Using non-negative matrix factorization for single-trial analysis of fMRI data

Ontological Dimensions of Cognitive-Neural Mappings

The growing literature reporting results of cognitive-neural mappings has increased calls for an adequate organizing ontology, or taxonomy, of these mappings. This enterprise is non-trivial, as relevant dimensions that might contribute to such an ontology are not yet agreed upon. We propose that any candidate dimensions should be evaluated on their ability to explain observed differences in functional neuroimaging activation patterns. In this study, we use a large sample of task-based functional magnetic resonance imaging (task-fMRI) results and a data-driven strategy to identify these dimensions. First, using a data-driven dimension reduction approach and multivariate distance matrix regression (MDMR), we quantify the variance among activation maps that is explained by existing ontological dimensions. We find that 'task paradigm' categories explain more variance among task-activation maps than other dimensions, including latent cognitive categories. Surprisingly, 'study ID', or the study from which each activation map was reported, explained close to 50% of the variance in activation patterns. Using a clustering approach that allows for overlapping clusters, we derived data-driven latent activation states, associated with re-occurring configurations of the canonical frontoparietal, salience, sensory-motor, and default mode network activation patterns. Importantly, with only four data-driven latent dimensions, one can explain greater variance among activation maps than all conventional ontological dimensions combined. These latent dimensions may inform a data-driven cognitive ontology, and suggest that current descriptions of cognitive processes and the tasks used to elicit them do not accurately reflect activation patterns commonly observed in the human brain.

A GICA-TVGL framework to study sex differences in resting state fMRI dynamic connectivity

BACKGROUND

Functional magnetic resonance imaging (fMRI) has been implemented widely to study brain connectivity. In particular, time-varying connectivity analysis has emerged as an important measure to uncover essential knowledge within the network. On the other hand, independent component analysis (ICA) has served as a powerful tool to preprocess fMRI data before performing network analysis. Together, they may lead to novel findings.

METHODS

We propose a new framework (GICA-TVGL) that combines group ICA (GICA) with time-varying graphical LASSO (TVGL) to improve the power of analyzing functional connectivity (FNC) changes, which is then applied for neuro-developmental study. To investigate the performance of our proposed approach, we apply it to capture dynamic FNC using both the Philadelphia Neurodevelopmental Cohort (PNC) and the Pediatric Imaging, Neurocognition, and Genetics (PING) datasets.

RESULTS

Our results indicate that females and males in young adult group possess substantial difference related to visual network. In addition, some other consistent conclusions have been reached by using these two datasets. Furthermore, the GICA-TVGL model indicated that females had a higher probability to stay in a stable state. Males had a higher tendency to remain in a globally disconnected mode.

COMPARISON WITH EXISTING METHOD

The performance of sliding window approach is largely affected by the window size selection. In addition, it also assumes temporal locality hypothesis.

CONCLUSION

Our proposed framework provides a feasible method to investigate brain dynamics and has the potential to become a widely used tool in neuroimaging studies.

N-BiC: A Method for Multi-Component and Symptom Biclustering of Structural MRI Data: Application to Schizophrenia

OBJECTIVE

We propose and develop a novel biclustering (N-BiC) approach for performing N-way biclustering of neuroimaging data. Our approach is applicable to an arbitrary number of features from both imaging and behavioral data (e.g., symptoms). We applied it to structural MRI data from patients with schizophrenia.

METHODS

It uses a source-based morphometry approach [i.e., independent component analysis of gray matter segmentation maps] to decompose the data into a set of spatial maps, each of which includes regions that covary among individuals. Then, the loading parameters for components of interest are entered to an exhaustive search, which incorporates a modified depth-first search technique to carry out the biclustering, with the goal of obtaining submatrices where the selected rows (individuals) show homogeneity in their expressions of selected columns (components) and vice versa.

RESULTS

Findings demonstrate that multiple biclusters have an evident association with distinct brain networks for the different types of symptoms in schizophrenia. The study identifies two components: inferior temporal gyrus (16) and brainstem (7), which are related to positive (distortion/excess of normal function) and negative (diminution/loss of normal function) symptoms in schizophrenia, respectively.

CONCLUSION

N-BiC is a data-driven method of biclustering MRI data that can exhaustively explore relationships/substructures from a dataset without any prior information with a higher degree of robustness than earlier biclustering applications.

SIGNIFICANCE

The use of such approaches is important to investigate the underlying biological substrates of mental illness by grouping patients into homogeneous subjects, as the schizophrenia diagnosis is known to be relatively nonspecific and heterogeneous.

A method to compare the discriminatory power of data-driven methods: Application to ICA and IVA

BACKGROUND

The widespread application of data-driven factorization-based methods, such as independent component analysis (ICA), to functional magnetic resonance imaging data facilitates the study of neural function and how it is disrupted by psychiatric disorders such as schizophrenia. While the increasing number of these methods motivates a comparison of their relative performance, such a comparison is difficult to perform on real fMRI data, since the ground truth is, relatively, unknown and the alignment of factors across different methods is impractical and imprecise.

NEW METHOD

We present a novel method, global difference maps (GDMs), to compare the results of different fMRI analysis techniques on real fMRI data, quantify their relative performances, and highlight the differences between the decompositions visually.

COMPARISON WITH EXISTING METHODS

We apply this method to compare the performances of two different factorization-based methods, ICA and its multiset extension independent vector analysis (IVA), for the analysis of fMRI data from 109 patients with schizophrenia and 138 healthy controls during the performance of three tasks.

RESULTS

Through this application of GDMs, we find that IVA can determine regions that are more discriminatory between patients and controls than ICA, though IVA is less effective at emphasizing regions found in only a subset of the tasks.

CONCLUSIONS

These results demonstrate that GDMs are an effective way to compare the performances of different factorization-based methods as well as regression-based analyses.

Microbiome Data Representation by Joint Nonnegative Matrix Factorization with Laplacian Regularization

Microbiome datasets are often comprised of different representations or views which provide complementary information to understand microbial communities, such as metabolic pathways, taxonomic assignments, and gene families. Data integration methods including approaches based on nonnegative matrix factorization (NMF) combine multi-view data to create a comprehensive view of a given microbiome study by integrating multi-view information. In this paper, we proposed a novel variant of NMF which called Laplacian regularized joint non-negative matrix factorization (LJ-NMF) for integrating functional and phylogenetic profiles from HMP. We compare the performance of this method to other variants of NMF. The experimental results indicate that the proposed method offers an efficient framework for microbiome data analysis.

Local dimension-reduced dynamical spatio-temporal models for resting state network estimation

To overcome the limitations of independent component analysis (ICA), today’s most popular analysis tool for investigating whole-brain spatial activation in resting state functional magnetic resonance imaging (fMRI), we present a new class of local dimension-reduced dynamical spatio-temporal model which dispenses the independence assumptions that severely limit deeper connectivity descriptions between spatial components. The new method combines novel concepts of group sparsity with contiguity-constrained clusterization to produce physiologically consistent regions of interest in illustrative fMRI data whose causal interactions may then be easily estimated, something impossible under the usual ICA assumptions.

Functional connectivity changes during a working memory task in rat via NMF analysis

Working memory (WM) is necessary in higher cognition. The brain as a complex network is formed by interconnections among neurons. Connectivity results in neural dynamics to support cognition. The first aim is to investigate connectivity dynamics in medial prefrontal cortex (mPFC) networks during WM. As brain neural activity is sparse, the second aim is to find the intrinsic connectivity property in a feature space. Using multi-channel electrode recording techniques, spikes were simultaneously obtained from mPFC of rats that performed a Y-maze WM task. Continuous time series converted from spikes were embedded in a low-dimensional space by non-negative matrix factorization (NMF). mPFC network in original space was constructed by measuring connections among neurons. And the same network in NMF space was constructed by computing connectivity values between the extracted NMF components. Causal density (Cd) and global efficiency (E) were estimated to present the network property. The results showed that Cd and E significantly peaked in the interval right before the maze choice point in correct trials. However, the increase did not emerge in error trials. Additionally, Cd and E in two spaces displayed similar trends in correct trials. The difference was that the measures in NMF space were significantly greater than those in original space. Our findings indicated that the anticipatory changes in mPFC networks may have an effect on future WM behavioral choices. Moreover, the NMF analysis achieves a better characterization for a brain network.

Local sparse component analysis for blind source separation: an application to resting state FMRI

We propose a new Blind Source Separation technique for whole-brain activity estimation that best profits from FMRI's intrinsic spatial sparsity. The Local Sparse Component Analysis (LSCA) combines wavelet analysis, group-separable regularizers, contiguity-constrained clusterization and principal components analysis (PCA) into a unique spatial sparse representation of FMRI images towards efficient dimensionality reduction without sacrificing physiological characteristics by avoiding artificial stochastic model constraints. The LSCA outperforms classical PCA source reconstruction for artificial data sets over many noise levels. A real FMRI data illustration reveals resting-state activities in regions hard to observe, such as thalamus and basal ganglia, because of their small spatial scale.

A review of feature reduction techniques in neuroimaging

Machine learning techniques are increasingly being used in making relevant predictions and inferences on individual subjects neuroimaging scan data. Previous studies have mostly focused on categorical discrimination of patients and matched healthy controls and more recently, on prediction of individual continuous variables such as clinical scores or age. However, these studies are greatly hampered by the large number of predictor variables (voxels) and low observations (subjects) also known as the curse-of-dimensionality or small-n-large-p problem. As a result, feature reduction techniques such as feature subset selection and dimensionality reduction are used to remove redundant predictor variables and experimental noise, a process which mitigates the curse-of-dimensionality and small-n-large-p effects. Feature reduction is an essential step before training a machine learning model to avoid overfitting and therefore improving model prediction accuracy and generalization ability. In this review, we discuss feature reduction techniques used with machine learning in neuroimaging studies.

Resting state functional magnetic resonance imaging reveals distinct brain activity in heavy cannabis users - a multi-voxel pattern analysis

Chronic cannabis use can cause cognitive, perceptual and personality alterations, which are believed to be associated with regional brain changes and possible changes in connectivity between functional regions. This study aims to identify the changes from resting state functional magnetic resonance imaging scans. A two-level multi-voxel pattern analysis was proposed to classify male cannabis users from normal controls. The first level analysis works on a voxel basis and identifies clusters for the input of a second level analysis, which works on the functional connectivity between these regions. We found distinct clusters for male cannabis users in the middle frontal gyrus, precentral gyrus, superior frontal gyrus, posterior cingulate cortex, cerebellum and some other regions. Based on the functional connectivity of these clusters, a high overall accuracy rate of 84-88% in classification accuracy was achieved. High correlations were also found between the overall classification accuracy and Barrett Barrett Impulsiveness Scale factor scores of attention and motor. Our result suggests regional differences in the brains of male cannabis users that span from the cerebellum to the prefrontal cortex, which are associated with differences in functional connectivity.

Constructing endophenotypes of complex diseases using non-negative matrix factorization and adjusted rand index

Complex diseases are typically caused by combinations of molecular disturbances that vary widely among different patients. Endophenotypes, a combination of genetic factors associated with a disease, offer a simplified approach to dissect complex trait by reducing genetic heterogeneity. Because molecular dissimilarities often exist between patients with indistinguishable disease symptoms, these unique molecular features may reflect pathogenic heterogeneity. To detect molecular dissimilarities among patients and reduce the complexity of high-dimension data, we have explored an endophenotype-identification analytical procedure that combines non-negative matrix factorization (NMF) and adjusted rand index (ARI), a measure of the similarity of two clusterings of a data set. To evaluate this procedure, we compared it with a commonly used method, principal component analysis with k-means clustering (PCA-K). A simulation study with gene expression dataset and genotype information was conducted to examine the performance of our procedure and PCA-K. The results showed that NMF mostly outperformed PCA-K. Additionally, we applied our endophenotype-identification analytical procedure to a publicly available dataset containing data derived from patients with late-onset Alzheimer's disease (LOAD). NMF distilled information associated with 1,116 transcripts into three metagenes and three molecular subtypes (MS) for patients in the LOAD dataset: MS1 (n1=80), MS2 (n2=73), and MS3 (n3=23). ARI was then used to determine the most representative transcripts for each metagene; 123, 89, and 71 metagene-specific transcripts were identified for MS1, MS2, and MS3, respectively. These metagene-specific transcripts were identified as the endophenotypes. Our results showed that 14, 38, 0, and 28 candidate susceptibility genes listed in AlzGene database were found by all patients, MS1, MS2, and MS3, respectively. Moreover, we found that MS2 might be a normal-like subtype. Our proposed procedure provides an alternative approach to investigate the pathogenic mechanism of disease and better understand the relationship between phenotype and genotype.

Correlated Noise: How it Breaks NMF, and What to Do About It

Non-negative matrix factorization (NMF) is a problem of decomposing multivariate data into a set of features and their corresponding activations. When applied to experimental data, NMF has to cope with noise, which is often highly correlated. We show that correlated noise can break the Donoho and Stodden separability conditions of a dataset and a regular NMF algorithm will fail to decompose it, even when given freedom to be able to represent the noise as a separate feature. To cope with this issue, we present an algorithm for NMF with a generalized least squares objective function (glsNMF) and derive multiplicative updates for the method together with proving their convergence. The new algorithm successfully recovers the true representation from the noisy data. Robust performance can make glsNMF a valuable tool for analyzing empirical data.

A new spatially constrained NMF with application to fMRI

In this paper the problem of BOLD detection is addressed. The focus here is on non-negative matrix factorization (NMF), which is a data driven method and able to provide part-based representation of data. A new constrained optimization problem is proposed for the purpose of BOLD detection. The proposed constraint imposes some prior spatial information of active area inside the brain, on the decomposition process. The constraint is built up based on the type of stimulus and available physiological knowledge of the brain performance. The simulation results on both synthetic and real fMRI data show that applying the proposed constraint improves the BOLD detection performance.

bioNMF: a web-based tool for nonnegative matrix factorization in biology

In the last few years, advances in high-throughput technologies are generating large amounts of biological data that require analysis and interpretation. Nonnegative matrix factorization (NMF) has been established as a very effective method to reveal information about the complex latent relationships in experimental data sets. Using this method as part of the exploratory data analysis, workflow would certainly help in the process of interpreting and understanding the complex biology mechanisms that are underlying experimental data. We have developed bioNMF, a web-based tool that implements the NMF methodology in different analysis contexts to support some of the most important reported applications in biology. This online tool provides a user-friendly interface, combined with a computational efficient parallel implementation of the NMF methods to explore the data in different analysis scenarios. In addition to the online access, bioNMF also provides the same functionality included in the website as a public web services interface, enabling users with more computer expertise to launch jobs into bioNMF server from their own scripts and workflows. bioNMF application is freely available at http://bionmf.dacya.ucm.es.