New Research In
Physical Sciences
Social Sciences
Featured Portals
Articles by Topic
Biological Sciences
Featured Portals
Articles by Topic
 Agricultural Sciences
 Anthropology
 Applied Biological Sciences
 Biochemistry
 Biophysics and Computational Biology
 Cell Biology
 Developmental Biology
 Ecology
 Environmental Sciences
 Evolution
 Genetics
 Immunology and Inflammation
 Medical Sciences
 Microbiology
 Neuroscience
 Pharmacology
 Physiology
 Plant Biology
 Population Biology
 Psychological and Cognitive Sciences
 Sustainability Science
 Systems Biology
Metagenes and molecular pattern discovery using matrix factorization

Communicated by Eric S. Lander, Massachusetts Institute of Technology, Cambridge, MA, December 20, 2003 (received for review November 1, 2003)
Abstract
We describe here the use of nonnegative matrix factorization (NMF), an algorithm based on decomposition by parts that can reduce the dimension of expression data from thousands of genes to a handful of metagenes. Coupled with a model selection mechanism, adapted to work for any stochastic clustering algorithm, NMF is an efficient method for identification of distinct molecular patterns and provides a powerful method for class discovery. We demonstrate the ability of NMF to recover meaningful biological information from cancerrelated microarray data. NMF appears to have advantages over other methods such as hierarchical clustering or selforganizing maps. We found it less sensitive to a priori selection of genes or initial conditions and able to detect alternative or contextdependent patterns of gene expression in complex biological systems. This ability, similar to semantic polysemy in text, provides a general method for robust molecular pattern discovery.
With the advent of DNA microarrays, it is now possible to simultaneously monitor expression of all genes in the genome. Increasingly, the challenge is to interpret such data to gain insight into biological processes and the mechanisms of human disease.
Various methods have been developed for clustering genes or samples that show similar expression patterns (1–5). However, these methods have serious limitations in their ability to capture the full structure inherent in the data. They typically focus on the predominant structures in a data set and fail to capture alternative structures and local behavior.
Hierarchical clustering (HC) is a frequently used and valuable approach. It has been successfully used to analyze temporal expression patterns (1), to predict patient outcome among lymphoma patients (2), and to provide molecular portraits of breast tumors (3). However, HC has the disadvantages that it imposes a stringent tree structure on the data, is highly sensitive to the metric used to assess similarity, and typically requires subjective evaluation to define clusters. Selforganizing maps (SOM) provide another powerful approach (4). They have been successfully used in similar applications, including identification of pathways involved in differentiation of hematopoietic cells and recognition of subtypes of leukemia (5). SOMs, however, can be unstable, yielding different decompositions of the data depending on the choice of initial conditions. Recently, various dimensionality reduction and matrix decomposition methods have been introduced (6–8). However, many questions remain to be resolved about such methods. These include the key issue of model selection (that is, how to select the dimensionality of the reduced representation) and the accuracy and robustness of the representation.
Here, we describe a technique for extracting relevant biological correlations, or “molecular logic,” in gene expression data. The method is designed to capture alternative structures inherent in the data and, by organizing both the genes and samples, to provide biological insight. The method is based on nonnegative matrix factorization (NMF). Lee and Seung (9) introduced NMF in its modern formulation as a method to decompose images. In this context, NMF yielded a decomposition of human faces into parts reminiscent of features such as eyes, nose, etc. By contrast, they noted that the application of traditional factorization methods, such as principal component analysis, to image data yielded components with no obvious visual interpretation. When applied to text, NMF gave some evidence of differentiating meanings of the same word depending on context (semantic polysemy) (9).
Here, we use NMF to describe the tens of thousands of genes in a genome in terms of a small number of metagenes. Samples can then be analyzed by summarizing their gene expression patterns in terms of expression patterns of the metagenes. The metagenes provide an interesting decomposition of genes, analogous to facial features in Lee and Seung's work (9) on images. The metagene expression patterns provide a robust clustering of samples. Importantly, we also introduce a methodology for model selection that highlights alternative decompositions and assesses their robustness.
We apply NMF and our model selection criterion to the problem of elucidating cancer subtypes by clustering tumor samples. We are able to demonstrate multiple robust decompositions of leukemia and brain cancer data sets.
Methods
Description of NMF Method. We consider a data set consisting of the expression levels of N genes in M samples (which may represent distinct tissues, experiments, or time points). For gene expression studies, the number N of genes is typically in the thousands, and the number M of experiments is typically <100. The data are represented by an expression matrix A of size N × M, whose rows contain the expression levels of the N genes in the M samples.
Our goal is to find a small number of metagenes, each defined as a positive linear combination of the N genes. We can then approximate the gene expression pattern of samples as positive linear combinations of these metagenes.
Mathematically, this corresponds to factoring matrix A into two matrices with positive entries, A ∼ WH. Matrix W has size N × k, with each of the k columns defining a metagene; entry w_{ij} is the coefficient of gene i in metagene j. Matrix H has size k × M, with each of the M columns representing the metagene expression pattern of the corresponding sample; entry h_{ij} represents the expression level of metagene i in sample j. Fig. 1 shows the simple case corresponding to k = 2.
Given a factorization A ∼ WH, we can use matrix H to group the M samples into k clusters. Each sample is placed into a cluster corresponding to the most highly expressed metagene in the sample; that is, sample j is placed in cluster i if the h_{ij} is the largest entry in column j (Fig. 1).
We note that there is a dual view of decomposition A ∼ WH, which defines metasamples (rather than metagenes) and clusters the genes (rather than the samples) according to the entries of W. We do not focus on this view here, but it is clearly of great interest.
NMF provides a natural way to cluster genes and samples, because it involves factorization into matrices with nonnegative entries. By contrast, principal component analysis provides a simple way to reduce dimensionality but requires that the matrices be orthogonal, which typically requires linear combination of components with arbitrary signs. NMF is more difficult algorithmically because of the nonnegativity requirement but provides a more intuitive decomposition of the data.
NMF Algorithm. Given a positive matrix A of size N × M and a desired rank k, the NMF algorithm iteratively computes an approximation A ∼ WH, where W and H are nonnegative matrices with respective sizes N × k and k × M. The method starts by randomly initializing matrices W and H, which are iteratively updated to minimize a divergence functional. The functional is related to the Poisson likelihood of generating A from W and H, D = Σ_{i}_{,}_{j} A_{i}_{,}_{j}log(A_{i}_{,}_{j}/(WH)_{i}_{,}_{j}) – A_{i}_{,}_{j} + (WH)_{i}_{,}_{j}. At each step, W and H are updated by using the coupled divergence equations (10): A simpler version of the NMF update equations that minimizes the norm of the residual AWH^{2} has also been derived in ref. 10. When applying the method to a medulloblastoma dataset (see Results), where we knew the underlying substructure, we observed that the divergencebased update equations were able to capture a subclass that the normbased update equations did not. This is why our implementation of NMF uses the divergence form (see Data Sets and software).
Model Selection. For any rank k, the NMF algorithm groups the samples into clusters. The key issue is to tell whether a given rank k decomposes the samples into “meaningful” clusters. For this purpose, we developed an approach to model selection that exploits the stochastic nature of the NMF algorithm. It is based on our group's previous work on consensus clustering (11) but adds a quantitative evaluation for robustness of the decomposition.
The NMF algorithm may or may not converge to the same solution on each run, depending on the random initial conditions. If a clustering into k classes is strong, we would expect that sample assignment to clusters would vary little from run to run. (Note that sample assignment depends only on the relative values in each column of H.)
For each run, the sample assignment can be defined by a connectivity matrix C of size M × M, with entry c_{ij} = 1 if samples i and j belong to the same cluster, and c_{ij} = 0 if they belong to different clusters. We can then compute the consensus matrix, C̄, defined as the average connectivity matrix over many clustering runs. (We select the number of runs by continuing until C̄ appears to stabilize; we typically find that 20–100 runs suffice in the applications below.) The entries of C̄ range from 0 to 1 and reflect the probability that samples i and j cluster together. If a clustering is stable, we would expect that C will tend not to vary among runs, and that the entries of C̄ will be close to 0 or 1. The dispersion between 0 and 1 thus measures the reproducibility of the class assignments with respect to random initial conditions. By using the offdiagonal entries of C̄ as a measure of similarity among samples, we can use average linkage HC to reorder the samples and thus the rows and columns of C̄.
We then evaluate the stability of clustering associated with a given rank k. Although visual inspection of the reordered matrix C̄ can provide substantial insight (see Fig. 3), it is important to have quantitative measure of stability for each value of k. We propose a measure based on the cophenetic correlation coefficient, ρ_{k}(C̄), which indicates the dispersion of the consensus matrix C̄. ρ_{k} is computed as the Pearson correlation of two distance matrices: the first, IC̄, is the distance between samples induced by the consensus matrix, and the second is the distance between samples induced by the linkage used in the reordering of C̄. In a perfect consensus matrix (all entries = 0 or 1), the cophenetic correlation coefficient equals 1. When the entries are scattered between 0 and 1, the cophenetic correlation coefficient is <1. We observe how ρ_{k} changes as k increases. We select values of k where the magnitude of the cophenetic correlation coefficient begins to fall (see below).
Results
We illustrate the use of NMF and our model selection criteria with three problems in elucidating cancer subtypes. The first involves acute leukemia, the second medulloblastoma, and the third a collection of central nervous system tumors.
Leukemia Data Set. The distinction between acute myelogenous leukemia (AML) and acute lymphoblastic leukemia (ALL), as well as the division of ALL into T and B cell subtypes, is well known. In an early gene expression analysis of cancer (5), we explored how SOM could rediscover these distinctions in a data set of 38 bone marrow samples (12). Here, we reuse this data set to compare various clustering methods with respect to their efficacy and stability in recovering these three subtypes and their hierarchy. We note that this data set has become a benchmark in the cancer classification community. It contains two ALL samples that are consistently misclassified or classified with low confidence by most methods. There are a number of possible explanations for this, including incorrect diagnosis of the samples. We have included them in our analysis but expect them to behave as outliers.
We first applied HC to the leukemia data. The tree structure produced by HC depends on the choice of linkage metric used to determine which groups of data points to join as the tree, or dendrogram, is constructed from the leaves upward. We used two metrics: the average linkage and averagegroup or centroid linkage methods. Given a tree, we obtained two clusters by cutting the tree at its top branching point. To test the stability of the clusters, we ran HC for various numbers of input genes.
HC proved unstable in that its performance varied substantially with respect to the number of input genes (Fig. 2). It correctly found the AML–ALL distinction only when using the average linkage metric and only in the range of 1,800–3,200 input genes (the only incorrect assignments involve one of the known outlier samples). We then examined whether the tree correctly found the next important distinction: between ALLT and B. In fact, inspection of the trees for various numbers of genes showed that ALLT, ALLB, and AML samples tend to be intermingled at lower levels, and that ALLB samples split into two groups in a more or less consistent fashion. For example, at n = 3,000 input genes (see supporting information, which is published on the PNAS web site), looking further down the tree, the ALL branch splits into two groups, with one group containing only B cell samples and the other containing B and T cell samples. The latter group finally splits at the next level into a B and a T cell group (exposing a second B cell subclass). Thus, the distinction between ALLB and T is not recovered a priori, inasmuch as the B cells never appear together by themselves in one branch.
We next examined the stability of SOM, which (like NMF) are defined by a stochastic procedure depending on initial conditions. We have previously shown SOM are capable of distinguishing between AML and ALL (5). However, the consensus matrix for the SOM with k = 2 classes reveals the classification is not stable. Depending on the initial conditions, SOM may split the data as [AML] vs. [ALLT + ALLB] or as [AML + ALLT] vs. [ALLB]. This ambiguity is reflected in an interference pattern in the consensus matrix (Fig. 3a). The metastability can be illustrated by a doublewell potential; the SOM follows one of the two trajectories depending on the initial conditions.
We might conjecture that a SOM with k = 3 classes would distinguish ALLT and B, but it does not. Instead, a similar metastable situation arises (see supporting information). Rather than converging only to the expected threeclass partition (ALLT, ALLB, AML), SOM also finds another minimum in which B and T cell ALL are mixed. As a result, the leukemias cannot be robustly clustered into the three main biological classes by a SOM with k = 3 classes. Only with four classes can SOM distinguish ALLT and B, with the latter split into two groups as we previously reported (5).
We then applied NMF to the data set. With rank k = 2, NMF consistently recovered the ALLAML biological distinction with high accuracy and robustness, with respect to the number of features or genes (Fig. 2). Moreover, NMF always converges toward the same attractor, ALLAML, regardless of initial condition (Fig. 3b).
Higher ranks k reveal further partitioning of the samples. Fig. 4a shows the consensus matrices generated for ranks k = 2, 3, 4, 5. Clear block diagonal patterns attest to the robustness of models with 2, 3, and 4 classes, whereas a rank5 factorization shows increased dispersion. This qualitative observation is reflected quantitatively in the decreased value of the cophenetic correlation ρ_{4} (Fig. 4b).
The clusters show a nested structure as k increases from 2 to 4, and the nesting captures the known subtypes. For k = 2, the classes correspond to ALL and AML samples. For k = 3, the partition reflects the ALLT and B distinction within the ALL class. For k = 4, a fourth class appears which is deemed robust by our model selection; its biological significance is unclear.
NMF has a number of strengths compared to HC and SOM in these studies. NMF appears to be more stable than HC with respect to the number of features or genes in the data set. It appears to be more stable than SOM in finding two clusters and in showing robust convergence to the three known biological classes for rank 3. Finally, NMF best elucidated the nested substructure of the data.
Medulloblastoma Data Set. We next analyzed gene expression data from childhood brain tumors known as medulloblastomas. The pathogenesis of these tumors is not well understood, but it is generally accepted that there are two known histological subclasses: classic and desmoplastic, whose differences can clearly be seen under the microscope. In previous work, we found genes whose expression was statistically correlated with those two histological classes (13).
We applied both HC and SOM to these data to see whether the desmoplastic subclass ever cleanly clustered by itself. Fig. 5 shows the dendrogram of the hierarchical structure obtained for the medulloblastoma data set. The desmoplastic samples are scattered among the leaves. There is no level of the tree where we can split the branches and expose a clear desmoplastic cluster. We applied SOM to the same data by using two to eight centroids and again were unable to find a distinct desmoplastic class.
When we applied NMF to the medulloblastoma data, we were able to expose a separate desmoplastic class. NMF predicted the existence of robust classes for k = 2, 3, and 5 (Fig. 6). The desmoplastic subtype cluster appears at k = 5, where one of the discovered classes is almost entirely made up of desmoplastic samples. Even if one were unaware of the underlying biology, this clustering would stand out because of the steep drop off in the cophenetic coefficient for k > 5. NMF sample assignments for k = 2, 3, and 5, display an approximate nesting of putative medulloblastoma classes, similar to that seen in the leukemia data set (see supporting information).
Central Nervous System Tumors. Finally, we present an analysis of four types of central nervous system embryonal tumors. The data set comes from our previous work (13) and consists of a total of 34 samples: 10 classic medulloblastomas, 10 malignant gliomas, 10 rhabdoids, and 4 normals, representing four distinct morphologies. The original paper (13) also analyzed eight samples from primitive nueroectodermal tumors; these did not form a distinct tight class or subclass using either supervised or unsupervised clustering and were not studied in this analysis.
Unsupervised HC does not give a clear fourclass split of the data (Fig. 7a). The dendrogram seems to suggest a split into two or three classes. Examining the actual tumor types, we find the split into two classes groups the normals and malignant gliomas on one branch and the medulloblastomas and rhabdoids on the other. At the next level, the medulloblastomas and rhabdoids are split in two subbranches, but the normal samples and gliomas stay largely clustered (see supporting information). The hierarchical dendrogram does not seem to suggest a preferred substructure consistent with the known four classes in the data.
SOM clustering of this data set (Fig. 7b) indicates that a threecentroid clustering is the most robust, with the highest cophenetic coefficient. As in the case of HC, the normal and malignant glioma samples consistently cluster together in this case (see supporting information). The fourcentroid clustering shows instability with a corresponding drop in ρ_{k.} We do not recover the correct split into four tumor types using a SOM approach.
NMF, together with consensus clustering, gave strong evidence for a fourclass split of the data with a correspondingly high cophenetic coefficient (Fig. 7c). Examining the tumor types of the samples (see supporting information), we find that only two of them are placed in the incorrect cluster. Thus, we see that NMF gives a more accurate clustering of this data set.
Discussion
We describe here the use of NMF to reduce the dimensionality of expression data from thousands of genes to a handful of metagenes. In addition, we describe a model selection methodology based on the consensus of sample assignment across random initial conditions. Although NMF is not hierarchical per se (9), we show that as the rank k increases the method uncovers substructures, whose robustness can be evaluated by a cophenetic correlation coefficient. These substructures may also give evidence of nesting subtypes. Thus, NMF can reveal hierarchical structure when it exists but does not force such structure on the data like HC does. In addition, agglomerative techniques like HC sometimes struggle to properly merge clusters with many samples. Thus, NMF may have an advantage in exposing meaningful global hierarchy.
In application to three cancer data sets, we show that NMF is able to recover biologically significant phenotypes and identify the known nested structure of leukemia classes. The use of consensus clustering with the NMF approach makes the selection of the number of classes an objective consideration of the quantitative cophenetic coefficient rather than a subjective evaluation. In the cases studied, NMF appears to be more accurate and robust to the choice of input genes than HC and more stable than SOM.
In ref. 9, Lee and Seung observed that NMF (in contrast to principal component analysis) yields a sparse partsbased representation of data useful for the recognition of features in human faces and in text. Parts are sets of elements that tend to cooccur in samples. The parts provide components or visible variables as a reduced representation of the original hidden variables. In our application to gene expression, parts refer to metagenes representing genes that tend to be coexpressed in samples. NMF decomposes gene expression patterns as an additive combination of a few metagene patterns. Just as NMF is able to distinguish different meanings of words used in different contexts (polysemy), NMF metagenes can overlap and thus expose the participation of a single gene in multiple pathways or processes. Such context dependency is not captured by standard twoway clustering methods or by supervised marker analysis that insists on mutual exclusion of features.
Whereas the original application of NMF focused on grouping elements into parts (using the matrix W), we take the dual viewpoint by focusing primarily on grouping samples into clusters using the metagene expression profiles given by the matrix H. The utility of NMF for gene expression sample clustering stems from its nonnegativity constraint, which facilitates the detection of sharp boundaries among classes. We observed that as more NMF iterations are performed, the metagene profiles become more localized in sample space and their supports overlap less (i.e., decreasing the offdiagonal portion of HH^{t}). At the end the metagene profiles are positive, sparse, localized, and relatively independent, which makes a natural compact decomposition for interpretation. In contrast, spectral decomposition (principal component analysis or singular value decomposition) of expression data produces eigengene profiles that are completely independent but complex, dense, and globally supported.
Despite its promising features, NMF has the limitation of somewhat greater algorithmic complexity, especially compared with the simplicity of HC. This can be addressed by casting the NMF update equations in a computationally efficient matrix form. Stabilization of connectivity matrices can also be used to monitor convergence and minimize the number of NMF iterations. This forms the basis of our implementation (see Data Sets and Software)
We note that Kim and Tidor, in a recent independent study (14), have applied NMF applications to cluster genes (rather than samples) and to predict functional relationships in yeast. Heger and Holm (15) have also recently applied NMF to a different biological problem: recognition of sequence patterns among related proteins.
In summary, NMF is a powerful technique for clustering expression data and can be combined with a quantitative evaluation of the robustness of the number of clusters. When applied to data where subtypes were known, but hidden from the algorithm, it performed well and captured the hierarchical nature of the data as the number of clusters was increased. The challenge that remains is to provide a meaningful biological interpretation to the NMF discovered classes when the class labels and substructure of the data set are unknown.
Data Sets and Software. Data sets are published as supporting information. The leukemia data, containing 38 bone marrow samples hybridized on Affymetrix Hu6800 chips, is a reduced version of the original data used in ref. 5. The medulloblastoma data with 34 tumors hybridized on Affymetrix HuGeneFL is data set B from ref. 13. Codes for NMF divergence reducing equations, as well as for model selection and reordering of the consensus matrices, are provided on our website as matlab (Mathworks, Natick, MA) mfiles.
Acknowledgments
We acknowledge useful discussions with members of the Cancer Genomics program (The Eli and Edythe L. Broad Institute, Massachusetts Institute of Technology and Harvard University), in particular Stefano Monti. This work was funded by grants from the National Institutes of Health. J.Ph.B. is funded by an Informatics Fellowship grant from AstraZeneca.
Footnotes

↵‡ To whom correspondence should be addressed. Email: mesirov{at}broad.mit.edu.

Abbreviations: NMF, nonnegative matrix factorization; HC, hierarchical clustering; SOM, selforganizing maps; AML, acute myelogenous leukemia; ALL, acute lymphoblastic leukemia.
 Received November 1, 2003.
 Copyright © 2004, The National Academy of Sciences
References
 ↵
Eisen, M., Spellman, P., Brown, P. & Botstein, D. (1998) Proc. Natl. Acad. Sci. USA 95, 14863–14868.pmid:9843981
 ↵
 ↵
 ↵
Tamayo, P., Slonim, D., Mesirov, J., Zhu, Q., Dmitrovsky, E., Lander, E. S. & Golub, T. R. (1999) Proc. Natl. Acad. Sci. USA 96, 2907–2912.pmid:10077610
 ↵
Golub, T. R., Slonim, D. K., Tamayo, P., Huard, C., Gaasenbeek, M., Mesirov, J. P., Coller, H., Loh, M. L., Downing, J. R., Caligiuri, M. A., et al. (1999) Science 286, 531–537.pmid:10521349
 ↵
Moloshok, T. D., Klevecz, R. R., Grant, J. D., Manion, F. J., Speier, W. F. 4th, & Ochs, M. F. (2002) Bioinformatics 18, 566–575.pmid:12016054
 ↵
Alter, O., Brown, P. O. & Botstein, D. (2000) Proc. Natl. Acad. Sci. USA 97, 10101–10106.pmid:10963673
 ↵
 ↵
Lee, D. D. & Seung, H. S. (2001) Adv. Neural Info. Proc. Syst. 13, 556–562.
 ↵
 ↵
Slonim, D. K., Tamayo, P., Mesirov, J. P., Golub, T. R. & Lander, E. S. (2000) Proceedings of the Fourth Annual International Conference on Computational Molecular Biology, RECOMB 2000, 263–272.
 ↵
 ↵
Kim, P. M. & Tidor, B. (2003) Genome Res. 13, 1706–1718.pmid:12840046
 ↵
Citation Manager Formats
More Articles of This Classification
Biological Sciences
Genetics
Related Content
 No related articles found.
Cited by...
 Germlineactivating mutations in PIK3CD compromise B cell development and function
 Immune signatures correlate with L1 retrotransposition in gastrointestinal cancers
 Integrative analysis of singlecell genomics data by coupled nonnegative matrix factorizations
 Singlecell reconstruction of developmental trajectories during zebrafish embryogenesis
 Braintobrain coupling during handholding is associated with pain reduction
 A novel approach for data integration and disease subtyping
 Global transcriptional regulatory network for Escherichia coli robustly connects gene expression to transcription factor activities
 Pooled Clustering of HighGrade Serous Ovarian Cancer Gene Expression Leads to Novel Consensus Subtypes Associated with Survival and Surgical Outcomes
 Whats normal? Oligosaccharide concentrations and profiles in milk produced by healthy women vary geographically
 Metabolic Profiling in FormalinFixed and ParaffinEmbedded Prostate Cancer Tissues
 Patterns of coordinated cortical remodeling during adolescence and their associations with functional specialization and evolutionary expansion
 In vitro patterning of pluripotent stem cellderived intestine recapitulates in vivo human development
 Comprehensive CrossPopulation Analysis of HighGrade Serous Ovarian Cancer Supports No More Than Three Subtypes
 Recurring Functional Interactions Predict Network Architecture of Interictal and Ictal States in Neocortical Epilepsy
 Accurate and scalable social recommendation using mixedmembership stochastic block models
 Significance of TP53 Mutation in Wilms Tumors with Diffuse Anaplasia: A Report from the Children's Oncology Group
 Phosphoproteomic profiling of mouse primary HSPCs reveals new regulators of HSPC mobilization
 Integrated Classification of Prostate Cancer Reveals a Novel Luminal Subtype with Poor Outcome
 Unique and shared signaling pathways cooperate to regulate the differentiation of human CD4+ T cells into distinct effector subsets
 Stabilitydriven nonnegative matrix factorization to interpret spatial gene expression and build local gene networks
 Distinct Subtypes of Gastric Cancer Defined by Molecular Characterization Include Novel Mutational Signatures with Prognostic Capability
 A CrossSpecies Analysis in Pancreatic Neuroendocrine Tumors Reveals Molecular Subtypes with Distinctive Clinical, Metastatic, Developmental, and Metabolic Characteristics
 Methods for biological data integration: perspectives and challenges
 Interleukin6/STAT3 Pathway Signaling Drives an Inflammatory Phenotype in Group A Ependymoma
 Novel Observations From NextGeneration RNA Sequencing of Highly Purified Human Adult and Fetal Islet Cell Subsets
 Metabolite profiling stratifies pancreatic ductal adenocarcinomas into subtypes with distinct sensitivities to metabolic inhibitors
 Cooccurring Genomic Alterations Define Major Subsets of KRASMutant Lung Adenocarcinoma with Distinct Biology, Immune Profiles, and Therapeutic Vulnerabilities
 The human transcriptome across tissues and individuals
 Gene Expression Profiling Reveals Distinct Molecular Signatures Associated With the Rupture of Intracranial Aneurysm
 FANCD2 Is a Potential Therapeutic Target and Biomarker in Alveolar Rhabdomyosarcoma Harboring the PAX3FOXO1 Fusion Gene
 The expression level of small noncoding RNAs derived from the first exon of proteincoding genes is predictive of cancer status
 Fast and Efficient Estimation of Individual Ancestry Coefficients
 A glioma classification scheme based on coexpression modules of EGFR and PDGFRA
 Molecular Network Analysis of Endometriosis Reveals a Role for cJunRegulated Macrophage Activation
 The evolution of drug resistance in clinical isolates of Candida albicans
 Inferring chromatinbound protein complexes from genomewide binding assays
 Analysis of the Small RNA Transcriptional Response in MultidrugResistant Staphylococcus aureus after Antimicrobial Exposure
 Murine Microenvironment Metaprofiles Associate with Human Cancer Etiology and Intrinsic Subtypes
 An RNA Profile Identifies Two Subsets of Multiple Sclerosis Patients Differing in Disease Activity
 "Good Enough Solutions" and the Genetics of Complex Diseases
 Meiosisinduced alterations in transcript architecture and noncoding RNA expression in S. cerevisiae
 HighRisk Ovarian Cancer Based on 126Gene Expression Signature Is Uniquely Characterized by Downregulation of Antigen Presentation Pathway
 FSTL5 Is a Marker of Poor Prognosis in NonWNT/NonSHH Medulloblastoma
 Adult Medulloblastoma Comprises Three Major Molecular Variants
 Integrative Genomic Analysis of Medulloblastoma Identifies a Molecular Subgroup That Drives Poor Clinical Outcome
 Medulloblastoma Comprises Four Distinct Molecular Variants
 Making sense of cancer genomic data
 Integrative Genomics Analyses Reveal Molecularly Distinct Subgroups of BCell Chronic Lymphocytic Leukemia Patients with 13q14 Deletion
 Fusion GeneNegative Alveolar Rhabdomyosarcoma Is Clinically and Molecularly Indistinguishable From Embryonal Rhabdomyosarcoma
 Neuropeptide Y functions as a facilitator of GDNFinduced budding of the Wolffian duct
 Detection of TreatmentInduced Changes in Signaling Pathways in Gastrointestinal Stromal Tumors Using Transcriptomic Data
 Unbiased Reconstruction of a Mammalian Transcriptional Network Mediating Pathogen Responses
 Integrative Transcriptome Analysis Reveals Common Molecular Subclasses of Human Hepatocellular Carcinoma
 Automated multidimensional phenotypic profiling using large public microarray repositories
 Statistical estimation of cellcycle progression and lineage commitment in Plasmodium falciparum reveals a homogeneous pattern of transcription in ex vivo culture
 Unsupervised Analysis of Transcriptomic Profiles Reveals Six Glioma Subtypes
 Molecular Characterization of Breast Cancer with HighResolution Oligonucleotide Comparative Genomic Hybridization Array
 C. elegans sequences that control transsplicing and operon premRNA processing
 Disease Gene Candidates Revealed by Expression Profiling of Retinal Ganglion Cell Development
 Metagene projection for crossplatform, crossspecies characterization of global transcriptional states
 Marked Genomic Differences Characterize Primary and Secondary Glioblastoma Subtypes and Identify Two Distinct Molecular and Clinical Secondary Glioblastoma Entities
 Gene Expression Profiling Reveals Reproducible Human Lung Adenocarcinoma Subtypes in Multiple Independent Patient Cohorts
 Identification of prognostic signatures in breast cancer microarray data using Bayesian techniques
 Inactivation of the Snf5 tumor suppressor stimulates cell cycle progression and cooperates with p53 loss in oncogenic transformation
 Genomic approaches to hematologic malignancies