment the nonlinear manifold embedded analysis reveals differences related both to the global properties of the FNC and regions of the brain, that are involved in higher order cognition functioning, goal-oriented tasks, social and moral reasoning. Siettos, C.I., Starke, J. (2016). Multiscale Modeling of Brain Dynamics: from Single Neurons and Networks to Mathematical Tools, WIREs Systems Biology and Medicine, 8(5), 438-458. Tenenbaum, J.B., De Silva, V., Langford, J.C. (2000). A global geometric framework for nonlinear dimensionality reduction, Science, 290 (5500), 2319-2323. Coifman,R.R., et al. (2005). Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps, Proceedings of the National Academy of Sciences of the United States of America, 102(21), 7426-7431.