With ever-increasing advancements in technology, neuroscientists are able to collect data in greater volumes and with finer resolution. The bottleneck in understanding how the brain works is consequently shifting away from the amount and type of data we can collect and toward what we actually do with the data. There has been a growing interest in leveraging this vast volume of data across levels of analysis, measurement techniques, and experimental paradigms to gain more insight into brain function. Such efforts are visible at an international scale, with the emergence of big data neuroscience initiatives, such as the BRAIN initiative (Bargmann et al., 2014), the Human Brain Project, the Human Connectome Project, and the National Institute of Mental Health's Research Domain Criteria initiative. With these large-scale projects, much thought has been given to data-sharing across groups (Poldrack and Gorgolewski, 2014; Sejnowski et al., 2014); however, even with such data-sharing initiatives, funding mechanisms, and infrastructure, there still exists the challenge of how to cohesively integrate all the data. At multiple stages and levels of neuroscience investigation, machine learning holds great promise as an addition to the arsenal of analysis tools for discovering how the brain works.

Typically data acquired through imaging techniques such as functional magnetic resonance imaging (fMRI), structural MRI (sMRI), and electroencephalography (EEG) are analyzed separately. However, fusing information from such complementary modalities promises to provide additional insight into connectivity across brain networks and changes due to disease. We propose a data fusion scheme at the feature level using canonical correlation analysis (CCA) to determine inter-subject covariations across modalities. As we show both with simulation results and application to real data, multimodal CCA (mCCA) proves to be a flexible and powerful method for discovering associations among various data types. We demonstrate the versatility of the method with application to two datasets, an fMRI and EEG, and an fMRI and sMRI dataset, both collected from patients diagnosed with schizophrenia and healthy controls. CCA results for fMRI and EEG data collected for an auditory oddball task reveal associations of the temporal and motor areas with the N2 and P3 peaks. For the application to fMRI and sMRI data collected for an auditory sensorimotor task, CCA results show an interesting joint relationship between fMRI and gray matter, with patients with schizophrenia showing more functional activity in motor areas and less activity in temporal areas associated with less gray matter as compared to healthy controls. Additionally, we compare our scheme with an independent component analysis based fusion method, joint-ICA that has proven useful for such a study and note that the two methods provide complementary perspectives on data fusion.

Fusion of information from multiple sets of data in order to extract a set of features that are most useful and relevant for the given task is inherent to many problems we deal with today. Since, usually, very little is known about the actual interaction among the data sets, it is highly desirable to minimize the underlying assumptions. This has been the main reason for the growing importance of data-driven methods, and in particular of independent component analysis (ICA) as it provides useful decompositions with a simple generative model and using only the assumption of statistical independence. A recent extension of ICA, independent vector analysis (IVA), generalizes ICA to multiple data sets by exploiting the statistical dependence across the data sets, and hence, as we discuss in this paper, provides an attractive solution to fusion of data from multiple data sets along with ICA. In this paper, we focus on two multivariate solutions for multimodal data fusion that let multiple modalities fully interact for the estimation of underlying features that jointly report on all modalities. One solution is the joint ICA model that has found wide application in medical imaging, and the second one is the transposed IVA model introduced here as a generalization of an approach based on multiset canonical correlation analysis. In the discussion, we emphasize the role of diversity in the decompositions achieved by these two models, and present their properties and implementation details to enable the user make informed decisions on the selection of a model along with its associated parameters. Discussions are supported by simulation results to help highlight the main issues in the implementation of these methods.

We present a novel method to extract classification features from functional magnetic resonance imaging (fMRI) data collected at rest or during the performance of a task. By combining a two-level feature identification scheme with kernel principal component analysis (KPCA) and Fisher's linear discriminant analysis (FLD), we achieve high classification rates in discriminating healthy controls from patients with schizophrenia. Experimental results using leave-one-out cross-validation show that features extracted from the default mode network (DMN) lead to a classification accuracy of over 90% in both data sets. Moreover, using a majority vote method that uses multiple features, we achieve a classification accuracy of 98% in auditory oddball (AOD) task and 93% in rest data. Several components, including DMN, temporal and medial visual regions, are consistently present in the set of features that yield high classification accuracy. The features we have extracted thus show promise to be used as biomarkers for schizophrenia. Results also suggest that there may be different advantages to using resting fMRI data or task fMRI data.

Human brain connectivity is complex. Graph-theory-based analysis has become a powerful and popular approach for analyzing brain imaging data, largely because of its potential to quantitatively illuminate the networks, the static architecture in structure and function, the organization of dynamic behavior over time, and disease related brain changes. The first step in creating brain graphs is to define the nodes and edges connecting them. We review a number of approaches for defining brain nodes including fixed versus data-driven nodes. Expanding the narrow view of most studies which focus on static and/or single modality brain connectivity, we also survey advanced approaches and their performances in building dynamic and multimodal brain graphs. We show results from both simulated and real data from healthy controls and patients with mental illnesses. We outline the advantages and challenges of these various techniques. By summarizing and inspecting recent studies which analyzed brain imaging data based on graph theory, this paper provides a guide for developing new powerful tools to explore complex brain networks.

We describe a framework based on Wirtinger calculus for adaptive signal processing that enables efficient derivation of algorithms by directly working in the complex domain and taking full advantage of the power of complex-domain nonlinear processing. We establish the basic relationships for optimization in the complex domain and the real-domain equivalences for first- and second-order derivatives by extending the work of Brandwood and van den Bos. Examples in the derivation of first- and second-order update rules are given to demonstrate the versatility of the approach.