A new method for spectral decomposition using a bilinear Bayesian approach

Unsupervised learning for medical data: A review of probabilistic factorization methods

We review popular unsupervised learning methods for the analysis of high-dimensional data encountered in, for example, genomics, medical imaging, cohort studies, and biobanks. We show that four commonly used methods, principal component analysis, K-means clustering, nonnegative matrix factorization, and latent Dirichlet allocation, can be written as probabilistic models underpinned by a low-rank matrix factorization. In addition to highlighting their similarities, this formulation clarifies the various assumptions and restrictions of each approach, which eases identifying the appropriate method for specific applications for applied medical researchers. We also touch upon the most important aspects of inference and model selection for the application of these methods to health data.

Inferring cellular and molecular processes in single-cell data with non-negative matrix factorization using Python, R and GenePattern Notebook implementations of CoGAPS

Non-negative matrix factorization (NMF) is an unsupervised learning method well suited to high-throughput biology. However, inferring biological processes from an NMF result still requires additional post hoc statistics and annotation for interpretation of learned features. Here, we introduce a suite of computational tools that implement NMF and provide methods for accurate and clear biological interpretation and analysis. A generalized discussion of NMF covering its benefits, limitations and open questions is followed by four procedures for the Bayesian NMF algorithm Coordinated Gene Activity across Pattern Subsets (CoGAPS). Each procedure will demonstrate NMF analysis to quantify cell state transitions in a public domain single-cell RNA-sequencing dataset. The first demonstrates PyCoGAPS, our new Python implementation that enhances runtime for large datasets, and the second allows its deployment in Docker. The third procedure steps through the same single-cell NMF analysis using our R CoGAPS interface. The fourth introduces a beginner-friendly CoGAPS platform using GenePattern Notebook, aimed at users with a working conceptual knowledge of data analysis but without a basic proficiency in the R or Python programming language. We also constructed a user-facing website to serve as a central repository for information and instructional materials about CoGAPS and its application programming interfaces. The expected timing to setup the packages and conduct a test run is around 15 min, and an additional 30 min to conduct analyses on a precomputed result. The expected runtime on the user's desired dataset can vary from hours to days depending on factors such as dataset size or input parameters.

Assessing reproducibility of matrix factorization methods in independent transcriptomes

Motivation

Matrix factorization (MF) methods are widely used in order to reduce dimensionality of transcriptomic datasets to the action of few hidden factors (metagenes). MF algorithms have never been compared based on the between-datasets reproducibility of their outputs in similar independent datasets. Lack of this knowledge might have a crucial impact when generalizing the predictions made in a study to others.

Results

We systematically test widely used MF methods on several transcriptomic datasets collected from the same cancer type (14 colorectal, 8 breast and 4 ovarian cancer transcriptomic datasets). Inspired by concepts of evolutionary bioinformatics, we design a novel framework based on Reciprocally Best Hit (RBH) graphs in order to benchmark the MF methods for their ability to produce generalizable components. We show that a particular protocol of application of independent component analysis (ICA), accompanied by a stabilization procedure, leads to a significant increase in the between-datasets reproducibility. Moreover, we show that the signals detected through this method are systematically more interpretable than those of other standard methods. We developed a user-friendly tool for performing the Stabilized ICA-based RBH meta-analysis. We apply this methodology to the study of colorectal cancer (CRC) for which 14 independent transcriptomic datasets can be collected. The resulting RBH graph maps the landscape of interconnected factors associated to biological processes or to technological artifacts. These factors can be used as clinical biomarkers or robust and tumor-type specific transcriptomic signatures of tumoral cells or tumoral microenvironment. Their intensities in different samples shed light on the mechanistic basis of CRC molecular subtyping.

Availability and implementation

The RBH construction tool is available from http://goo.gl/DzpwYp

Supplementary information

Supplementary data are available at Bioinformatics online.

Enter the Matrix: Factorization Uncovers Knowledge from Omics

Omics data contain signals from the molecular, physical, and kinetic inter- and intracellular interactions that control biological systems. Matrix factorization (MF) techniques can reveal low-dimensional structure from high-dimensional data that reflect these interactions. These techniques can uncover new biological knowledge from diverse high-throughput omics data in applications ranging from pathway discovery to timecourse analysis. We review exemplary applications of MF for systems-level analyses. We discuss appropriate applications of these methods, their limitations, and focus on the analysis of results to facilitate optimal biological interpretation. The inference of biologically relevant features with MF enables discovery from high-throughput data beyond the limits of current biological knowledge - answering questions from high-dimensional data that we have not yet thought to ask.

Weighted averaging in spectroscopic studies improves statistical power

Purpose

In vivo MRS is often characterized by a spectral signal‐to‐noise ratio (SNR) that varies highly between experiments. A common design for spectroscopic studies is to compare the ratio of two spectral peak amplitudes between groups, e.g. individual PCr/γ‐ATP ratios in ³¹P‐MRS. The uncertainty on this ratio is often neglected. We wished to explore this assumption.

Theory

The canonical theory for the propagation of uncertainty on the ratio of two spectral peaks and its incorporation in the Frequentist hypothesis testing framework by weighted averaging is presented.

Methods

Two retrospective re‐analyses of studies comparing spectral peak ratios and one prospective simulation were performed using both the weighted and unweighted methods.

Results

It was found that propagating uncertainty correctly improved statistical power in all cases considered, which could be used to reduce the number of subjects required to perform an MR study.

Conclusion

The variability of in vivo spectroscopy data is often accounted for by requiring it to meet an SNR threshold. A theoretically sound propagation of the variable uncertainty caused by quantifying spectra of differing SNR is therefore likely to improve the power of in vivo spectroscopy studies. Magn Reson Med 78:2082–2094, 2017. © 2017 The Authors Magnetic Resonance in Medicine published by Wiley Periodicals, Inc. on behalf of International Society for Magnetic Resonance in Medicine. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Data analysis and tissue type assignment for glioblastoma multiforme

Glioblastoma multiforme (GBM) is characterized by high infiltration. The interpretation of MRSI data, especially for GBMs, is still challenging. Unsupervised methods based on NMF by Li et al. (2013, NMR in Biomedicine) and Li et al. (2013, IEEE Transactions on Biomedical Engineering) have been proposed for glioma recognition, but the tissue types is still not well interpreted. As an extension of the previous work, a tissue type assignment method is proposed for GBMs based on the analysis of MRSI data and tissue distribution information. The tissue type assignment method uses the values from the distribution maps of all three tissue types to interpret all the information in one new map and color encodes each voxel to indicate the tissue type. Experiments carried out on in vivo MRSI data show the feasibility of the proposed method. This method provides an efficient way for GBM tissue type assignment and helps to display information of MRSI data in a way that is easy to interpret.

Pattern identification in time-course gene expression data with the CoGAPS matrix factorization

Patterns in time-course gene expression data can represent the biological processes that are active over the measured time period. However, the orthogonality constraint in standard pattern-finding algorithms, including notably principal components analysis (PCA), confounds expression changes resulting from simultaneous, non-orthogonal biological processes. Previously, we have shown that Markov chain Monte Carlo nonnegative matrix factorization algorithms are particularly adept at distinguishing such concurrent patterns. One such matrix factorization is implemented in the software package CoGAPS. We describe the application of this software and several technical considerations for identification of age-related patterns in a public, prefrontal cortex gene expression dataset.

Statistical mechanics approach to the sample deconvolution problem

In a multicellular organism different cell types express a gene in different amounts. Samples from which gene expression levels can be measured typically contain a mixture of different cell types; the resulting measurements thus give only averages over the different cell types present. Based on fluctuations in the mixture proportions from sample to sample it is in principle possible to reconstruct the underlying expression levels of each cell type: to deconvolute the sample. We use a statistical mechanics approach to the problem of deconvoluting such partial concentrations from mixed samples, explore this approach using Markov chain Monte Carlo simulations, and give analytical results for when and how well samples can be unmixed.

Hierarchical non-negative matrix factorization (hNMF): a tissue pattern differentiation method for glioblastoma multiforme diagnosis using MRSI

MRSI has shown potential in the diagnosis and prognosis of glioblastoma multiforme (GBM) brain tumors, but its use is limited by difficult data interpretation. When the analyzed MRSI data present more than two tissue patterns, conventional non-negative matrix factorization (NMF) implementation may lead to a non-robust estimation. The aim of this article is to introduce an effective approach for the differentiation of GBM tissue patterns using MRSI data. A hierarchical non-negative matrix factorization (hNMF) method that can blindly separate the most important spectral sources in short-TE ¹H MRSI data is proposed. This algorithm consists of several levels of NMF, where only two tissue patterns are computed at each level. The method is demonstrated on both simulated and in vivo short-TE ¹H MRSI data in patients with GBM. For the in vivo study, the accuracy of the recovered spectral sources was validated using expert knowledge. Results show that hNMF is able to accurately estimate the three tissue patterns present in the tumoral and peritumoral area of a GBM, i.e. normal, tumor and necrosis, thus providing additional useful information that can help in the diagnosis of GBM. Moreover, the hNMF results can be displayed as easily interpretable maps showing the contribution of each tissue pattern to each voxel.

Recovery of Metabolomic Spectral Sources using Non-negative Matrix Factorization

¹H magnetic resonance spectra (MRS) of biofluids contain rich biochemical information about the metabolic status of an organism. Through the application of pattern recognition and classification algorithms, such data have been shown to provide information for disease diagnosis as well as the effects of potential therapeutics. In this paper we describe a novel approach, using non-negative matrix factorization (NMF), for rapidly identifying metabolically meaningful spectral patterns in¹H MRS. We show that the intensities of these identified spectral patterns can be related to the onset of, and recovery from, toxicity in both a time-related and dose-related fashion. These patterns can be seen as a new type of biomarker for the biological effect under study. We demonstrate, using k-means clustering, that the recovered patterns can be used to characterize the metabolic status of the animal during the experiment.

Matrix Factorization for Transcriptional Regulatory Network Inference

Inference of Transcriptional Regulatory Networks (TRNs) provides insight into the mechanisms driving biological systems, especially mammalian development and disease. Many techniques have been developed for TRN estimation from indirect biochemical measurements. Although successful when initially tested in model organisms, these regulatory models often fail when applied to data from multicellular organisms where multiple regulation and gene reuse increase dramatically. Non-negative matrix factorization techniques were initially introduced to find non-orthogonal patterns in data, making them ideal techniques for inference in cases of multiple regulation. We review these techniques and their application to TRN analysis.

Application of genomic and proteomic technologies in biomarker discovery

Sequencing of the human genome was completed in 2001. Building on the technology and experience of whole-exome sequencing, numerous cancer genomes have been sequenced, including head and neck squamous cell carcinoma (HNSCC) in 2011. Although DNA sequencing data reveals a complex genome with numerous mutations, the biologic interaction and clinical significance of the overall genetic aberrations are largely unknown. Comprehensive analyses of the tumors using genomics and proteomics beyond sequencing data can potentially accelerate the rate and number of biomarker discoveries to improve biology-driven classification of tumors for prognosis and patient selection for a specific therapy. In this review, we will summarize the current genomic and proteomic technologies, general biomarker-discovery paradigms using the technology and published data in HNSCC-including potential clinical applications and limitations.

MetaboHunter: an automatic approach for identification of metabolites from 1H-NMR spectra of complex mixtures

BACKGROUND

One-dimensional 1H-NMR spectroscopy is widely used for high-throughput characterization of metabolites in complex biological mixtures. However, the accurate identification of individual compounds is still a challenging task, particularly in spectral regions with higher peak densities. The need for automatic tools to facilitate and further improve the accuracy of such tasks, while using increasingly larger reference spectral libraries becomes a priority of current metabolomics research.

RESULTS

We introduce a web server application, called MetaboHunter, which can be used for automatic assignment of 1H-NMR spectra of metabolites. MetaboHunter provides methods for automatic metabolite identification based on spectra or peak lists with three different search methods and with possibility for peak drift in a user defined spectral range. The assignment is performed using as reference libraries manually curated data from two major publicly available databases of NMR metabolite standard measurements (HMDB and MMCD). Tests using a variety of synthetic and experimental spectra of single and multi metabolite mixtures show that MetaboHunter is able to identify, in average, more than 80% of detectable metabolites from spectra of synthetic mixtures and more than 50% from spectra corresponding to experimental mixtures. This work also suggests that better scoring functions improve by more than 30% the performance of MetaboHunter's metabolite identification methods.

CONCLUSIONS

MetaboHunter is a freely accessible, easy to use and user friendly 1H-NMR-based web server application that provides efficient data input and pre-processing, flexible parameter settings, fast and automatic metabolite fingerprinting and results visualization via intuitive plotting and compound peak hit maps. Compared to other published and freely accessible metabolomics tools, MetaboHunter implements three efficient methods to search for metabolites in manually curated data from two reference libraries.

Identification and quantification of metabolites in (1)H NMR spectra by Bayesian model selection

MOTIVATION

Nuclear magnetic resonance (NMR) spectroscopy is widely used for high-throughput characterization of metabolites in complex biological mixtures. However, accurate interpretation of the spectra in terms of identities and abundances of metabolites can be challenging, in particular in crowded regions with heavy peak overlap. Although a number of computational approaches for this task have recently been proposed, they are not entirely satisfactory in either accuracy or extent of automation.

RESULTS

We introduce a probabilistic approach Bayesian Quantification (BQuant), for fully automated database-based identification and quantification of metabolites in local regions of (1)H NMR spectra. The approach represents the spectra as mixtures of reference profiles from a database, and infers the identities and the abundances of metabolites by Bayesian model selection. We show using a simulated dataset, a spike-in experiment and a metabolomic investigation of plasma samples that BQuant outperforms the available automated alternatives in accuracy for both identification and quantification.

AVAILABILITY

The R package BQuant is available at: http://www.stat.purdue.edu/~ovitek/BQuant-Web/.

CoGAPS: an R/C++ package to identify patterns and biological process activity in transcriptomic data

SUMMARY

Coordinated Gene Activity in Pattern Sets (CoGAPS) provides an integrated package for isolating gene expression driven by a biological process, enhancing inference of biological processes from transcriptomic data. CoGAPS improves on other enrichment measurement methods by combining a Markov chain Monte Carlo (MCMC) matrix factorization algorithm (GAPS) with a threshold-independent statistic inferring activity on gene sets. The software is provided as open source C++ code built on top of JAGS software with an R interface.

AVAILABILITY

The R package CoGAPS and the C++ package GAPS-JAGS are provided open source under the GNU Lesser Public License (GLPL) with a users manual containing installation and operating instructions. CoGAPS is available through Bioconductor and depends on the rjags package available through CRAN to interface CoGAPS with GAPS-JAGS. URL: http://www.cancerbiostats.onc.jhmi.edu/cogaps.cfm .

Nonnegative matrix factorization with Gaussian process priors

We present a general method for including prior knowledge in a nonnegative matrix factorization (NMF), based on Gaussian process priors. We assume that the nonnegative factors in the NMF are linked by a strictly increasing function to an underlying Gaussian process specified by its covariance function. This allows us to find NMF decompositions that agree with our prior knowledge of the distribution of the factors, such as sparseness, smoothness, and symmetries. The method is demonstrated with an example from chemical shift brain imaging.

Matrix factorisation methods applied in microarray data analysis

Numerous methods have been applied to microarray data to group genes into clusters that show similar expression patterns. These methods assign each gene to a single group, which does not reflect the widely held view among biologists that most, if not all, genes in eukaryotes are involved in multiple biological processes and therefore will be multiply regulated. Here, we review several methods of matrix factorisation that identify patterns of behaviour in transcriptional response and assign genes to multiple patterns. We focus on these methods rather than traditional clustering methods applied to microarray data, which assign one gene to one cluster.

Knowledge-based data analysis comes of age

The emergence of high-throughput technologies for measuring biological systems has introduced problems for data interpretation that must be addressed for proper inference. First, analysis techniques need to be matched to the biological system, reflecting in their mathematical structure the underlying behavior being studied. When this is not done, mathematical techniques will generate answers, but the values and reliability estimates may not accurately reflect the biology. Second, analysis approaches must address the vast excess in variables measured (e.g. transcript levels of genes) over the number of samples (e.g. tumors, time points), known as the 'large-p, small-n' problem. In large-p, small-n paradigms, standard statistical techniques generally fail, and computational learning algorithms are prone to overfit the data. Here we review the emergence of techniques that match mathematical structure to the biology, the use of integrated data and prior knowledge to guide statistical analysis, and the recent emergence of analysis approaches utilizing simple biological models. We show that novel biological insights have been gained using these techniques.

Detection of treatment-induced changes in signaling pathways in gastrointestinal stromal tumors using transcriptomic data

Cell signaling plays a central role in the etiology of cancer. Numerous therapeutics in use or under development target signaling proteins; however, off-target effects often limit assignment of positive clinical response to the intended target. As direct measurements of signaling protein activity are not generally feasible during treatment, there is a need for more powerful methods to determine if therapeutics inhibit their targets and when off-target effects occur. We have used the Bayesian Decomposition algorithm and data on transcriptional regulation to create a novel methodology, Differential Expression for Signaling Determination (DESIDE), for inferring signaling activity from microarray measurements. We applied DESIDE to deduce signaling activity in gastrointestinal stromal tumor cell lines treated with the targeted therapeutic imatinib mesylate (Gleevec). We detected the expected reduced activity in the KIT pathway, as well as unexpected changes in the p53 pathway. Pursuing these findings, we have determined that imatinib-induced DNA damage is responsible for the increased activity of p53, identifying a novel off-target activity for this drug. We then used DESIDE on data from resected, post-imatinib treatment tumor samples and identified a pattern in these tumors similar to that at late time points in the cell lines, and this pattern correlated with initial clinical response. The pattern showed increased activity of ETS domain-containing protein Elk-1 and signal transducers and activators of transcription 3 transcription factors, which are associated with the growth of side population cells. DESIDE infers the global reprogramming of signaling networks during treatment, permitting treatment modification that leverages ongoing drug development efforts, which is crucial for personalized medicine.

Matrix factorization for recovery of biological processes from microarray data

We explore a number of matrix factorization methods in terms of their ability to identify signatures of biological processes in a large gene expression study. We focus on the ability of these methods to find signatures in terms of gene ontology enhancement and on the interpretation of these signatures in the samples. Two Bayesian approaches, Bayesian Decomposition (BD) and Bayesian Factor Regression Modeling (BFRM), perform best. Differences in the strength of the signatures between the samples suggest that BD will be most useful for systems modeling and BFRM for biomarker discovery.

Automated tissue segmentation and blind recovery of (1)H MRS imaging spectral patterns of normal and diseased human brain

Constrained non-negative matrix factorization (cNMF) with iterative data selection is described and demonstrated as a data analysis method for fast and automatic recovery of biochemically meaningful and diagnostically specific spectral patterns of the human brain from (1)H MRS imaging ((1)H MRSI) data. To achieve this goal, cNMF decomposes in vivo multidimensional (1)H MRSI data into two non-negative matrices representing (a) the underlying tissue-specific spectral patterns and (b) the spatial distribution of the corresponding metabolite concentrations. Central to the proposed approach is automatic iterative data selection which uses prior knowledge about the spatial distribution of the spectra to remove voxels that are due to artifacts and undesired metabolites/tissues such as the strong lipid and water components. The automatic recovery of diagnostic spectral patterns is demonstrated for long-TE (1)H MRSI data on normal human brain, multiple sclerosis, and serial brain tumor. The results show the ability of cNMF with iterative data selection to automatically and simultaneously recover tissue-specific spectral patterns and achieve segmentation of normal and diseased human brain tissue, concomitant with simplification of information content. These features of cNMF, which permit rapid recovery, reduction and interpretation of the complex diagnostic information content of large multi-dimensional spectroscopic imaging data sets, have the potential to enhance the clinical utility of in vivo(1)H MRSI.

A novel Bayesian approach to quantify clinical variables and to determine their spectroscopic counterparts in 1H NMR metabonomic data

BACKGROUND

A key challenge in metabonomics is to uncover quantitative associations between multidimensional spectroscopic data and biochemical measures used for disease risk assessment and diagnostics. Here we focus on clinically relevant estimation of lipoprotein lipids by 1H NMR spectroscopy of serum.

RESULTS

A Bayesian methodology, with a biochemical motivation, is presented for a real 1H NMR metabonomics data set of 75 serum samples. Lipoprotein lipid concentrations were independently obtained for these samples via ultracentrifugation and specific biochemical assays. The Bayesian models were constructed by Markov chain Monte Carlo (MCMC) and they showed remarkably good quantitative performance, the predictive R-values being 0.985 for the very low density lipoprotein triglycerides (VLDL-TG), 0.787 for the intermediate, 0.943 for the low, and 0.933 for the high density lipoprotein cholesterol (IDL-C, LDL-C and HDL-C, respectively). The modelling produced a kernel-based reformulation of the data, the parameters of which coincided with the well-known biochemical characteristics of the 1H NMR spectra; particularly for VLDL-TG and HDL-C the Bayesian methodology was able to clearly identify the most characteristic resonances within the heavily overlapping information in the spectra. For IDL-C and LDL-C the resulting model kernels were more complex than those for VLDL-TG and HDL-C, probably reflecting the severe overlap of the IDL and LDL resonances in the 1H NMR spectra.

CONCLUSION

The systematic use of Bayesian MCMC analysis is computationally demanding. Nevertheless, the combination of high-quality quantification and the biochemical rationale of the resulting models is expected to be useful in the field of metabonomics.

Gene function inference from gene expression of deletion mutants

Expression data from knockout mutants is a powerful tool for gene function inference, permitting observation of the phenotype of a deleted gene on the organismal scale. A computational method is demonstrated herein to assess gene function from gene expression measured in deletion mutants using Bayesian decomposition, a matrix factorization technique that permits the extraction of patterns and functional units from the data, i.e., sets of genes belonging to the same pathways shared by sets of knockout mutants. ClutrFree, a cluster visualization program is used to aid in the interpretation of functional units and the assessment of gene functions for a subset of unknown genes.

MACHINE LEARNING FOR DETECTION AND DIAGNOSIS OF DISEASE

Machine learning offers a principled approach for developing sophisticated, automatic, and objective algorithms for analysis of high-dimensional and multimodal biomedical data. This review focuses on several advances in the state of the art that have shown promise in improving detection, diagnosis, and therapeutic monitoring of disease. Key in the advancement has been the development of a more in-depth understanding and theoretical analysis of critical issues related to algorithmic construction and learning theory. These include trade-offs for maximizing generalization performance, use of physically realistic constraints, and incorporation of prior knowledge and uncertainty. The review describes recent developments in machine learning, focusing on supervised and unsupervised linear methods and Bayesian inference, which have made significant impacts in the detection and diagnosis of disease in biomedicine. We describe the different methodologies and, for each, provide examples of their application to specific domains in biomedical diagnostics.

Determination of strongly overlapping signaling activity from microarray data

BACKGROUND

As numerous diseases involve errors in signal transduction, modern therapeutics often target proteins involved in cellular signaling. Interpretation of the activity of signaling pathways during disease development or therapeutic intervention would assist in drug development, design of therapy, and target identification. Microarrays provide a global measure of cellular response, however linking these responses to signaling pathways requires an analytic approach tuned to the underlying biology. An ongoing issue in pattern recognition in microarrays has been how to determine the number of patterns (or clusters) to use for data interpretation, and this is a critical issue as measures of statistical significance in gene ontology or pathways rely on proper separation of genes into groups.

RESULTS

Here we introduce a method relying on gene annotation coupled to decompositional analysis of global gene expression data that allows us to estimate specific activity on strongly coupled signaling pathways and, in some cases, activity of specific signaling proteins. We demonstrate the technique using the Rosetta yeast deletion mutant data set, decompositional analysis by Bayesian Decomposition, and annotation analysis using ClutrFree. We determined from measurements of gene persistence in patterns across multiple potential dimensionalities that 15 basis vectors provides the correct dimensionality for interpreting the data. Using gene ontology and data on gene regulation in the Saccharomyces Genome Database, we identified the transcriptional signatures of several cellular processes in yeast, including cell wall creation, ribosomal disruption, chemical blocking of protein synthesis, and, critically, individual signatures of the strongly coupled mating and filamentation pathways.

CONCLUSION

This works demonstrates that microarray data can provide downstream indicators of pathway activity either through use of gene ontology or transcription factor databases. This can be used to investigate the specificity and success of targeted therapeutics as well as to elucidate signaling activity in normal and disease processes.

Bayesian decomposition analysis of bacterial phylogenomic profiles

BACKGROUND

The past two decades have seen the appearance of new infectious diseases and the reemergence of old diseases previously thought to be under control. At the same time, the effectiveness of the existing antibacterials is rapidly decreasing due to the spread of multidrug-resistant pathogens.

AIM

The aim of this study was to the identify candidate molecular targets (e.g. enzymes) within essential metabolic pathways specific to a significant subset of bacterial pathogens as the first step in the rational design of new antibacterial drugs.

METHODS

We constructed a dataset of phylogenomic profiles (vectors that encode the similarity, measured by BLAST scores, of a gene across many species) for a series of 31 pathogenic bacteria of interest with 1073 genes taken from the reference organisms Escherichia coli and Mycobacterium tuberculosis. We applied Bayesian Decomposition, a matrix decomposition algorithm, to identify functional metabolic units comprising overlapping sets of genes in this dataset.

RESULTS

Although no information on phylogeny was provided to the system, Bayesian Decomposition retrieved the known bacteria phylogenic relationships on the basis of the proteins necessary for survival. In addition, a set of genes required by all bacteria was identified, as well as components and enzymes specific to subsets of bacteria.

CONCLUSION

The use of phylogenomic profiles and Bayesian Decomposition provide important insights for the design of new antibacterial therapeutics.

Nonnegative matrix factorization for rapid recovery of constituent spectra in magnetic resonance chemical shift imaging of the brain

We present an algorithm for blindly recovering constituent source spectra from magnetic resonance (MR) chemical shift imaging (CSI) of the human brain. The algorithm, which we call constrained nonnegative matrix factorization (cNMF), does not enforce independence or sparsity, instead only requiring the source and mixing matrices to be nonnegative. It is based on the nonnegative matrix factorization (NMF) algorithm, extending it to include a constraint on the positivity of the amplitudes of the recovered spectra. This constraint enables recovery of physically meaningful spectra even in the presence of noise that causes a significant number of the observation amplitudes to be negative. We demonstrate and characterize the algorithm's performance using 31P volumetric brain data, comparing the results with two different blind source separation methods: Bayesian spectral decomposition (BSD) and nonnegative sparse coding (NNSC). We then incorporate the cNMF algorithm into a hierarchical decomposition framework, showing that it can be used to recover tissue-specific spectra given a processing hierarchy that proceeds coarse-to-fine. We demonstrate the hierarchical procedure on 1H brain data and conclude that the computational efficiency of the algorithm makes it well-suited for use in diagnostic work-up.

Bayesian decomposition: analyzing microarray data within a biological context

The detection and correct identification of cancer, especially at an early stage, are vitally important for patient survival and quality of life. Since signaling pathways play critical roles in cancer development and metastasis, methods that reliably assess the activity of these pathways are critical to understand cancer and the response to therapy. Bayesian Decomposition (BD) identifies signatures of expression that can be linked directly to signaling pathway activity, allowing the changes in mRNA levels to be used as downstream indicators of pathway activity. Here, we demonstrate this ability by identifying the downstream expression signal associated with the mating response in Saccharomyces cerevisiae and showing that this signal disappears in deletion mutants of genes critical to the MAPK signaling cascade used to trigger the response. We also show the use of BD in the context of supervised learning, by analyzing the Mus musculus tissue-specific data set provided by Project Normal. The algorithm correctly removes routine metabolic processes, allowing tissue-specific signatures of expression to be identified. Gene ontology is used to interpret these signatures. Since a number of modern therapeutics specifically target signaling proteins, it is important to be able to identify changes in signaling pathways in order to use microarray data to interpret cancer response. By removing routine metabolic signatures and linking specific signatures to signaling pathway activity, BD makes it possible to link changes in microarray results to signaling pathways.

Independent component analysis for automated decomposition of in vivo magnetic resonance spectra

Fully automated methods for analyzing MR spectra would be of great benefit for clinical diagnosis, in particular for the extraction of relevant information from large databases for subsequent pattern recognition analysis. Independent component analysis (ICA) provides a means of decomposing signals into their constituent components. This work investigates the use of ICA for automatically extracting features from in vivo MR spectra. After its limits are assessed on artificial data, the method is applied to a set of brain tumor spectra. ICA automatically, and in an unsupervised fashion, decomposes the signals into interpretable components. Moreover, the spectral decomposition achieved by the ICA leads to the separation of some tissue types, which confirms the biochemical relevance of the components.

NMR spectral quantitation by principal component analysis

The use of principal component analysis (PCA) for simultaneous spectral quantitation of a single resonant peak across a series of spectra has gained popularity among the NMR community. The approach is fast, requires no assumptions regarding the peak lineshape and provides quantitation even for peaks with very low signal-to-noise ratio. PCA produces estimates of all peak parameters: area, frequency, phase and linewidth. If desired, these estimates can be used to correct the original data so that the peak in all spectra has the same lineshape. This ability makes PCA useful not only for direct peak quantitation, but also for processing spectral data prior to application of pattern recognition/classification techniques. This article briefly reviews the theoretical basis of PCA for spectral quantitation, addresses issues of data processing prior to PCA, describes suitable and unsuitable datasets for PCA applications and summarizes the developments and the limitations of the method.

A multiscale approach for analyzing in vivo spectroscopic imaging data

A multiscale approach for analyzing in vivo magnetic resonance spectroscopic imaging (SI) data is described in this paper. With this method, fitting is performed at multiple spatial scales in a coarse-to-fine order. Results obtained at one scale are used as prior knowledge in fitting spectra at the next scale. The multiscale approach was validated with simulated data and demonstrated with proton SI datasets of the human brains. The results showed that this method improved the robustness and efficiency of the fitting and facilitated the automatic analysis of in vivo SI data.