With the rapid development of high-throughput technologies, a growing amount of multi-omics data are collected, giving rise to a great demand for combining such data for biomedical discovery. Due to the cost and time to label the data manually, the number of labelled samples is limited. This motivated the need for semi-supervised learning algorithms. In this work, we applied a graph-based semi-supervised learning (GSSL) to classify a severe chronic mental disorder, schizophrenia (SZ). An advantage of GSSL is that it can simultaneously analyse more than two types of data, while many existing models focus on pairwise data analysis. In particular, we applied GSSL to the analysis of single nucleotide polymorphism (SNP), functional magnetic resonance imaging (fMRI) and DNA methylation data, which accounts for genetics, brain imaging (endophenotypes), and environmental factors (epigenomics) respectively. While parameter selection has been an open challenge for most models, another key contribution of this work is that we explored the parameter space to interpret their meaning and established practical guidelines. Based on the practical significance of each hyper-parameter, a relatively small range of candidate values can be determined in a data-driven way to both optimize and speed up the parameter tuning process. We validated the model through both synthetic data and a real SZ dataset of 184 subjects from the Mental Illness and Neuroscience Discovery (MIND) Clinical Imaging Consortium. In comparison to several existing approaches, our algorithm achieved better performance in terms of classification accuracy. We also confirmed the significance of several brain regions associated with SZ.

Recent advances in imaging genetics produce large amounts of data including functional MRI images, single nucleotide polymorphisms (SNPs), and cognitive assessments. Understanding the complex interactions among these heterogeneous and complementary data has the potential to help with diagnosis and prevention of mental disorders. However, limited efforts have been made due to the high dimensionality, group structure, and mixed type of these data. In this paper we present a novel method to detect conditional associations between imaging genetics data. We use projected distance correlation to build a conditional dependency graph among high-dimensional mixed data, then use multiple testing to detect significant group level associations (e.g., ROI-gene). In addition, we introduce a scalable algorithm based on orthogonal greedy algorithm, yielding the greedy projected distance correlation (G-PDC). This can reduce the computational cost, which is critical for analyzing large-volume of imaging genomics data. The results from our simulations demonstrate a higher degree of accuracy with GPDC than distance correlation, Pearson's correlation and partial correlation, especially when the correlation is nonlinear. Finally, we apply our method to the Philadelphia Neurodevelopmental data cohort with 866 samples including fMRI images and SNP profiles. The results uncover several statistically significant and biologically interesting interactions, which are further validated with many existing studies. The Matlab code is available at https://sites.google.com/site/jianfang86/gPDC.

Functional connectivity (FC) estimated from functional magnetic resonance imaging (fMRI) time series, especially during resting state periods, provides a powerful tool to assess human brain functional architecture in health, disease, and developmental states. Recently, the focus of connectivity analysis has shifted toward the subnetworks of the brain, which reveals co-activating patterns over time. Most prior works produced a dense set of high-dimensional vectors, which are hard to interpret. In addition, their estimations to a large extent were based on an implicit assumption of spatial and temporal stationarity throughout the fMRI scanning session. In this paper, we propose an approach called dynamic sparse connectivity patterns (dSCPs), which takes advantage of both matrix factorization and time-varying fMRI time series to improve the estimation power of FC. The feasibility of analyzing dynamic FC with our model is first validated through simulated experiments. Then, we use our framework to measure the difference between young adults and children with real fMRI data set from the Philadelphia Neurodevelopmental Cohort (PNC). The results from the PNC data set showed significant FC differences between young adults and children in four different states. For instance, young adults had reduced connectivity between the default mode network and other subnetworks, as well as hyperconnectivity within the visual system in states 1 and 3, and hypoconnectivity in state 2. Meanwhile, they exhibited temporal correlation patterns that changed over time within functional subnetworks. In addition, the dSCPs model indicated that older people tend to spend more time within a relatively connected FC pattern. Overall, the proposed method provides a valid means to assess dynamic FC, which could facilitate the study of brain networks.

Reducing the number of false discoveries is presently one of the most pressing issues in the life sciences. It is of especially great importance for many applications in neuroimaging and genomics, where data sets are typically high-dimensional, which means that the number of explanatory variables exceeds the sample size. The false discovery rate (FDR) is a criterion that can be employed to address that issue. Thus it has gained great popularity as a tool for testing multiple hypotheses. Canonical correlation analysis (CCA) is a statistical technique that is used to make sense of the cross-correlation of two sets of measurements collected on the same set of samples (e.g., brain imaging and genomic data for the same mental illness patients), and sparse CCA extends the classical method to high-dimensional settings. Here, we propose a way of applying the FDR concept to sparse CCA, and a method to control the FDR. The proposed FDR correction directly influences the sparsity of the solution, adapting it to the unknown true sparsity level. Theoretical derivation as well as simulation studies show that our procedure indeed keeps the FDR of the canonical vectors below a user-specified target level. We apply the proposed method to an imaging genomics data set from the Philadelphia Neurodevelopmental Cohort. Our results link the brain connectivity profiles derived from brain activity during an emotion identification task, as measured by functional magnetic resonance imaging, to the corresponding subjects' genomic data.

In this paper, we consider the problem of estimating multiple sparse, co-activated brain regions from functional magnetic resonance imaging (fMRI) observations belonging to different classes. More precisely, we propose a method to analyze similarities and differences in functional connectivity between children and young adults. Often, analysis is conducted on each class separately, and differences across classes are identified with an additional postprocessing step using adequate statistical tools. Here, we propose to rely on a generalized fused Lasso penalty, which allows us to make use of the entire data set in order to estimate connectivity patterns that are either shared across classes, or specific to a given group. By using the entire population during the estimation, we hope to increase the power of our analysis. The proposed model falls in the category of population-wise matrix decomposition, and a simple and efficient alternating direction method of multipliers algorithm is introduced to solve the associated optimization problem. After validating our approach on simulated data, experiments are performed on resting-state fMRI imaging from the Philadelphia neurodevelopmental cohort data set, comprised of normally developing children from ages 8 to 21. Developmental differences were observed in various brain regions, as a total of three class-specific resting-state components were identified. Statistical analysis of the estimated subject-specific features, as well as classification results (based on age groups, up to 81% accuracy, samples) related to these components demonstrate that the proposed method is able to properly extract meaningful shared and class-specific sub-networks.

Among the challenges arising in brain imaging genetic studies, estimating the potential links between neurological and genetic variability within a population is key. In this paper, we propose a multivariate, multimodal formulation for variable selection that leverages co-expression patterns across various data modalities. Our approach is based on an intuitive combination of two widely used statistical models: sparse regression and canonical correlation analysis (CCA). While the former seeks multivariate linear relationships between a given phenotype and associated observations, the latter searches to extract co-expression patterns between sets of variables belonging to different modalities. In the following, we propose to rely on a "CCA-type" formulation in order to regularize the classical multimodal sparse regression problem (essentially incorporating both CCA and regression models within a unified formulation). The underlying motivation is to extract discriminative variables that are also co-expressed across modalities. We first show that the simplest formulation of such model can be expressed as a special case of collaborative learning methods. After discussing its limitation, we propose an extended, more flexible formulation, and introduce a simple and efficient alternating minimization algorithm to solve the associated optimization problem. We explore the parameter space and provide some guidelines regarding parameter selection. Both the original and extended versions are then compared on a simple toy data set and a more advanced simulated imaging genomics data set in order to illustrate the benefits of the latter. Finally, we validate the proposed formulation using single nucleotide polymorphisms data and functional magnetic resonance imaging data from a population of adolescents ( subjects, age 16.9 ± 1.9 years from the Philadelphia Neurodevelopmental Cohort) for the study of learning ability. Furthermore, we carry out a significance analysis of the resulting features that allow us to carefully extract brain regions and genes linked to learning and cognitive ability.

Functional magnetic resonance imaging (fMRI) is a powerful tool to analyze brain development and neuronal activity. Identifying discriminative brain regions between various groups within a population has generated great interest in recent years. In this work, we consider the problem of estimating multiple sparse, co-activated brain regions from fMRI observations belonging to different classes. More precisely, we propose a method to analyze functional connectivity differences between children and young adults. Often, analysis is conducted on each class separately. Here, we propose to rely on a generalized fused Lasso penalty to extract both class-specific and shared co-expressed regions. In order to validate our method, experiments are performed on an fMRI dataset comprised of normally developing children from 8 to 21. The results demonstrate that the proposed method is able to properly extract meaningful sub-networks, which results in improved classification accuracy between the two classes.

In this paper, an original observation model for multiresolution optical flow estimation is introduced. Multiresolution frameworks, often based on coarse-to-fine warping strategies, are widely used by state-of-the-art optical flow methods. They allow the recovery of large motions by successive estimations of the flow field at several resolution levels. Although such approaches perform very efficiently and usually lead to faster minimizations, they generally consider independent problems at each resolution levels and do not exploit the existing interactions between scales (especially the influences of fine scales on larger ones). In this paper, we tackle this issue by proposing a flexible framework, inspired from fluid mechanics, able to partly counter these limitations. For each resolution level, our process filters the equations of interest and decomposes the key variables into resolved (i.e., at a given resolution) and unresolved (i.e., at finer resolutions) components. This enables to derive a new data term that takes into account, at coarse resolutions, the influence of their unresolved parts. From this new term, we propose two different estimation strategies, depending on whether we explicitly know the type of relations between the different scales (as for physical processes) or not. In order to test the efficiency of this new observation model, we have embedded it in a simple multiresolution Lucas-Kanade estimator. Comparing the usual optical flow constraint equation with this new term in the same motion estimation procedure, it clearly appears that the proposed term leads to more consistent estimates and prevents from errors propagation apparition during the estimation. In all situations (synthetic, real, physical images or not), our new term is able to greatly improve the results compared with usual conservation constraints.

Multi-scale frameworks based on coarse-to-fine warping strategies are widely used in the state-of-the-art optical flow methods. While they allow the estimation of large motions and usually lead to a faster minimization, they can also create strong dependencies between the successive estimates at different scale levels, yielding sometimes the propagation of undesirable errors from coarse to fine scales without any mean of correction. In this paper, we propose a more flexible framework inspired from fluid mechanics able to partly counter this issue. It relies on filtering equations where the variable of interest (i.e. the velocity field) is decomposed into resolved and unresolved components at each scale. We then derive a new data term that allows to take into account, in the coarse scales, information about smaller scale levels in order to avoid errors propagation during the estimation. Embedded in a simple Lucas-Kanade estimator, our new term is able to greatly improve the results from usual conservation constraints, as shown in the experimental part.