Decoding the encoding of functional brain networks: An fMRI classification comparison of non-negative matrix factorization (NMF), independent component analysis (ICA), and sparse coding algorithms

Effects of transcranial direct current stimulation on brain activity and cortical functional connectivity in children with autism spectrum disorders

Introduction

Transcranial direct current stimulation (tDCS) has emerged as a therapeutic option to mitigate symptoms in individuals with autism spectrum disorder (ASD). Our study investigated the effects of a two-week regimen of tDCS targeting the left dorsolateral prefrontal cortex (DLPFC) in children with ASD, examining changes in rhythmic brain activity and alterations in functional connectivity within key neural networks: the default mode network (DMN), sensorimotor network (SMN), and dorsal attention network (DAN).

Methods

We enrolled twenty-six children with ASD and assigned them randomly to either an active stimulation group (n=13) or a sham stimulation group (n=13). The active group received tDCS at an intensity of 1mA to the left DLPFC for a combined duration of 10 days. Differences in electrical brain activity were pinpointed using standardized low-resolution brain electromagnetic tomography (sLORETA), while functional connectivity was assessed via lagged phase synchronization.

Results

Compared to the typically developing children, children with ASD exhibited lower current source density across all frequency bands. Post-treatment, the active stimulation group demonstrated a significant increase in both current source density and resting state network connectivity. Such changes were not observed in the sham stimulation group.

Conclusion

tDCS targeting the DLPFC may bolster brain functional connectivity in patients with ASD, offering a substantive groundwork for potential clinical applications.

Performance Evaluation of Matrix Factorization for fMRI Data

A hypothesis in the study of the brain is that sparse coding is realized in information representation of external stimuli, which has been experimentally confirmed for visual stimulus recently. However, unlike the specific functional region in the brain, sparse coding in information processing in the whole brain has not been clarified sufficiently. In this study, we investigate the validity of sparse coding in the whole human brain by applying various matrix factorization methods to functional magnetic resonance imaging data of neural activities in the brain. The result suggests the sparse coding hypothesis in information representation in the whole human brain, because extracted features from the sparse matrix factorization (MF) method, sparse principal component analysis (SparsePCA), or method of optimal directions (MOD) under a high sparsity setting or an approximate sparse MF method, fast independent component analysis (FastICA), can classify external visual stimuli more accurately than the nonsparse MF method or sparse MF method under a low sparsity setting.

EEG Connectivity Diversity Differences between Children with Autism and Typically Developing Children: A Comparative Study

Autism spectrum disorder (ASD) is a neurodevelopmental disorder characterized by deficits in social interaction and communication, and repetitive or stereotyped behaviors. Previous studies have reported altered brain connectivity in ASD children compared to typically developing children. In this study, we investigated the diversity of connectivity patterns between children with ASD and typically developing children using phase lag entropy (PLE), a measure of the variability of phase differences between two time series. We also developed a novel wavelet-based PLE method for the calculation of PLE at specific scales. Our findings indicated that the diversity of connectivity in ASD children was higher than that in typically developing children at Delta and Alpha frequency bands, both within brain regions and across hemispheric brain regions. These findings provide insight into the underlying neural mechanisms of ASD and suggest that PLE may be a useful tool for investigating brain connectivity in ASD.

Constrained CPD of Complex-Valued Multi-Subject fMRI Data via Alternating Rank-R and Rank-1 Least Squares

Complex-valued shift-invariant canonical polyadic decomposition (CPD) under a spatial phase sparsity constraint (pcsCPD) shows excellent separation performance when applied to band-pass filtered complex-valued multi-subject fMRI data. However, some useful information may also be eliminated when using a band-pass filter to suppress unwanted noise. As such, we propose an alternating rank- R and rank-1 least squares optimization to relax the CPD model. Based upon this optimization method, we present a novel constrained CPD algorithm with temporal shift-invariance and spatial sparsity and orthonormality constraints. More specifically, four steps are conducted until convergence for each iteration of the proposed algorithm: 1) use rank- R least-squares fit under spatial phase sparsity constraint to update shared spatial maps after phase de-ambiguity; 2) use orthonormality constraint to minimize the cross-talk between shared spatial maps; 3) update the aggregating mixing matrix using rank- R least-squares fit; 4) utilize shift-invariant rank-1 least-squares on a series of rank-1 matrices reconstructed by each column of the aggregating mixing matrix to update shared time courses, and subject-specific time delays and intensities. The experimental results of simulated and actual complex-valued fMRI data show that the proposed algorithm improves the estimates for task-related sensorimotor and auditory networks, compared to pcsCPD and tensorial spatial ICA. The proposed alternating rank- R and rank-1 least squares optimization is also flexible to improve CPD-related algorithm using alternating least squares.

Brain disorder prediction with dynamic multivariate spatio-temporal features: Application to Alzheimer’s disease and autism spectrum disorder

The dynamic functional connectivity (dFC) in functional magnetic resonance imaging (fMRI) is beneficial for the analysis and diagnosis of neurological brain diseases. The dFCs between regions of interest (ROIs) are generally delineated by a specific template and clustered into multiple different states. However, these models inevitably fell into the model-driven self-contained system which ignored the diversity at spatial level and the dynamics at time level of the data. In this study, we proposed a spatial and time domain feature extraction approach for Alzheimer’s disease (AD) and autism spectrum disorder (ASD)-assisted diagnosis which exploited the dynamic connectivity among independent functional sub networks in brain. Briefly, independent sub networks were obtained by applying spatial independent component analysis (SICA) to the preprocessed fMRI data. Then, a sliding window approach was used to segment the time series of the spatial components. After that, the functional connections within the window were obtained sequentially. Finally, a temporal signal-sensitive long short-term memory (LSTM) network was used for classification. The experimental results on Alzheimer’s Disease Neuroimaging Initiative (ADNI) and Autism Brain Imaging Data Exchange (ABIDE) datasets showed that the proposed method effectively predicted the disease at the early stage and outperformed the existing algorithms. The dFCs between the different components of the brain could be used as biomarkers for the diagnosis of diseases such as AD and ASD, providing a reliable basis for the study of brain connectomics.

Morphological Component Analysis of functional MRI Brain Networks

OBJECTIVE

Sparse representations have been utilized to identify functional connectivity (FC) of networks, while ICA employs the assumption of independence among the network sources to demonstrate FC. Here, we investigate a sparse decomposition method based on Morphological Component Analysis and K-SVD dictionary learning-MCA-KSVD-and contrast the effect of the sparsity constraint vs. the independency constraint on FC and denoising.

METHODS

Using a K-SVD algorithm, fMRI signals are decomposed into morphological components which have sparse spatial overlap. We present simulations when the independency assumption of ICA fails and MCA-KSVD recovers more accurate spatial-temporal structures. Denoising performance of both methods is investigated at various noise levels. A comprehensive experimental study was conducted on resting-state and task fMRI.

RESULTS

Validations show that ICA is advantageous when network components are well-separated and sparse. In such cases, the MCA-KSVD method has modest value over ICA in terms of network delineation but is significantly more effective in reducing spatial and temporal noise. Results demonstrate that the sparsity constraint yields sparser networks with higher spatial resolution while suppressing weak signals. Temporally, this localization effect yields higher contrast-to-noise ratios (CNRs) of time series.

CONCLUSION

While marginally improving the spatial decomposition, MCA-KSVD denoises fMRI data much more effectively than ICA, preserving network structures and improving CNR, especially for weak networks.

SIGNIFICANCE

A sparsity-based decomposition approach may be useful for investigating functional connectivity in noisy cases. It may serve as an efficient decomposition method for reduced acquisition time and may prove useful for detecting weak network activations.

Co-sparse Non-negative Matrix Factorization

Non-negative matrix factorization, which decomposes the input non-negative matrix into product of two non-negative matrices, has been widely used in the neuroimaging field due to its flexible interpretability with non-negativity property. Nowadays, especially in the neuroimaging field, it is common to have at least thousands of voxels while the sample size is only hundreds. The non-negative matrix factorization encounters both computational and theoretical challenge with such high-dimensional data, i.e., there is no guarantee for a sparse and part-based representation of data. To this end, we introduce a co-sparse non-negative matrix factorization method to high-dimensional data by simultaneously imposing sparsity in both two decomposed matrices. Instead of adding some sparsity induced penalty such as l ₁ norm, the proposed method directly controls the number of non-zero elements, which can avoid the bias issues and thus yield more accurate results. We developed an alternative primal-dual active set algorithm to derive the co-sparse estimator in a computationally efficient way. The simulation studies showed that our method achieved better performance than the state-of-art methods in detecting the basis matrix and recovering signals, especially under the high-dimensional scenario. In empirical experiments with two neuroimaging data, the proposed method successfully detected difference between Alzheimer's patients and normal person in several brain regions, which suggests that our method may be a valuable toolbox for neuroimaging studies.

Enhanced design matrix for task-related fMRI data analysis

In this paper, we introduce a novel methodology for the analysis of task-related fMRI data. In particular, we propose an alternative way for constructing the design matrix, based on the newly suggested Information-Assisted Dictionary Learning (IADL) method. This technique offers an enhanced potential, within the conventional GLM framework, (a) to efficiently cope with uncertainties in the modeling of the hemodynamic response function, (b) to accommodate unmodeled brain-induced sources, beyond the task-related ones, as well as potential interfering scanner-induced artifacts, uncorrected head-motion residuals and other unmodeled physiological signals, and (c) to integrate external knowledge regarding the natural sparsity of the brain activity that is associated with both the experimental design and brain atlases. The capabilities of the proposed methodology are evaluated via a realistic synthetic fMRI-like dataset, and demonstrated using a test case of a challenging fMRI study, which verifies that the proposed approach produces substantially more consistent results compared to the standard design matrix method. A toolbox extension for SPM is also provided, to facilitate the use and reproducibility of the proposed methodology.

Graph auto-encoding brain networks with applications to analyzing large-scale brain imaging datasets

There has been a huge interest in studying human brain connectomes inferred from different imaging modalities and exploring their relationships with human traits, such as cognition. Brain connectomes are usually represented as networks, with nodes corresponding to different regions of interest (ROIs) and edges to connection strengths between ROIs. Due to the high-dimensionality and non-Euclidean nature of networks, it is challenging to depict their population distribution and relate them to human traits. Current approaches focus on summarizing the network using either pre-specified topological features or principal components analysis (PCA). In this paper, building on recent advances in deep learning, we develop a nonlinear latent factor model to characterize the population distribution of brain graphs and infer their relationships to human traits. We refer to our method as Graph AuTo-Encoding (GATE). We applied GATE to two large-scale brain imaging datasets, the Adolescent Brain Cognitive Development (ABCD) study and the Human Connectome Project (HCP) for adults, to study the structural brain connectome and its relationship with cognition. Numerical results demonstrate huge advantages of GATE over competitors in terms of prediction accuracy, statistical inference, and computing efficiency. We found that the structural connectome has a stronger association with a wide range of human cognitive traits than was apparent using previous approaches.

Identification of Methamphetamine Abstainers by Resting-State Functional Magnetic Resonance Imaging

Methamphetamine (MA) can cause brain structural and functional impairment, but there are few studies on whether this difference will sustain on MA abstainers. The purpose of this study is to investigate the correlation of brain networks in MA abstainers. In this study, 47 people detoxified for at least 14 months and 44 normal people took a resting-state functional magnetic resonance imaging (RS-fMRI) scan. A dynamic (i.e., time-varying) functional connectivity (FC) is obtained by applying sliding windows in the time courses on the independent components (ICs). The windowed correlation data for each IC were then clustered by k-means. The number of subjects in each cluster was used as a new feature for individual identification. The results show that the classifier achieved satisfactory performance (82.3% accuracy, 77.7% specificity, and 85.7% sensitivity). We find that there are significant differences in the brain networks of MA abstainers and normal people in the time domain, but the spatial differences are not obvious. Most of the altered functional connections (time-varying) are identified to be located at dorsal default mode network. These results have shown that changes in the correlation of the time domain may play an important role in identifying MA abstainers. Therefore, our findings provide valuable insights in the identification of MA and elucidate the pathological mechanism of MA from a resting-state functional integration point of view.

A generative-discriminative framework that integrates imaging, genetic, and diagnosis into coupled low dimensional space

We propose a novel optimization framework that integrates imaging and genetics data for simultaneous biomarker identification and disease classification. The generative component of our model uses a dictionary learning framework to project the imaging and genetic data into a shared low dimensional space. We have coupled both the data modalities by tying the linear projection coefficients to the same latent space. The discriminative component of our model uses logistic regression on the projection vectors for disease diagnosis. This prediction task implicitly guides our framework to find interpretable biomarkers that are substantially different between a healthy and disease population. We exploit the interconnectedness of different brain regions by incorporating a graph regularization penalty into the joint objective function. We also use a group sparsity penalty to find a representative set of genetic basis vectors that span a low dimensional space where subjects are easily separable between patients and controls. We have evaluated our model on a population study of schizophrenia that includes two task fMRI paradigms and single nucleotide polymorphism (SNP) data. Using ten-fold cross validation, we compare our generative-discriminative framework with canonical correlation analysis (CCA) of imaging and genetics data, parallel independent component analysis (pICA) of imaging and genetics data, random forest (RF) classification, and a linear support vector machine (SVM). We also quantify the reproducibility of the imaging and genetics biomarkers via subsampling. Our framework achieves higher class prediction accuracy and identifies robust biomarkers. Moreover, the implicated brain regions and genetic variants underlie the well documented deficits in schizophrenia.

An Overview of ICA/BSS-Based Application to Alzheimer's Brain Signal Processing

Alzheimer's disease (AD) is by far the most common cause of dementia associated with aging. Early and accurate diagnosis of AD and ability to track progression of the disease is increasingly important as potential disease-modifying therapies move through clinical trials. With the advent of biomedical techniques, such as computerized tomography (CT), electroencephalography (EEG), magnetoencephalography (MEG), positron emission tomography (PET), magnetic resonance imaging (MRI), and functional magnetic resonance imaging (fMRI), large amounts of data from Alzheimer's patients have been acquired and processed from which AD-related information or "signals" can be assessed for AD diagnosis. It remains unknown how best to mine complex information from these brain signals to aid in early diagnosis of AD. An increasingly popular technique for processing brain signals is independent component analysis or blind source separation (ICA/BSS) that separates blindly observed signals into original signals that are as independent as possible. This overview focuses on ICA/BSS-based applications to AD brain signal processing.

Sparse representation of complex-valued fMRI data based on spatiotemporal concatenation of real and imaginary parts

BACKGROUND

Spatial sparsity has been found to be in line with the intrinsic characteristic of brain activation. However, identifying a sparse representation of complex-valued fMRI data is challenging due to high noise within the phase data.

NEW METHODS

We propose to reduce the noise by combining real and imaginary parts of complex-valued fMRI data along spatial and temporal dimensions to form a real-valued spatiotemporal concatenation model. This model not only enables flexible usage of existing real-valued sparse representation algorithms but also allows for the reconstruction of complex-valued spatial and temporal components from their real and imaginary estimates. We propose to select components from both real and imaginary estimates to reconstruct the complex-valued component, using phase denoising to recover weak brain activity from high-amplitude noise.

RESULTS

The K-SVD algorithm was used to obtain a sparse representation within the spatiotemporal concatenation model. The results from simulated and experimental complex-valued fMRI datasets validated the efficacy of our method.

COMPARISON WITH EXISTING METHODS

Compared to a magnitude-only approach, the proposed method detected additional voxels manifest within several specific regions expected to be involved but likely missing from the magnitude-only data, e.g., in the anterior cingulate cortex region. Simulation results showed that the additional voxels were accurate and unique information from the phase data. Compared to a complex-valued dictionary learning algorithm, our method exhibited lower noise for both magnitude and phase maps.

CONCLUSIONS

The proposed method is robust to noise and effective for identifying a sparse representation of the natively complex-valued fMRI data.

Independent component analysis: An introduction

Independent component analysis (ICA) is a widely-used blind source separation technique. ICA has been applied to many applications. ICA is usually utilized as a black box, without understanding its internal details. Therefore, in this paper, the basics of ICA are provided to show how it works to serve as a comprehensive source for researchers who are interested in this field. This paper starts by introducing the definition and underlying principles of ICA. Additionally, different numerical examples in a step-by-step approach are demonstrated to explain the preprocessing steps of ICA and the mixing and unmixing processes in ICA. Moreover, different ICA algorithms, challenges, and applications are presented.

Effects of using different software packages for BOLD analysis in planning a neurosurgical treatment in patients with brain tumours

BACKGROUND

The authors of the present thesis carried out a comparative analysis of three different computer software packages - FSL, SPM and FuncTool - for the processing of fMRI scans.

PURPOSE

The aim of the thesis was the analysis of the volume of regions functionally active during the stimulation of the centres evaluated as well as the location of those regions in relation to the tumour boundaries, and then the comparison of the results.

MATERIAL AND METHODS

Thirty eight patients with a diagnosed tumour of the left hemisphere, qualified for a neurosurgical operation, underwent fMRI. The functions of speech, motion and sensation were evaluated. Imaging data were processed for all the acquired scans with the use of each of the three software packages assessed.

RESULTS

For the FuncTool software package the calculated differences in the distances were several times greater than those calculated using FSL and SPM. The differences in the volume of the functionally active regions derived from the calculations with the use of the FSL and SPM software packages were statistically different for four out of the six functions evaluated.

CONCLUSIONS

The conclusions of the analysis in question showed that the FSL and SPM packages could be used interchangeably in the functional mapping of the brain with the purpose of the planning of neurosurgical operations. The FuncTool software package is less precise than FSL and SPM.

Shift-Invariant Canonical Polyadic Decomposition of Complex-Valued Multi-Subject fMRI Data With a Phase Sparsity Constraint

Canonical polyadic decomposition (CPD) of multi-subject complex-valued fMRI data can be used to provide spatially and temporally shared components among groups with both magnitude and phase information. However, the CPD model is not well formulated due to the large subject variability in the spatial and temporal modalities, as well as the high noise level in complex-valued fMRI data. Considering that the shift-invariant CPD can model temporal variability across subjects, we propose to further impose a phase sparsity constraint on the shared spatial maps to denoise the complex-valued components and to model the inter-subject spatial variability as well. More precisely, subject-specific time delays are first estimated for the complex-valued shared time courses in the framework of real-valued shift-invariant CPD. Source phase sparsity is then imposed on the complex-valued shared spatial maps. A smoothed l₀ norm is specifically used to reduce voxels with large phase values after phase de-ambiguity based on the small phase characteristic of BOLD-related voxels. The results from both the simulated and experimental fMRI data demonstrate improvements of the proposed method over three complex-valued algorithms, namely, tensor-based spatial ICA, shift-invariant CPD and CPD without spatiotemporal constraints. When comparing with a real-valued algorithm combining shift-invariant CPD and ICA, the proposed method detects 178.7% more contiguous task-related activations.

Altered Functional Connectivity in Children With Low-Function Autism Spectrum Disorders

Neuroimaging studies have shown that autism spectrum disorders (ASDs) may be associated with abnormalities in brain structures and functions at rest as well as during cognitive tasks. However, it remains unclear if functional connectivity (FC) of all brain neural networks is also changed in these subjects. In this study, we acquired functional magnetic resonance imaging scans from 93 children with ASD and 79 matched healthy subjects. Group independent component analysis was executed for all of the participants to estimate FC. One-sample t-tests were then performed to obtain the networks for each group. Group differences in the different brain networks were tested using two-sample t-tests. Finally, relationships between abnormal FC and clinical variables were investigated with Pearson’s correlation analysis. The results from one-sample t-tests revealed nine networks with similar spatial patterns in these two groups. When compared with the controls, children with ASD showed increased connectivity in the right dorsolateral superior frontal gyrus and left middle frontal gyrus (MFG) within the occipital pole network. Children with ASD also showed decreased connectivity in the left gyrus rectus, left middle occipital gyrus, right angular gyrus, right MFG and right inferior frontal gyrus (IFG), orbital part within the lateral visual network (LVN), the left IFG, right precuneus, and right angular gyrus within the left frontoparietal (cognition) network. Furthermore, the mean FC values within the LVN showed significant positive correlations with total score of the Childhood Autism Rating Scale. Our findings indicate that abnormal FC extensively exists within some networks in children with ASD. This abnormal FC may constitute a biomarker of ASD. Our results are an important contribution to the study of neuropathophysiological mechanisms in children with ASD.

A Novel Signal Separation Method Based on Improved Sparse Non-Negative Matrix Factorization

In order to separate and extract compound fault features of a vibration signal from a single channel, a novel signal separation method is proposed based on improved sparse non-negative matrix factorization (SNMF). In view of the traditional SNMF failure to perform well in the underdetermined blind source separation, a constraint reference vector is introduced in the SNMF algorithm, which can be generated by the pulse method. The square wave sequences are constructed as the constraint reference vector. The output separated signal is constrained by the vector, and the vector will update according to the feedback of the separated signal. The redundancy of the mixture signal will be reduced during the constantly updating of the vector. The time-frequency distribution is firstly applied to capture the local fault features of the vibration signal. Then the high dimension feature matrix of time-frequency distribution is factorized to select local fault features with the improved SNMF method. Meanwhile, the compound fault features can be separated and extracted automatically by using the sparse property of the improved SNMF method. Finally, envelope analysis is used to identify the feature of the output separated signal and realize compound faults diagnosis. The simulation and test results show that the proposed method can effectively solve the separation of compound faults for rotating machinery, which can reduce the dimension and improve the efficiency of algorithm. It is also confirmed that the feature extraction and separation capability of proposed method is superior to the traditional SNMF algorithm.

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.

Sparse coding reveals greater functional connectivity in female brains during naturalistic emotional experience

Functional neuroimaging is widely used to examine changes in brain function associated with age, gender or neuropsychiatric conditions. FMRI (functional magnetic resonance imaging) studies employ either laboratory-designed tasks that engage the brain with abstracted and repeated stimuli, or resting state paradigms with little behavioral constraint. Recently, novel neuroimaging paradigms using naturalistic stimuli are gaining increasing attraction, as they offer an ecologically-valid condition to approximate brain function in real life. Wider application of naturalistic paradigms in exploring individual differences in brain function, however, awaits further advances in statistical methods for modeling dynamic and complex dataset. Here, we developed a novel data-driven strategy that employs group sparse representation to assess gender differences in brain responses during naturalistic emotional experience. Comparing to independent component analysis (ICA), sparse coding algorithm considers the intrinsic sparsity of neural coding and thus could be more suitable in modeling dynamic whole-brain fMRI signals. An online dictionary learning and sparse coding algorithm was applied to the aggregated fMRI signals from both groups, which was subsequently factorized into a common time series signal dictionary matrix and the associated weight coefficient matrix. Our results demonstrate that group sparse representation can effectively identify gender differences in functional brain network during natural viewing, with improved sensitivity and reliability over ICA-based method. Group sparse representation hence offers a superior data-driven strategy for examining brain function during naturalistic conditions, with great potential for clinical application in neuropsychiatric disorders.

Collective sparse symmetric non-negative matrix factorization for identifying overlapping communities in resting-state brain functional networks

Resting-state functional magnetic resonance imaging (rs-fMRI) provides a valuable tool to study spontaneous brain activity. Using rs-fMRI, researchers have extensively studied the organization of the brain functional network and found several consistent communities consisting of functionally connected but spatially separated brain regions across subjects. However, increasing evidence in many disciplines has shown that most realistic complex networks have overlapping community structure. Only recently has the overlapping community structure drawn increasing interest in the domain of brain network studies. Another issue is that the inter-subject variability is often not directly reflected in the process of community detection at the group level. In this paper, we propose a novel method called collective sparse symmetric non-negative matrix factorization (cssNMF) to address these issues. The cssNMF approach identifies the group-level overlapping communities across subjects and in the meantime preserves the information of individual variation in brain functional network organization. To comprehensively validate cssNMF, a simulated fMRI dataset with ground-truth, a real rs-fMRI dataset with two repeated sessions and another different real rs-fMRI dataset have been used for performance comparison in the experiment. Experimental results show that the proposed cssNMF method accurately and stably identifies group-level overlapping communities across subjects as well as individual differences in network organization with neurophysiologically meaningful interpretations. This research extends our understanding of the common underlying community structures and individual differences in community strengths in brain functional network organization.

Link prediction based on non-negative matrix factorization

With the rapid expansion of internet, the complex networks has become high-dimensional, sparse and redundant. Besides, the problem of link prediction in such networks has also obatined increasingly attention from different types of domains like information science, anthropology, sociology and computer sciences. It makes requirements for effective link prediction techniques to extract the most essential and relevant information for online users in internet. Therefore, this paper attempts to put forward a link prediction algorithm based on non-negative matrix factorization. In the algorithm, we reconstruct the correlation between different types of matrix through the projection of high-dimensional vector space to a low-dimensional one, and then use the similarity between the column vectors of the weight matrix as the scoring matrix. The experiment results demonstrate that the algorithm not only reduces data storage space but also effectively makes the improvements of the prediction performance during the process of sustaining a low time complexity.