Abstract
BackgroundAnalysis 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.ResultsWhile 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.ConclusionsWe 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.Electronic supplementary materialThe online version of this article (doi:10.1186/1471-2105-15-239) contains supplementary material, which is available to authorized users.
Highlights
Analysis of data from multiple sources has the potential to enhance knowledge discovery by capturing underlying structures, which are, otherwise, difficult to extract
Matrix factorization-based data fusion studies have been successfully applied in social network analysis [9,10], signal processing [11,12] and bioinformatics [1,2,4,5,13]
Results and discussion we first compare the performance of our model with the traditional coupled matrix and tensor factorizations (CMTF) model using simulated coupled data sets in terms of identifying shared/unshared components
Summary
Analysis of data from multiple sources has the potential to enhance knowledge discovery by capturing underlying structures, which are, otherwise, difficult to extract. Mixtures studied by NMR spectroscopy (a.k.a. DOSY - diffusion-ordered spectroscopy [18,19]) can be represented as a third-order tensor with modes: mixtures, chemical shift and gradient levels [20,21] while LC-MS measurements of the same mixtures can be represented using a mixtures by features matrix (see Figure 1). DOSY - diffusion-ordered spectroscopy [18,19]) can be represented as a third-order tensor with modes: mixtures, chemical shift and gradient levels [20,21] while LC-MS measurements of the same mixtures can be represented using a mixtures by features matrix (see Figure 1) Joint factorization of such heterogeneous data has been studied to analyze multi-relational data, in social networks [15,22,23,24]
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