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Introduction: Longitudinal metabolomics data from a meal challenge test contains both fasting and dynamic signals, that may be related to metabolic health and diseases. Recent work has explored the multiway structure of time-resolved metabolomics data by arranging it as a three-way array with modes: subjects, metabolites, and time. The analysis of such dynamic data (where the fasting data is subtracted from postprandial states) reveals dynamic markers of various phenotypes, and differences between fasting and dynamic states. However, there is still limited success in terms of extracting static and dynamic biomarkers for the same subject stratifications. Objectives: Through joint analysis of fasting and dynamic metabolomics data, our goal is to capture static and dynamic biomarkers of a phenotype for the same subject stratifications providing a complete picture, that will be more effective for precision health. Methods: We jointly analyze fasting and dynamic metabolomics data collected during a meal challenge test from the COPSAC 2000 cohort using coupled matrix and tensor factorizations (CMTF), where the dynamic data (subjects by metabolites by time) is coupled with the fasting data (subjects by metabolites) in the subjects mode. Results: The proposed data fusion approach extracts shared subject stratifications in terms of BMI (body mass index) from fasting and dynamic signals as well as the static and dynamic metabolic biomarker patterns corresponding to those stratifications. Specifically, we observe a subject stratification showing the positive association with all fasting VLDLs and higher BMI. For the same subject stratification, a subset of dynamic VLDLs (mainly the smaller sizes) correlates negatively with higher BMI. Higher correlations of the subject quantifications with the phenotype of interest are observed using such a data fusion approach compared to individual analyses of the fasting and postprandial state. Conclusion: The CMTF-based approach provides a complete picture of static and dynamic biomarkers for the same subject stratifications—when markers are present in both fasting and dynamic states. [ABSTRACT FROM AUTHOR]

Computational phenotyping allows for unsupervised discovery of subgroups of patients as well as corresponding co‐occurring medical conditions from electronic health records (EHR). Typically, EHR data contains demographic information, diagnoses and laboratory results. Discovering (novel) phenotypes has the potential to be of prognostic and therapeutic value. Providing medical practitioners with transparent and interpretable results is an important requirement and an essential part for advancing precision medicine. Low‐rank data approximation methods such as matrix (e.g., nonnegative matrix factorization) and tensor decompositions (e.g., CANDECOMP/PARAFAC) have demonstrated that they can provide such transparent and interpretable insights. Recent developments have adapted low‐rank data approximation methods by incorporating different constraints and regularizations that facilitate interpretability further. In addition, they offer solutions for common challenges within EHR data such as high dimensionality, data sparsity and incompleteness. Especially extracting temporal phenotypes from longitudinal EHR has received much attention in recent years. In this paper, we provide a comprehensive review of low‐rank approximation‐based approaches for computational phenotyping. The existing literature is categorized into temporal versus static phenotyping approaches based on matrix versus tensor decompositions. Furthermore, we outline different approaches for the validation of phenotypes, that is, the assessment of clinical significance. This article is categorized under:Algorithmic Development > Structure DiscoveryFundamental Concepts of Data and Knowledge > Explainable AITechnologies > Machine Learning [ABSTRACT FROM AUTHOR]

Data-driven solutions are playing an increasingly important role in numerous practical problems across multiple disciplines. The shift from the traditional model-driven approaches to those that are data driven naturally emphasizes the importance of the explainability of solutions, as, in this case, the connection to a physical model is often not obvious. Explainability is a broad umbrella and includes interpretability, but it also implies that the solutions need to be complete, in that one should be able to “audit” them, ask appropriate questions, and hence gain further insight about their inner workings. Thus, interpretability, reproducibility, and, ultimately, our ability to generalize these solutions to unseen scenarios and situations are all strongly tied to the starting point of explainability. [ABSTRACT FROM AUTHOR]

Two-way arrays or matrices are often not enough to represent all the information content of the data, and standard two- way analysis techniques commonly applied on matrices may fail to find the underlying structures in multimodal data sets. Multiway data analysis has recently become popular as an exploratory analysis tool in discovering the structures in higher-order data sets, where data have more than two modes. We provide a review of significant contributions in the literature on multiway models, algorithms as well as their applications in diverse disciplines including chemometrics, neuroscience, social network analysis, text mining, and computer vision. Index Terms--Multiway data analysis, tensor, higher-order singular value decomposition, multilinear algebra.

Analysis of time-evolving data is crucial to understand the functioning of dynamic systems such as the brain. For instance, analysis of functional magnetic resonance imaging (fMRI) data collected during a task may reveal spatial regions of interest, and how they evolve during the task. However, capturing underlying spatial patterns as well as their change in time is challenging. The traditional approach in fMRI data analysis is to assume that underlying spatial regions of interest are static. In this article, using fractional amplitude of low-frequency fluctuations (fALFF) as an effective way to summarize the variability in fMRI data collected during a task, we arrange time-evolving fMRI data as a subjects by voxels by time windows tensor, and analyze the tensor using a tensor factorization-based approach called a PARAFAC2 model to reveal spatial dynamics. The PARAFAC2 model jointly analyzes data from multiple time windows revealing subject-mode patterns, evolving spatial regions (also referred to as networks) and temporal patterns. We compare the PARAFAC2 model with matrix factorization-based approaches relying on independent components, namely, joint independent component analysis (ICA) and independent vector analysis (IVA), commonly used in neuroimaging data analysis. We assess the performance of the methods in terms of capturing evolving networks through extensive numerical experiments demonstrating their modeling assumptions. In particular, we show that (i) PARAFAC2 provides a compact representation in all modes, i.e., subjects, time , and voxels , revealing temporal patterns as well as evolving spatial networks, (ii) joint ICA is as effective as PARAFAC2 in terms of revealing evolving networks but does not reveal temporal patterns, (iii) IVA's performance depends on sample size, data distribution and covariance structure of underlying networks. When these assumptions are satisfied, IVA is as accurate as the other methods, (iv) when subject-mode patterns differ from one time window to another, IVA is the most accurate. Furthermore, we analyze real fMRI data collected during a sensory motor task, and demonstrate that a component indicating statistically significant group difference between patients with schizophrenia and healthy controls is captured, which includes primary and secondary motor regions, cerebellum, and temporal lobe, revealing a meaningful spatial map and its temporal change. [ABSTRACT FROM AUTHOR]

Coupled matrix and tensor factorizations (CMTF) are frequently used to jointly analyze data from multiple sources, a task also called data fusion. However, different characteristics of datasets stemming from multiple sources pose many challenges in data fusion and require to employ various regularizations, constraints, loss functions and different types of coupling structures between datasets. In this paper, we propose a flexible algorithmic framework for coupled matrix and tensor factorizations which utilizes Alternating Optimization (AO) and the Alternating Direction Method of Multipliers (ADMM). The framework facilitates the use of a variety of constraints, loss functions and couplings with linear transformations in a seamless way. Numerical experiments on simulated and real datasets demonstrate that the proposed approach is accurate, and computationally efficient with comparable or better performance than available CMTF methods for Frobenius norm loss, while being more flexible. Using Kullback-Leibler divergence on count data, we demonstrate that the algorithm yields accurate results also for other loss functions. [ABSTRACT FROM AUTHOR]

Abstract Background Recently, we demonstrated that human mesenchymal stem cells (hMSC) stimulated with dexamethazone undergo gene focusing during osteogenic differentiation (Stem Cells Dev 14(6): 1608–20, 2005). Here, we examine the protein expression profiles of three additional populations of hMSC stimulated to undergo osteogenic differentiation via either contact with pro-osteogenic extracellular matrix (ECM) proteins (collagen I, vitronectin, or laminin-5) or osteogenic media supplements (OS media). Specifically, we annotate these four protein expression profiles, as well as profiles from naïve hMSC and differentiated human osteoblasts (hOST), with known gene ontologies and analyze them as a tensor with modes for the expressed proteins, gene ontologies, and stimulants. Results Direct component analysis in the gene ontology space identifies three components that account for 90% of the variance between hMSC, osteoblasts, and the four stimulated hMSC populations. The directed component maps the differentiation stages of the stimulated stem cell populations along the differentiation axis created by the difference in the expression profiles of hMSC and hOST. Surprisingly, hMSC treated with ECM proteins lie closer to osteoblasts than do hMSC treated with OS media. Additionally, the second component demonstrates that proteomic profiles of collagen I- and vitronectin-stimulated hMSC are distinct from those of OS-stimulated cells. A three-mode tensor analysis reveals additional focus proteins critical for characterizing the phenotypic variations between naïve hMSC, partially differentiated hMSC, and hOST. Conclusion The differences between the proteomic profiles of OS-stimulated hMSC and ECM-hMSC characterize different transitional phenotypes en route to becoming osteoblasts. This conclusion is arrived at via a three-mode tensor analysis validated using hMSC plated on laminin-5.

Fusing complementary information from different modalities can lead to the discovery of more accurate diagnostic biomarkers for psychiatric disorders. However, biomarker discovery through data fusion is challenging since it requires extracting interpretable and reproducible patterns from data sets, consisting of shared/unshared patterns and of different orders. For example, multi-channel electroencephalography (EEG) signals from multiple subjects can be represented as a third-order tensor with modes: subject, time, and channel, while functional magnetic resonance imaging (fMRI) data may be in the form of subject by voxel matrices. Traditional data fusion methods rearrange higher-order tensors, such as EEG, as matrices to use matrix factorization-based approaches. In contrast, fusion methods based on coupled matrix and tensor factorizations (CMTF) exploit the potential multi-way structure of higher-order tensors. The CMTF approach has been shown to capture underlying patterns more accurately without imposing strong constraints on the latent neural patterns, i.e., biomarkers. In this paper, EEG, fMRI, and structural MRI (sMRI) data collected during an auditory oddball task (AOD) from a group of subjects consisting of patients with schizophrenia and healthy controls, are arranged as matrices and higher-order tensors coupled along the subject mode, and jointly analyzed using structure-revealing CMTF methods [also known as advanced CMTF (ACMTF)] focusing on unique identification of underlying patterns in the presence of shared/unshared patterns. We demonstrate that joint analysis of the EEG tensor and fMRI matrix using ACMTF reveals significant and biologically meaningful components in terms of differentiating between patients with schizophrenia and healthy controls while also providing spatial patterns with high resolution and improving the clustering performance compared to the analysis of only the EEG tensor. We also show that these patterns are reproducible, and study reproducibility for different model parameters. In comparison to the joint independent component analysis (jICA) data fusion approach, ACMTF provides easier interpretation of EEG data by revealing a single summary map of the topography for each component. Furthermore, fusion of sMRI data with EEG and fMRI through an ACMTF model provides structural patterns; however, we also show that when fusing data sets from multiple modalities, hence of very different nature, preprocessing plays a crucial role. [ABSTRACT FROM AUTHOR]

Tensor factorisations have proven useful to model amplitude and spectral information of brain recordings. Here, we assess the usefulness of tensor factorisations in the multiway analysis of other brain signal features in the context of complexity measures recently proposed to inspect multiscale dynamics. We consider the “refined composite multiscale entropy” ( rcMSE ), which computes entropy “profiles” showing levels of physiological complexity over temporal scales for individual signals. We compute the rcMSE of resting-state magnetoencephalogram (MEG) recordings from 36 patients with Alzheimer's disease and 26 control subjects. Instead of traditional simple visual examinations, we organise the entropy profiles as a three-way tensor to inspect relationships across temporal and spatial scales and subjects with multiway data analysis techniques based on PARAFAC and PARAFAC2 factorisations. A PARAFAC2 model with two factors was appropriate to account for the interactions in the entropy tensor between temporal scales and MEG channels for all subjects. Moreover, the PARAFAC2 factors had information related to the subjects’ diagnosis, achieving a cross-validated area under the ROC curve of 0.77. This confirms the suitability of tensor factorisations to represent electrophysiological brain data efficiently despite the unsupervised nature of these techniques. This article is part of a Special Issue entitled ‘Neural data analysis’. [ABSTRACT FROM AUTHOR]

With a goal of identifying biomarkers/patterns related to certain conditions or diseases, metabolomics focuses on the detection of chemical substances in biological samples such as urine and blood using a number of analytical techniques, including nuclear magnetic resonance (NMR) spectroscopy, liquid chromatography-mass spectrometry (LC–MS), and fluorescence spectroscopy. Data sets measured using these methods provide partly complementary information, and their joint analysis has the potential to reveal underlying structures, which are, otherwise, difficult to extract. While we can collect vast amounts of data using different analytical methods, data fusion remains a challenging task, in particular, when the goal is to capture the underlying factors and use them for interpretation, e.g., for biomarker identification. Furthermore, many data fusion applications require joint analysis of heterogeneous (i.e., in the form of higher order tensors and matrices) data sets with shared/unshared factors. In order to jointly analyze such heterogeneous data sets, we formulate data fusion as a coupled matrix and tensor factorization (CMTF) problem, which has already proved useful in many data mining applications, and discuss its extension to a structure-revealing data fusion model, i.e., a data fusion model that can identify shared and unshared factors. The traditional methods commonly used for data fusion in the presence of shared/unshared factors are matrix factorization-based methods. Using both simulations and prototypical experimental coupled data sets, we assess the performance of various state-of-the-art data fusion methods and demonstrate that while matrix factorization-based approaches have limitations when used for joint analysis of heterogeneous data sets, the structure-revealing CMTF model can successfully capture the underlying factors by exploiting the low-rank structure of higher order data sets. [ABSTRACT FROM PUBLISHER]

Background: Analysis of data from multiple sources has the potential to enhance knowledge discovery by capturing underlying structures, which are, otherwise, difficult to extract. Fusing data from multiple sources has already proved useful in many applications in social network analysis, signal processing and bioinformatics. However, data fusion is challenging since data from multiple sources are often (i) heterogeneous (i.e., in the form of higher-order tensors and matrices), (ii) incomplete, and (iii) have both shared and unshared components. In order to address these challenges, in this paper, we introduce a novel unsupervised data fusion model based on joint factorization of matrices and higher-order tensors. Results: While the traditional formulation of coupled matrix and tensor factorizations modeling only shared factors fails to capture the underlying structures in the presence of both shared and unshared factors, the proposed data fusion model has the potential to automatically reveal shared and unshared components through modeling constraints. Using numerical experiments, we demonstrate the effectiveness of the proposed approach in terms of identifying shared and unshared components. Furthermore, we measure a set of mixtures with known chemical composition using both LC-MS (Liquid Chromatography - Mass Spectrometry) and NMR (Nuclear Magnetic Resonance) and demonstrate that the structure-revealing data fusion model can (i) successfully capture the chemicals in the mixtures and extract the relative concentrations of the chemicals accurately, (ii) provide promising results in terms of identifying shared and unshared chemicals, and (iii) reveal the relevant patterns in LC-MS by coupling with the diffusion NMR data. Conclusions: We have proposed a structure-revealing data fusion model that can jointly analyze heterogeneous, incomplete data sets with shared and unshared components and demonstrated its promising performance as well as potential limitations on both simulated and real data. [ABSTRACT FROM AUTHOR]

The structure/function relationship is fundamental to our understanding of biological systems at all levels, and drives most, if not all, techniques for detecting, diagnosing, and treating disease. However, at the tissue level of biological complexity we encounter a gap in the structure/function relationship: having accumulated an extraordinary amount of detailed information about biological tissues at the cellular and subcellular level, we cannot assemble it in a way that explains the correspondingly complex biological functions these structures perform. To help close this information gap we define here several quantitative temperospatial features that link tissue structure to its corresponding biological function. Both histological images of human tissue samples and fluorescence images of three-dimensional cultures of human cells are used to compare the accuracy of in vitro culture models with their corresponding human tissues. To the best of our knowledge, there is no prior work on a quantitative comparison of histology and in vitro samples. Features are calculated from graph theoretical representations of tissue structures and the data are analyzed in the form of matrices and higher-order tensors using matrix and tensor factorization methods, with a goal of differentiating between cancerous and healthy states of brain, breast, and bone tissues. We also show that our techniques can differentiate between the structural organization of native tissues and their corresponding in vitro engineered cell culture models. [ABSTRACT FROM AUTHOR]

Background: Systems biology refers to multidisciplinary approaches designed to uncover emergent properties of biological systems. Stem cells are an attractive target for this analysis, due to their broad therapeutic potential. A central theme of systems biology is the use of computational modeling to reconstruct complex systems from a wealth of reductionist, molecular data (e.g., gene/ protein expression, signal transduction activity, metabolic activity, etc.). A number of deterministic, probabilistic, and statistical learning models are used to understand sophisticated cellular behaviors such as protein expression during cellular differentiation and the activity of signaling networks. However, many of these models are bimodal i.e., they only consider row-column relationships. In contrast, multiway modeling techniques (also known as tensor models) can analyze multimodal data, which capture much more information about complex behaviors such as cell differentiation. In particular, tensors can be very powerful tools for modeling the dynamic activity of biological networks over time. Here, we review the application of systems biology to stem cells and illustrate application of tensor analysis to model collagen-induced osteogenic differentiation of human mesenchymal stem cells. Results: We applied Tucker1, Tucker3, and Parallel Factor Analysis (PARAFAC) models to identify protein/gene expression patterns during extracellular matrix-induced osteogenic differentiation of human mesenchymal stem cells. In one case, we organized our data into a tensor of type protein/ gene locus link x gene ontology category x osteogenic stimulant, and found that our cells expressed two distinct, stimulus-dependent sets of functionally related genes as they underwent osteogenic differentiation. In a second case, we organized DNA microarray data in a three-way tensor of gene IDs x osteogenic stimulus x replicates, and found that application of tensile strain to a collagen I substrate accelerated the osteogenic differentiation induced by a static collagen I substrate. Conclusion: Our results suggest gene- and protein-level models whereby stem cells undergo transdifferentiation to osteoblasts, and lay the foundation for mechanistic, hypothesis-driven studies. Our analysis methods are applicable to a wide range of stem cell differentiation models. [ABSTRACT FROM AUTHOR]

A previous study has shown effects of the New Nordic Diet (NND) to stimulate weight loss and lower systolic and diastolic blood pressure in obese Danish women and men in a randomized, controlled dietary intervention study. This work demonstrates long-term metabolic effects of the NND as compared with an Average Danish Diet (ADD) in blood plasma and reveals associations between metabolic changes and health beneficial effects of the NND including weight loss. A total of 145 individuals completed the intervention and blood samples were taken along with clinical examinations before the intervention started (week 0) and after 12 and 26 weeks. The plasma metabolome was measured using GC-MS, and the final metabolite table contained 144 variables. Significant and novel metabolic effects of the diet, resulting weight loss, gender, and intervention study season were revealed using PLS-DA and ASCA. Several metabolites reflecting specific differences in the diets, especially intake of plant foods and seafood, and in energy metabolism related to ketone bodies and gluconeogenesis formed the predominant metabolite pattern discriminating the intervention groups. Among NND subjects, higher levels of vaccenic acid and 3-hydroxybutanoic acid were related to a higher weight loss, while higher concentrations of salicylic, lactic, and N-aspartic acids and 1,5-anhydro-d-sorbitol were related to a lower weight loss. Specific gender and seasonal differences were also observed. The study strongly indicates that healthy diets high in fish, vegetables, fruit, and whole grain facilitated weight loss and improved insulin sensitivity by increasing ketosis and gluconeogenesis in the fasting state.

In many disciplines, data from multiple sources are acquired and jointly analyzed for enhanced knowledge discovery. For instance, in metabolomics, different analytical techniques are used to measure biological fluids in order to identify the chemicals related to certain diseases. It is widely-known that, some of these analytical methods, e.g., LC-MS (Liquid Chromatography - Mass Spectrometry) and NMR (Nuclear Magnetic Resonance) spectroscopy, provide complementary data sets and their joint analysis may enable us to capture a larger proportion of the complete metabolome belonging to a specific biological system. Fusing data from multiple sources has proved useful in many fields including bioinformatics, signal processing and social network analysis. However, identification of common (shared) and individual (unshared) structures across multiple data sets remains a major challenge in data fusion studies. With a goal of addressing this challenge, we propose a novel unsupervised data fusion model. Our contributions are two-fold: (i) We formulate a data fusion model based on joint factorization of matrices and higher-order tensors, which can automatically reveal common and individual components. (ii) We demonstrate that the proposed approach provides promising results in joint analysis of metabolomics data sets consisting of fluorescence and NMR measurements of plasma samples in terms of separation of colorectal cancer patients from controls.

Background: Recently, we demonstrated that human mesenchymal stem cells (hMSC) stimulated with dexamethazone undergo gene focusing during osteogenic differentiation (Stem Cells Dev 14(6): 1608-20, 2005). Here, we examine the protein expression profiles of three additional populations of hMSC stimulated to undergo osteogenic differentiation via either contact with pro-osteogenic extracellular matrix (ECM) proteins (collagen I, vitronectin, or laminin-5) or osteogenic media supplements (OS media). Specifically, we annotate these four protein expression profiles, as well as profiles from naïve hMSC and differentiated human osteoblasts (hOST), with known gene ontologies and analyze them as a tensor with modes for the expressed proteins, gene ontologies, and stimulants., Results: Direct component analysis in the gene ontology space identifies three components that account for 90% of the variance between hMSC, osteoblasts, and the four stimulated hMSC populations. The directed component maps the differentiation stages of the stimulated stem cell populations along the differentiation axis created by the difference in the expression profiles of hMSC and hOST. Surprisingly, hMSC treated with ECM proteins lie closer to osteoblasts than do hMSC treated with OS media. Additionally, the second component demonstrates that proteomic profiles of collagen I- and vitronectin-stimulated hMSC are distinct from those of OS-stimulated cells. A three-mode tensor analysis reveals additional focus proteins critical for characterizing the phenotypic variations between naïve hMSC, partially differentiated hMSC, and hOST., Conclusion: The differences between the proteomic profiles of OS-stimulated hMSC and ECM-hMSC characterize different transitional phenotypes en route to becoming osteoblasts. This conclusion is arrived at via a three-mode tensor analysis validated using hMSC plated on laminin-5.

With a goal of automating visual analysis of electroencephalogram (EEG) data and assessing the performance of various features in seizure recognition, we introduce a mathematical model capable of recognizing patient-specific epileptic seizures with high accuracy. We represent multi-channel scalp EEG using a set of features. These features expected to have distinct trends during seizure and non-seizure periods include features from both time and frequency domains. The contributions of this paper are threefold. First, we rearrange multi-channel EEG signals as a third-order tensor called an Epilepsy Feature Tensor with modes: time epochs, features and electrodes. Second, we model the Epilepsy Feature Tensor using a multilinear regression model, i.e., Multilinear Partial Least Squares regression, which is the generalization of Partial Least Squares (PLS) regression to higher-order datasets. This two-step approach facilitates EEG data analysis from multiple electrodes represented by several features from different domains. Third, we identify which features are more significant for seizure recognition. Our results based on the analysis of 19 seizures from 5 epileptic patients demonstrate that multiway analysis of an Epilepsy Feature Tensor can detect (patient-specific) seizures with classification accuracy ranging between 77-96%.