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1.  Structure-revealing data fusion 
BMC Bioinformatics  2014;15(1):239.
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.
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.
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.
Electronic supplementary material
The online version of this article (doi:10.1186/1471-2105-15-239) contains supplementary material, which is available to authorized users.
PMCID: PMC4117975  PMID: 25015427
Data fusion; Coupled matrix and tensor factorizations; Optimization; Sparsity; NMR; DOSY; MS
2.  Coupled Analysis of In Vitro and Histology Tissue Samples to Quantify Structure-Function Relationship 
PLoS ONE  2012;7(3):e32227.
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.
PMCID: PMC3316529  PMID: 22479315
3.  Multiway modeling and analysis in stem cell systems biology 
BMC Systems Biology  2008;2:63.
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.
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 × gene ontology category × 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 × osteogenic stimulus × replicates, and found that application of tensile strain to a collagen I substrate accelerated the osteogenic differentiation induced by a static collagen I substrate.
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.
PMCID: PMC2527292  PMID: 18625054
4.  Proteomics reveals multiple routes to the osteogenic phenotype in mesenchymal stem cells 
BMC Genomics  2007;8:380.
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.
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.
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.
PMCID: PMC2148065  PMID: 17949499

Results 1-4 (4)