Riemannian manifold-based disentangled representation learning for multi-site functional connectivity analysis.

Functional connectivity (FC), derived from resting-state functional magnetic resonance imaging (rs-fMRI), has been widely used to characterize brain abnormalities in disorders. FC is usually defined as a correlation matrix that is a symmetric positive definite (SPD) matrix lying on the Riemannian manifold. Recently, a number of learning-based methods have been proposed for FC analysis, while the geometric properties of Riemannian manifold have not yet been fully explored in previous studies. Also, most existing methods are designed to target one imaging site of fMRI data, which may result in limited training data for learning reliable and robust models. In this paper, we propose a novel Riemannian Manifold-based Disentangled Representation Learning (RM-DRL) framework which is capable of learning invariant representations from fMRI data across multiple sites for brain disorder diagnosis. In RM-DRL, we first employ an SPD-based encoder module to learn a latent unified representation of FC from different sites, which can preserve the Riemannian geometry of the SPD matrices. In latent space, a disentangled representation module is then designed to split the learned features into domain-specific and domain-invariant parts, respectively. Finally, a decoder module is introduced to ensure that sufficient information can be preserved during disentanglement learning. These designs allow us to introduce four types of training objectives to improve the disentanglement learning. Our RM-DRL method is evaluated on the public multi-site ABIDE dataset, showing superior performance compared with several state-of-the-art methods.