Learning and Mining Functional Connectivity Networks Based on Brain fMRI Data

Functional Connectivity Network (FCN) is an important tool to reveal the brain working mechanism, mine the biomarkers of neurological/mental disorders and explore the human cognitive behaviors. In recent years, the development of functional Magnetic Resonance Imaging (fMRI) technology has become the main data source for learning the FCNs. Learn- ing the FCNs based on fMRI data, and further mining their potential information is now an important area of research. However, learning a “good” FCN, and further mining its brain connectivity patterns is a challenging problem, due to the weakness of fMRI signals, the noisy fMRI data, together with our limited understanding of the brain. Previous stud- ies have shown that the existing FCN learning methods can only operate well on some specific data, but their performances tend to drop significantly once subtle changes, such as scales, sources and even preprocessing pipelines, occur in the fMRI data. This means that, until now, the learning algorithms cannot capture the essential connectivity pattern of the brain. In this thesis, we study the FCN learning and mining problem and its ap- plications, according to the characteristics of fMRI data and the priors of the brain. The main contributions include: • A novel method namely Time-constrained Multiset Canonical Correlation Analy- sis (TMCCA) is proposed to extract representative Blood Oxygen Level Dependent (BOLD) signals for subsequent FCN estimation and classification. Prior to FCN esti- mation and classification, extracting representative BOLD signals from brain Regions of Interest (ROIs) is a critical step. Traditional extraction methods include averaging, finding peaks and dimensionality reduction etc., often leading to signal cancellation and information loss. Different from traditional methods that treat equally all BOLD signals in a ROI, the proposed method assigns weights to different BOLD signals, and learns the optimal weights to make the extracted representative signals jointly maximize the multiple correlations between ROIs. Importantly, time-constraint is incorporated into our proposed method, which can effectively encode nonlinear rela- tionship among BOLD signals. To evaluate the effectiveness of the proposed method, the extracted BOLD signals is used to estimate FCN and, in turn, identify brain dis- orders, including Mild Cognitive Impairment (MCI) and Autism Spectrum Disorder (ASD). Experimental results demonstrate that our proposed TMCCA can lead to better performance than traditional methods. • A probabilistic explanation of Correlation’s Correlation (CC) aimed at constructing high-order FCN is studied. Pearson’s Correlation (PC) is the most widely accepted method for constructing FCNs and provides a basis for designing new FCN estima- tion schemes. A recent study proposes to use two sequential PC operations, namely CC, for constructing high-order FCNs. Despite its empirical effectiveness in identi- fying neurological disorders and detecting subtle changes of connections in different subject groups, CC is defined intuitively without a solid and sustainable theoretical foundation. For understanding CC more rigorously and providing a systematic FCN learning framework, we reformulate it in the Bayesian view with a prior of matrix- variate normal distribution. In addition, we develop a Bayesian High-order Method (BHM) to automatically and simultaneously estimate the high- and low-order FCN based on this probabilistic framework. An efficient optimization algorithm is also pro- posed. Finally, we evaluate the performance of BHM in identifying subjects with ASD from typical controls based on the estimated FCNs. Experimental results suggest that the automatically learned high- and low-order FCNs yield a superior performance over the artificially defined FCNs via conventional CC and PC. • The inclusion of label information in FCN learning is studied. Most traditional meth- ods tend to focus on learning FCNs independently of the classification task. This practice neglects the valuable label information crucial for accurate classification. Be- sides, the methodology of constructing brain networks in an isolated, individualistic manner sidesteps the consistent information among individuals. To address these is- sues, we developed a new FCN joint learning strategy named Label-Guided Low-rank Approximation (LGLA). It integrates label information of training subjects into the constructing FCN process, concomitantly utilizing the information of unlabeled sub- jects for auxiliary training. This concurrent process aims to transfer latent information of training subjects to testing subjects, optimizing enhanced discriminative FCN fea- tures tailored to testing subjects. Specifically, we enforce the similarity of subjects from the same class and the dissimilarity of subjects from different classes using a norm similarity measure with an indicator function. Besides, a low-rank constraint among LGLA aims to simultaneously consider FCNs of among all the individuals when learning the FCN of the testing subject. This is achieved by utilizing a low-rank constraint to are utilized with the aim to capture their shared consistent informa- tion The incorporation of label information and the low-rank constraint result in a convex optimization problem, which can be solved efficiently. Experimental results on real datasets for identifying Subcortical Vascular Cognitive Impairment (SVCI) demonstrate the effectiveness of our proposed FCN learning method. Additionally, we further explored the brain network features and discovered potential biomarkers for personalized diagnosis. • A novel method for jointly selecting nodes and edges from the estimated FCNs is studied. Before the identification task, selecting features from the estimated FCN is a necessary step for reducing computational cost, alleviating the risk of overfitting, and finding potential biomarkers of brain diseases. In the current literature, either node-based features (e.g., local clustering coefficients) or edge-based features (e.g., ad- jacency weights) are generally considered. Despite their popularity, these schemes can only capture one granularity (node or edge) of information in the FCN, which might be insufficient for the classification task and the interpretation of the classification result. To address this issue, we first assign the edges to different node groups. Then, sparse group Least Absolute Shrinkage and Selection Operator (sgLASSO) is used to select groups (nodes) and edges in the groups to achieve a better classification per- formance. Such a technique enables us to simultaneously locate discriminative brain regions, as well as connections between these brain regions, making the classifica- tion results more interpretable. Experimental results show that the proposed method achieves better classification performance than state-of-the-art methods. Moreover, by exploring brain network features that contributed most to MCI identification, we discover potential biomarkers for MCI diagnosis.