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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]

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]

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]

Abstract: Recent technological advances enable us to collect huge amounts of data from multiple sources. Jointly analyzing such multi-relational data from different sources, i.e., data fusion (also called multi-block, multi-view or multi-set data analysis), often enhances knowledge discovery. For instance, in metabolomics, biological fluids are measured using a variety of analytical techniques such as Liquid Chromatography–Mass Spectrometry and Nuclear Magnetic Resonance Spectroscopy. Data measured using different analytical methods may be complementary and their fusion may help in the identification of chemicals related to certain diseases. Data fusion has proved useful in many fields including social network analysis, collaborative filtering, neuroscience and bioinformatics. In this paper, unlike many studies demonstrating the success of data fusion, we explore the limitations as well as the advantages of data fusion. We formulate data fusion as a coupled matrix and tensor factorization (CMTF) problem, which jointly factorizes multiple data sets in the form of higher-order tensors and matrices by extracting a common latent structure from the shared mode. Using numerical experiments on simulated and real data sets, we assess the performance of coupled analysis compared to the analysis of a single data set in terms of missing data estimation and demonstrate cases where coupled analysis outperforms analysis of a single data set and vice versa. [Copyright &y& Elsevier]

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]

Abstract: The problem of incomplete data – i.e., data with missing or unknown values – in multi-way arrays is ubiquitous in biomedical signal processing, network traffic analysis, bibliometrics, social network analysis, chemometrics, computer vision, communication networks, etc. We consider the problem of how to factorize data sets with missing values with the goal of capturing the underlying latent structure of the data and possibly reconstructing missing values (i.e., tensor completion). We focus on one of the most well-known tensor factorizations that captures multi-linear structure, CANDECOMP/PARAFAC (CP). In the presence of missing data, CP can be formulated as a weighted least squares problem that models only the known entries. We develop an algorithm called CP-WOPT (CP Weighted OPTimization) that uses a first-order optimization approach to solve the weighted least squares problem. Based on extensive numerical experiments, our algorithm is shown to successfully factorize tensors with noise and up to 99% missing data. A unique aspect of our approach is that it scales to sparse large-scale data, e.g., 1000×1000×1000 with five million known entries (0.5% dense). We further demonstrate the usefulness of CP-WOPT on two real-world applications: a novel EEG (electroencephalogram) application where missing data is frequently encountered due to disconnections of electrodes and the problem of modeling computer network traffic where data may be absent due to the expense of the data collection process. [Copyright &y& Elsevier]

Abstract-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. [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]

Matrix factorization methods are extensively employed to understand complex data. In this paper, we introduce the cross-product penalized component analysis (X-CAN), a matrix factorization based on the optimization of a loss function that allows a trade-off between variance maximization and structural preservation, with a focus on highlighting differences between groups of observations and/or variables. The approach is based on previous developments, notably (i) the Sparse Principal Component Analysis (SPCA) framework based on the LASSO, (ii) extensions of SPCA to constrain both modes of the factorization, like co-clustering or the Penalized Matrix Decomposition (PMD), and (iii) the Group-wise Principal Component Analysis (GPCA) method. The result is a flexible modeling approach that can be used for data exploration in a large variety of problems. We demonstrate its use with applications from different disciplines. • We introduce the cross-product penalized component analysis (X-CAN) method. • We demonstrate its use with applications from different disciplines. • We discuss good practices of application, including different ways to define suitable cross-product matrices. • We discuss the interpretation of X-CAN results. [ABSTRACT FROM AUTHOR]

Background: Analysis of time-resolved postprandial metabolomics data can improve the understanding of metabolic mechanisms, potentially revealing biomarkers for early diagnosis of metabolic diseases and advancing precision nutrition and medicine. Postprandial metabolomics measurements at several time points from multiple subjects can be arranged as a subjects by metabolites by time points array. Traditional analysis methods are limited in terms of revealing subject groups, related metabolites, and temporal patterns simultaneously from such three-way data. Results: We introduce an unsupervised multiway analysis approach based on the CANDECOMP/PARAFAC (CP) model for improved analysis of postprandial metabolomics data guided by a simulation study. Because of the lack of ground truth in real data, we generate simulated data using a comprehensive human metabolic model. This allows us to assess the performance of CP models in terms of revealing subject groups and underlying metabolic processes. We study three analysis approaches: analysis of fasting-state data using principal component analysis, T0-corrected data (i.e., data corrected by subtracting fasting-state data) using a CP model and full-dynamic (i.e., full postprandial) data using CP. Through extensive simulations, we demonstrate that CP models capture meaningful and stable patterns from simulated meal challenge data, revealing underlying mechanisms and differences between diseased versus healthy groups. Conclusions: Our experiments show that it is crucial to analyze both fasting-state and T0-corrected data for understanding metabolic differences among subject groups. Depending on the nature of the subject group structure, the best group separation may be achieved by CP models of T0-corrected or full-dynamic data. This study introduces an improved analysis approach for postprandial metabolomics data while also shedding light on the debate about correcting baseline values in longitudinal data analysis. [ABSTRACT FROM AUTHOR]

Background: Analysis of dynamic metabolomics data holds the promise to improve our understanding of underlying mechanisms in metabolism. For example, it may detect changes in metabolism due to the onset of a disease. Dynamic or time-resolved metabolomics data can be arranged as a three-way array with entries organized according to a subjects mode, a metabolites mode and a time mode. While such time-evolving multiway data sets are increasingly collected, revealing the underlying mechanisms and their dynamics from such data remains challenging. For such data, one of the complexities is the presence of a superposition of several sources of variation: induced variation (due to experimental conditions or inborn errors), individual variation, and measurement error. Multiway data analysis (also known as tensor factorizations) has been successfully used in data mining to find the underlying patterns in multiway data. To explore the performance of multiway data analysis methods in terms of revealing the underlying mechanisms in dynamic metabolomics data, simulated data with known ground truth can be studied. Results: We focus on simulated data arising from different dynamic models of increasing complexity, i.e., a simple linear system, a yeast glycolysis model, and a human cholesterol model. We generate data with induced variation as well as individual variation. Systematic experiments are performed to demonstrate the advantages and limitations of multiway data analysis in analyzing such dynamic metabolomics data and their capacity to disentangle the different sources of variations. We choose to use simulations since we want to understand the capability of multiway data analysis methods which is facilitated by knowing the ground truth. Conclusion: Our numerical experiments demonstrate that despite the increasing complexity of the studied dynamic metabolic models, tensor factorization methods CANDECOMP/PARAFAC(CP) and Parallel Profiles with Linear Dependences (Paralind) can disentangle the sources of variations and thereby reveal the underlying mechanisms and their dynamics. [ABSTRACT FROM AUTHOR]

In metabolomics studies, liquid chromatography mass spectrometry (LC-MS) provides comprehensive information on biological samples. However, extraction of few relevant metabolites from this large and complex data is cumbersome. To resolve this issue, we have employed sparse principal component analysis (SPCA) to capture the underlying patterns and select relevant metabolites from LC-MS plasma profiles. The study involves a small pilot cohort with 270 subjects where each subject's time since last meal (TSLM) has been recorded prior to plasma sampling. Our results have demonstrated that both PCA and SPCA can capture the TSLM patterns. Nevertheless, SPCA provides more easily interpretable loadings in terms of selection of relevant metabolites, which are identified as amino acids and lyso-lipids. This study demonstrates the utility of SPCA as a pattern recognition and variable selection tool in metabolomics. Furthermore, amino acids and lyso-lipids are determined as dominating compounds in response to TSLM. [ABSTRACT FROM AUTHOR]