Coupled Harmonic Bases for Longitudinal Characterization of Brain Networks

Integrating Multimodal and Longitudinal Neuroimaging Data with Multi-Source Network Representation Learning

Uncovering the complex network of the brain is of great interest to the field of neuroimaging. Mining from these rich datasets, scientists try to unveil the fundamental biological mechanisms in the human brain. However, neuroimaging data collected for constructing brain networks is generally costly, and thus extracting useful information from a limited sample size of brain networks is demanding. Currently, there are two common trends in neuroimaging data collection that could be exploited to gain more information: 1) multimodal data, and 2) longitudinal data. It has been shown that these two types of data provide complementary information. Nonetheless, it is challenging to learn brain network representations that can simultaneously capture network properties from multimodal as well as longitudinal datasets. Here we propose a general fusion framework for multi-source learning of brain networks - multimodal brain network fusion with longitudinal coupling (MMLC). In our framework, three layers of information are considered, including cross-sectional similarity, multimodal coupling, and longitudinal consistency. Specifically, we jointly factorize multimodal networks and construct a rotation-based constraint to couple network variance across time. We also adopt the consensus factorization as the group consistent pattern. Using two publicly available brain imaging datasets, we demonstrate that MMLC may better predict psychometric scores than some other state-of-the-art brain network representation learning algorithms. Additionally, the discovered significant brain regions are synergistic with previous literature. Our new approach may boost statistical power and sheds new light on neuroimaging network biomarkers for future psychometric prediction research by integrating longitudinal and multimodal neuroimaging data.

Learning Common Harmonic Waves on Stiefel Manifold - A New Mathematical Approach for Brain Network Analyses

Converging evidence shows that disease-relevant brain alterations do not appear in random brain locations, instead, their spatial patterns follow large-scale brain networks. In this context, a powerful network analysis approach with a mathematical foundation is indispensable to understand the mechanisms of neuropathological events as they spread through the brain. Indeed, the topology of each brain network is governed by its native harmonic waves, which are a set of orthogonal bases derived from the Eigen-system of the underlying Laplacian matrix. To that end, we propose a novel connectome harmonic analysis framework that provides enhanced mathematical insights by detecting frequency-based alterations relevant to brain disorders. The backbone of our framework is a novel manifold algebra appropriate for inference across harmonic waves. This algebra overcomes the limitations of using classic Euclidean operations on irregular data structures. The individual harmonic differences are measured by a set of common harmonic waves learned from a population of individual Eigen-systems, where each native Eigen-system is regarded as a sample drawn from the Stiefel manifold. Specifically, a manifold optimization scheme is tailored to find the common harmonic waves, which reside at the center of the Stiefel manifold. To that end, the common harmonic waves constitute a new set of neurobiological bases to understand disease progression. Each harmonic wave exhibits a unique propagation pattern of neuropathological burden spreading across brain networks. The statistical power of our novel connectome harmonic analysis approach is evaluated by identifying frequency-based alterations relevant to Alzheimer's disease, where our learning-based manifold approach discovers more significant and reproducible network dysfunction patterns than Euclidean methods.

Multimodal Fusion of Brain Networks with Longitudinal Couplings

In recent years, brain network analysis has attracted considerable interests in the field of neuroimaging analysis. It plays a vital role in understanding biologically fundamental mechanisms of human brains. As the upward trend of multi-source in neuroimaging data collection, effective learning from the different types of data sources, e.g. multimodal and longitudinal data, is much in demand. In this paper, we propose a general coupling framework, the multimodal neuroimaging network fusion with longitudinal couplings (MMLC), to learn the latent representations of brain networks. Specifically, we jointly factorize multimodal networks, assuming a linear relationship to couple network variance across time. Experimental results on two large datasets demonstrate the effectiveness of the proposed framework. The new approach integrates information from longitudinal, multimodal neuroimaging data and boosts statistical power to predict psychometric evaluation measures.