Coupled Matrix Tensor Factorization Research Articles

Integrating Nutrient Biomarkers, Cognitive Function, and Structural MRI Data to Build Multivariate Phenotypes of Healthy Aging

BackgroundResearch in the emerging field of nutritional cognitive neuroscience demonstrates that many aspects of nutrition—from entire diets to specific nutrients—affect cognitive performance and brain health. ObjectivesAlthough previous research has primarily examined the bivariate relationship between nutrition and cognition or nutrition and brain health, this study sought to investigate the joint relationship between these essential and interactive elements of human health. MethodsWe applied a state-of-the-art data fusion method, coupled matrix tensor factorization, to characterize the joint association between measures of nutrition (52 nutrient biomarkers), cognition (Wechsler Abbreviated Test of Intelligence and Wechsler Memory Scale), and brain health (high-resolution MRI measures of structural brain volume) within a cross-sectional sample of 111 healthy older adults, with an average age of 69.1 y, 62% being female, and an average body mass index of 26.0 kg/m2. ResultsData fusion uncovered latent factors that capture the joint association between specific nutrient profiles, cognitive measures, and cortical volumes, demonstrating the respects in which these health domains are coupled. A hierarchical cluster analysis further revealed systematic differences between a subset of variables contributing to the underlying latent factors, providing evidence for multivariate phenotypes that represent high and low levels of performance across multiple health domains. The primary features that distinguish between each phenotype were as follows: 1) nutrient biomarkers for monounsaturated and polyunsaturated fatty acids; 2) cognitive measures of immediate, auditory, and delayed memory; and 3) brain volumes within frontal, temporal, and parietal cortexes. ConclusionsBy incorporating innovations in nutritional epidemiology (nutrient biomarker analysis), cognitive neuroscience (high-resolution structural brain imaging), and statistics (data fusion), this study provides an interdisciplinary synthesis of methods that elucidate how nutrition, cognition, and brain health are integrated through lifestyle choices that affect healthy aging.

Exploring Neural Mechanisms of Reward Processing Using Coupled Matrix Tensor Factorization: A Simultaneous EEG-fMRI Investigation.

It is crucial to understand the neural feedback mechanisms and the cognitive decision-making of the brain during the processing of rewards. Here, we report the first attempt for a simultaneous electroencephalography (EEG)-functional magnetic resonance imaging (fMRI) study in a gambling task by utilizing tensor decomposition. First, the single-subject EEG data are represented as a third-order spectrogram tensor to extract frequency features. Next, the EEG and fMRI data are jointly decomposed into a superposition of multiple sources characterized by space-time-frequency profiles using coupled matrix tensor factorization (CMTF). Finally, graph-structured clustering is used to select the most appropriate model according to four quantitative indices. The results clearly show that not only are the regions of interest (ROIs) found in other literature activated, but also the olfactory cortex and fusiform gyrus which are usually ignored. It is found that regions including the orbitofrontal cortex and insula are activated for both winning and losing stimuli. Meanwhile, regions such as the superior orbital frontal gyrus and anterior cingulate cortex are activated upon winning stimuli, whereas the inferior frontal gyrus, cingulate cortex, and medial superior frontal gyrus are activated upon losing stimuli. This work sheds light on the reward-processing progress, provides a deeper understanding of brain function, and opens a new avenue in the investigation of neurovascular coupling via CMTF.

Coupled support tensor machine classification for multimodal neuroimaging data

AbstractMultimodal data arise in various applications where information about the same phenomenon is acquired from multiple sensors and across different imaging modalities. Learning from multimodal data is of great interest in machine learning and statistics research as this offers the possibility of capturing complementary information among modalities. Multimodal modeling helps to explain the interdependence between heterogeneous data sources, discovers new insights that may not be available from a single modality, and improves decision‐making. Recently, coupled matrix–tensor factorization has been introduced for multimodal data fusion to jointly estimate latent factors and identify complex interdependence among the latent factors. However, most of the prior work on coupled matrix–tensor factors focuses on unsupervised learning and there is little work on supervised learning using the jointly estimated latent factors. This paper considers the multimodal tensor data classification problem. A coupled support tensor machine (C‐STM) built upon the latent factors jointly estimated from the advanced coupled matrix–tensor factorization is proposed. C‐STM combines individual and shared latent factors with multiple kernels and estimates a maximal‐margin classifier for coupled matrix–tensor data. The classification risk of C‐STM is shown to converge to the optimal Bayes risk, making it a statistically consistent rule. C‐STM is validated through simulation studies as well as a simultaneous analysis on electroencephalography with functional magnetic resonance imaging data. The empirical evidence shows that C‐STM can utilize information from multiple sources and provide a better classification performance than traditional single‐mode classifiers.

Early soft and flexible fusion of electroencephalography and functional magnetic resonance imaging via double coupled matrix tensor factorization for multisubject group analysis.

Data fusion refers to the joint analysis of multiple datasets that provide different (e.g., complementary) views of the same task. In general, it can extract more information than separate analyses can. Jointly analyzing electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) measurements has been proved to be highly beneficial to the study of the brain function, mainly because these neuroimaging modalities have complementary spatiotemporal resolution: EEG offers good temporal resolution while fMRI is better in its spatial resolution. The EEG–fMRI fusion methods that have been reported so far ignore the underlying multiway nature of the data in at least one of the modalities and/or rely on very strong assumptions concerning the relation of the respective datasets. For example, in multisubject analysis, it is commonly assumed that the hemodynamic response function is a priori known for all subjects and/or the coupling across corresponding modes is assumed to be exact (hard). In this article, these two limitations are overcome by adopting tensor models for both modalities and by following soft and flexible coupling approaches to implement the multimodal fusion. The obtained results are compared against those of parallel independent component analysis and hard coupling alternatives, with both synthetic and real data (epilepsy and visual oddball paradigm). Our results demonstrate the clear advantage of using soft and flexible coupled tensor decompositions in scenarios that do not conform with the hard coupling assumption.

Tensor-structured decomposition improves systems serology analysis.

Systems serology provides a broad view of humoral immunity by profiling both the antigen‐binding and Fc properties of antibodies. These studies contain structured biophysical profiling across disease‐relevant antigen targets, alongside additional measurements made for single antigens or in an antigen‐generic manner. Identifying patterns in these measurements helps guide vaccine and therapeutic antibody development, improve our understanding of diseases, and discover conserved regulatory mechanisms. Here, we report that coupled matrix–tensor factorization (CMTF) can reduce these data into consistent patterns by recognizing the intrinsic structure of these data. We use measurements from two previous studies of HIV‐ and SARS‐CoV‐2‐infected subjects as examples. CMTF outperforms standard methods like principal components analysis in the extent of data reduction while maintaining equivalent prediction of immune functional responses and disease status. Under CMTF, model interpretation improves through effective data reduction, separation of the Fc and antigen‐binding effects, and recognition of consistent patterns across individual measurements. Data reduction also helps make prediction models more replicable. Therefore, we propose that CMTF is an effective general strategy for data exploration in systems serology.

Column-Wise Element Selection for Computationally Efficient Nonnegative Coupled Matrix Tensor Factorization

Coupled Matrix Tensor Factorization (CMTF) facilitates the integration and analysis of multiple data sources and helps discover meaningful information. Nonnegative CMTF (N-CMTF) has been employed in many applications for identifying latent patterns, prediction, and recommendation. However, due to the added complexity with coupling between tensor and matrix data, existing N-CMTF algorithms exhibit poor computation efficiency. In this paper, a computationally efficient N-CMTF factorization algorithm is presented based on the column-wise element selection, preventing frequent gradient updates. Theoretical and empirical analyses show that the proposed N-CMTF factorization algorithm is not only more accurate but also more computationally efficient than existing algorithms in approximating the tensor as well as in identifying the underlying nature of factors.

Identifying Covid-19 misinformation tweets and learning their spatio-temporal topic dynamics using Nonnegative Coupled Matrix Tensor Factorization.

Social media platforms like Twitter have become an easy portal for billions of people to connect and exchange their thoughts. Unfortunately, people commonly use these platforms to share misinformation which can influence other people adversely. The spread of misinformation is unavoidable in an extraordinary situation like Covid-19, and the consequences can be dreadful. This paper proposes a two-step ranking-based misinformation detection (RMiD) technique. Firstly, a novel ranking-based approach leveraging the scalable information retrieval infrastructure is applied to detect misinformation from a huge collection of unlabelled tweets based on a related but very small labelled misinformation data set. Secondly, the identified misinformation tweets are represented as a coupled matrix tensor model and Nonnegative Coupled Matrix Tensor Factorization is applied to learn their spatio-temporal topic dynamics. The experimental analysis shows that RMiD is capable of detecting misinformation with better coverage and less noise in comparison with existing techniques. Moreover, the coupled matrix tensor representation has improved the quality of topics discovered from unlabelled data up to 4% by leveraging the semantic similarity of terms in labelled data.Supplementary InformationThe online version supplementary material available at 10.1007/s13278-021-00767-7.

Correlated coupled matrix tensor factorization method for simultaneous EEG-fMRI data fusion

ObjectiveFusion of EEG and fMRI data provides complementary information about the brain functions. Thus, data fusion should employ all dimensions of data to both extract the shared information, and distinguish the dissimilarities of modalities. MethodIn this paper, we present a new method based on Advanced Coupled Matrix Tensor Factorization (ACMTF) method to decompose the EEG tensor and fMRI matrix. We remove the confining assumption of identical shared components in ACMTF and propose an approach to maximize the correlation between the shared components of EEG and fMRI in the common mode, while removing the smearing effect of hemodynamic response function on fMRI data. This method is called Correlated Coupled Matrix Tensor Factorization (CCMTF). ResultsTwo simulation scenarios with different noise levels are performed to evaluate the performance of the proposed CCMTF method. The simulation results show 30.1% and 23.38% average improvement of Match Scores over ACMTF and N-way Partial Least Square (N-PLS) methods, respectively. The proposed method is also applied to a real dataset of an auditory oddball paradigm. The results of real data analysis show that the proposed CCMTF method estimates the unknown number of shared components between EEG and fMRI data, with p-value less than 0.007. Conclusion and SignificanceIn addition to the improvement of match score, the simulation results demonstrate that CCMTF has higher performance than ACMTF for fusion of EEG and fMRI datasets in case of extracting the dissimilarities in modalities, and it provides more convenient interpretation of the results, in comparison to N-PLS method.

Removing the Effect of Hemodynamic Response Function in Joint Factorization of EEG and fMRI Datasets

Purpose: One of the most well-known multimodality techniques is the integration of EEG and fMRI datasets. Convolution of EEG signals with hemodynamic response function is one of the most important methods to consider the effect of HRF in the fusion of EEG and fMRI data. However, the latencies and amplitudes of ERPs and fMRI spatial components are affected by the low pass filtering effect of HRF in each trial. Materials and Methods: In this paper, we have proposed a new method based on Advanced Coupled Matrix Tensor Factorization model to jointly factorize the EEG tensor and fMRI matrix while we simultaneously remove the effect of HRF through decomposition of fMRI dataset. Results: Applying the proposed method to an auditory oddball paradigm of simultaneous EEG-fMRI recording, the well-known ERP of oddball paradigm and the corresponding fMRI spatial maps are estimated. Conclusion: The results demonstrate that our proposed approach is strongly capable of extracting the ERPs and their corresponding fMRI spatial components, while simultaneously estimates the trial to trial variations of these factors with accurate amplitude and latency in each trial.

S3CMTF: Fast, accurate, and scalable method for incomplete coupled matrix-tensor factorization.

How can we extract hidden relations from a tensor and a matrix data simultaneously in a fast, accurate, and scalable way? Coupled matrix-tensor factorization (CMTF) is an important tool for this purpose. Designing an accurate and efficient CMTF method has become more crucial as the size and dimension of real-world data are growing explosively. However, existing methods for CMTF suffer from lack of accuracy, slow running time, and limited scalability. In this paper, we propose S3CMTF, a fast, accurate, and scalable CMTF method. In contrast to previous methods which do not handle large sparse tensors and are not parallelizable, S3CMTF provides parallel sparse CMTF by carefully deriving gradient update rules. S3CMTF asynchronously updates partial gradients without expensive locking. We show that our method is guaranteed to converge to a quality solution theoretically and empirically. S3CMTF further boosts the performance by carefully storing intermediate computation and reusing them. We theoretically and empirically show that S3CMTF is the fastest, outperforming existing methods. Experimental results show that S3CMTF is up to 930× faster than existing methods while providing the best accuracy. S3CMTF shows linear scalability on the number of data entries and the number of cores. In addition, we apply S3CMTF to Yelp rating tensor data coupled with 3 additional matrices to discover interesting patterns.

Coupled Graph and Tensor Factorization for Recommender Systems and Community Detection

Joint analysis of data from multiple information repositories facilitates uncovering the underlying structure in heterogeneous datasets. Single and coupled matrix-tensor factorization (CMTF) has been widely used in this context for imputation-based recommendation from ratings, social network, and other user-item data. When this side information is in the form of item-item correlation matrices or graphs, existing CMTF algorithms may fall short. Alleviating current limitations, we introduce a novel model coined coupled graph-tensor factorization (CGTF) that judiciously accounts for graph-related side information. The CGTF model has the potential to overcome practical challenges, such as missing slabs from the tensor and/or missing rows/columns from the correlation matrices. A novel alternating direction method of multipliers (ADMM) is also developed that recovers the nonnegative factors of CGTF. Our algorithm enjoys closed-form updates that result in reduced computational complexity and allow for convergence claims. A novel direction is further explored by employing the interpretable factors to detect graph communities having the tensor as side information. The resulting community detection approach is successful even when some links in the graphs are missing. Results with real data sets corroborate the merits of the proposed methods relative to state-of-the-art competing factorization techniques in providing recommendations and detecting communities.

Turbo-SMT: Parallel Coupled Sparse Matrix-Tensor Factorizations and Applications.

How can we correlate the neural activity in the human brain as it responds to typed words, with properties of these terms (like 'edible', 'fits in hand')? In short, we want to find latent variables, that jointly explain both the brain activity, as well as the behavioral responses. This is one of many settings of the Coupled Matrix-Tensor Factorization (CMTF) problem. Can we enhance any CMTF solver, so that it can operate on potentially very large datasets that may not fit in main memory? We introduce Turbo-SMT, a meta-method capable of doing exactly that: it boosts the performance of any CMTF algorithm, produces sparse and interpretable solutions, and parallelizes any CMTF algorithm, producing sparse and interpretable solutions (up to 65 fold). Additionally, we improve upon ALS, the work-horse algorithm for CMTF, with respect to efficiency and robustness to missing values. We apply Turbo-SMT to BrainQ, a dataset consisting of a (nouns, brain voxels, human subjects) tensor and a (nouns, properties) matrix, with coupling along the nouns dimension. Turbo-SMT is able to find meaningful latent variables, as well as to predict brain activity with competitive accuracy. Finally, we demonstrate the generality of Turbo-SMT, by applying it on a Facebook dataset (users, 'friends', wall-postings); there, Turbo-SMT spots spammer-like anomalies.

Tensor Analysis and Fusion of Multimodal Brain Images

Current high-throughput data acquisition technologies probe dynamical systems with different imaging modalities, generating massive data sets at different spatial and temporal resolutions posing challenging problems in multimodal data fusion. A case in point is the attempt to parse out the brain structures and networks that underpin human cognitive processes by analysis of different neuroimaging modalities (functional MRI, EEG, NIRS etc.). We emphasize that the multimodal, multi-scale nature of neuroimaging data is well reflected by a multi-way (tensor) structure where the underlying processes can be summarized by a relatively small number of components or "atoms". We introduce Markov-Penrose diagrams - an integration of Bayesian DAG and tensor network notation in order to analyze these models. These diagrams not only clarify matrix and tensor EEG and fMRI time/frequency analysis and inverse problems, but also help understand multimodal fusion via Multiway Partial Least Squares and Coupled Matrix-Tensor Factorization. We show here, for the first time, that Granger causal analysis of brain networks is a tensor regression problem, thus allowing the atomic decomposition of brain networks. Analysis of EEG and fMRI recordings shows the potential of the methods and suggests their use in other scientific domains.

Turbo-SMT: Accelerating Coupled Sparse Matrix-Tensor Factorizations by 200×.

How can we correlate the neural activity in the human brain as it responds to typed words, with properties of these terms (like 'edible', 'fits in hand')? In short, we want to find latent variables, that jointly explain both the brain activity, as well as the behavioral responses. This is one of many settings of the Coupled Matrix-Tensor Factorization (CMTF) problem. Can we accelerate any CMTF solver, so that it runs within a few minutes instead of tens of hours to a day, while maintaining good accuracy? We introduce TURBO-SMT, a meta-method capable of doing exactly that: it boosts the performance of any CMTF algorithm, by up to 200×, along with an up to 65 fold increase in sparsity, with comparable accuracy to the baseline. We apply TURBO-SMT to BRAINQ, a dataset consisting of a (nouns, brain voxels, human subjects) tensor and a (nouns, properties) matrix, with coupling along the nouns dimension. TURBO-SMT is able to find meaningful latent variables, as well as to predict brain activity with competitive accuracy.