Tensor Methods for Joint Analysis and Fusion of Brain Imaging Data: Application to fMRI and MEG Analysis and Fusion

Abstract

Brain imaging has been playing an increasingly important role in clinical diagnosis and exploratory biomedical research. Imaging biomarkers are useful in diagnosing neurodegenerative disorders and guiding personalized medicine. On the other hand, high-throughput data acquisition has generated large, multidimensional and heterogeneous brain imaging data. The complexity of analyzing these data has arisen due to their high dimensionality, multimodal nature, noise and issues such as missing data. Matrix and tensor factorizations provide an attractive framework for working with such data as they provide useful decompositions that are directly interpretable. Typical matrix factorization approaches employed in multi-subject single modality brain imaging studies including magnetoencephalography (MEG), electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) concatenate datasets into a two-dimensional (2D) matrix structure, thus preventing explicit interactions among multiple modes of brain imaging data and producing highly nonunique solutions with lower statistical power. In addition, utilizing a single imaging modality may have limitations such as low sensitivity, poor image quality, and low temporal/spatial resolution, resulting in lower statistical power of biomarkers. Tensor factorizations and multimodal data fusion have emerged as a promising solution to the computational challenges of high-dimensional and multimodal brain imaging data. In contrast to matrix factorization, tensor factorizations preserve multilinear interactions, effectively summarize brain processes by low-dimensional distinct latent factors, and hence can better address the curse of dimensionality and can result in better sensitivity. This dissertation summarizes the important issues discussed above and provides a computational framework for addressing typical challenges during data collection, analysis, and fusion of multiset/multimodal brain imaging data. First, we develop novel optimization methods for geometrical four-dimensional (4D) fMRI data completion on the Riemannian tensor train (TT) manifold, which preserves the 4D structure and relationships in the data. Exploiting the geometry-aware Riemannian optimization and taking into account the natural 4D representation of fMRI data provides significant gains compared with the most common three-dimensional (3D) and 2D fMRI data formats based on traditional Euclidean geometry. We demonstrate that TT decomposition combined with generalized geometrical statistical learning provides a powerful approach for robust interpolation and estimation of missing brain voxels, which results in significantly higher sensitivity (p < 0.05) of estimated imaging biomarkers such as resting state networks (RSNs). Second, we develop a multiway latent component analysis framework for the discovery of brain developmental patterns and tensor group-level statistical inference with application to multi-subject MEG data using canonical polyadic (CP) tensor decomposition. The group-level tensor decomposition takes into account the multilinear nature of MEG data and enables the estimation of interpretable unique latent spatiotemporal brain patterns with high discriminatory power using a multiway data-driven source separation. We demonstrate that tensor group-level statistical inference enables a region-of-interest (ROI)-independent statistical assessment of identified latent sources, alleviating the multiple comparison problem due to dimensionality reduction, which results in significantly higher sensitivity of latent components than traditional state-of-the-art methods such as nonparametric statistical testing. Finally, we propose multimodal high-order MEG and fMRI data fusion using a coupled tensor/matrix factorization (CMTF) model to take advantage of complementary nature of these imaging modalities to further enhance the discovery of brain patterns and study brain development and function on a millisecond scale. Using the CMTF model, we extracted distinct brain patterns that revealed fine-grained spatiotemporal brain dynamics and stimuli processing pathways, such as sensory processing, attention, response preparation, and execution. We demonstrate that latent joint components extracted from multimodal tensor/matrix fusion provide higher statistical power (p < 0.05) between high- and low-performance subjects than single-modality data-driven models. Additionally, we show that joint latent components demonstrate significant associations with major cognitive domains such as general intelligence and executive function, thus relating cognitive development status to latent brain components. To conclude, the proposed tensor-based methods provide a powerful computational framework for multiway latent analysis, high-order data completion, and multimodal data-driven fusion that enable robust identification of distinct brain developmental patterns with high discriminatory power and explain brain function and high-level cognition in time and space. Employing tensor decompositions and multimodal data fusion shows great promise as a valuable tool for the prospective assessment of developmental status, brain function, and high-level cognition directly from MEG and fMRI measurements.