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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]

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]

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]