Modulated Modularity Clustering as an Exploratory Tool for Functional Genomic Inference
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{"title"=>"Modulated modularity clustering as an exploratory tool for functional genomic inference", "type"=>"journal", "authors"=>[{"first_name"=>"Eric A.", "last_name"=>"Stone", "scopus_author_id"=>"35265221900"}, {"first_name"=>"Julien F.", "last_name"=>"Ayroles", "scopus_author_id"=>"14049977200"}], "year"=>2009, "source"=>"PLoS Genetics", "identifiers"=>{"pui"=>"354733151", "pmid"=>"19424432", "scopus"=>"2-s2.0-67149122033", "sgr"=>"67149122033", "isbn"=>"1553-7390", "issn"=>"15537390", "doi"=>"10.1371/journal.pgen.1000479"}, "id"=>"06063c4e-4155-3ffe-857b-9fdc7f4f33bb", "abstract"=>"In recent years, the advent of high-throughput assays, coupled with their diminishing cost, has facilitated a systems approach to biology. As a consequence, massive amounts of data are currently being generated, requiring efficient methodology aimed at the reduction of scale. Whole-genome transcriptional profiling is a standard component of systems-level analyses, and to reduce scale and improve inference clustering genes is common. Since clustering is often the first step toward generating hypotheses, cluster quality is critical. Conversely, because the validation of cluster-driven hypotheses is indirect, it is critical that quality clusters not be obtained by subjective means. In this paper, we present a new objective-based clustering method and demonstrate that it yields high-quality results. Our method, modulated modularity clustering (MMC), seeks community structure in graphical data. MMC modulates the connection strengths of edges in a weighted graph to maximize an objective function (called modularity) that quantifies community structure. The result of this maximization is a clustering through which tightly-connected groups of vertices emerge. Our application is to systems genetics, and we quantitatively compare MMC both to the hierarchical clustering method most commonly employed and to three popular spectral clustering approaches. We further validate MMC through analyses of human and Drosophila melanogaster expression data, demonstrating that the clusters we obtain are biologically meaningful. We show MMC to be effective and suitable to applications of large scale. In light of these features, we advocate MMC as a standard tool for exploration and hypothesis generation.", "link"=>"http://www.mendeley.com/research/modulated-modularity-clustering-exploratory-tool-functional-genomic-inference", "reader_count"=>138, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>15, "Student > Doctoral Student"=>8, "Researcher"=>34, "Student > Ph. D. Student"=>43, "Student > Postgraduate"=>2, "Other"=>9, "Student > Master"=>12, "Student > Bachelor"=>5, "Lecturer"=>1, "Professor"=>9}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>15, "Student > Doctoral Student"=>8, "Researcher"=>34, "Student > Ph. D. Student"=>43, "Student > Postgraduate"=>2, "Other"=>9, "Student > Master"=>12, "Student > Bachelor"=>5, "Lecturer"=>1, "Professor"=>9}, "reader_count_by_subject_area"=>{"Unspecified"=>5, "Engineering"=>1, "Environmental Science"=>4, "Biochemistry, Genetics and Molecular Biology"=>6, "Mathematics"=>5, "Agricultural and Biological Sciences"=>96, "Medicine and Dentistry"=>4, "Neuroscience"=>1, "Physics and Astronomy"=>1, "Chemistry"=>1, "Computer Science"=>13, "Immunology and Microbiology"=>1}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>1}, "Medicine and Dentistry"=>{"Medicine and Dentistry"=>4}, "Neuroscience"=>{"Neuroscience"=>1}, "Chemistry"=>{"Chemistry"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>1}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>96}, "Computer Science"=>{"Computer Science"=>13}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>6}, "Mathematics"=>{"Mathematics"=>5}, "Unspecified"=>{"Unspecified"=>5}, "Environmental Science"=>{"Environmental Science"=>4}}, "reader_count_by_country"=>{"South Korea"=>1, "Norway"=>1, "United States"=>12, "Brazil"=>2, "United Kingdom"=>3, "France"=>3, "Germany"=>1, "Estonia"=>1, "Spain"=>1}, "group_count"=>3}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/899345"], "description"=>"<p>Five clustering methods are compared in two simulation studies. Studies are grouped by row, so that the same 10,000 simulated datasets were used to evaluate default MMC and the four remaining methods with . A second set of 10,000 datasets was used to compare the methods with . Columns 2–4 report three related measures of performance. Column 2 considers only pairs of variables that share a cluster according to <a href=\"http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1000479#pgen-1000479-g002\" target=\"_blank\">Figure 2</a> (e.g. (1, 2) but not (1, 3)) and records the percentage of such pairs that are correctly clustered together. Column 3 considers only pairs of variables that do not share a cluster and records the percentage of such pairs that are correctly placed in separate clusters. Column 4 considers all variable pairs and records the overall percentage correct. These measures are used in <a href=\"http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1000479#pgen-1000479-g004\" target=\"_blank\">Figure 4</a> as well.</p>", "links"=>[], "tags"=>["clustering", "methods", "simulated"], "article_id"=>569805, "categories"=>["Genetics", "Medicine"], "users"=>["Eric A. Stone", "Julien F. Ayroles"], "doi"=>"https://dx.doi.org/10.1371/journal.pgen.1000479.t001", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_Clustering_Methods_over_10_000_Simulated_Datasets_/569805", "title"=>"Comparison of Clustering Methods over 10,000 Simulated Datasets.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2009-05-08 02:43:25"}
  • {"files"=>["https://ndownloader.figshare.com/files/899150"], "description"=>"<p>Clustering of a set of 673 transcripts associated with HDL-C concentration; shown is the reordered matrix of pairwise correlations between transcriptional profiles. The nine clusters identified by MMC are numbered and arranged as in <a href=\"http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1000479#pgen-1000479-g005\" target=\"_blank\">Figure 5</a>.</p>", "links"=>[], "tags"=>["san", "antonio"], "article_id"=>569612, "categories"=>["Genetics", "Medicine"], "users"=>["Eric A. Stone", "Julien F. Ayroles"], "doi"=>"https://dx.doi.org/10.1371/journal.pgen.1000479.g006", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_MMC_analysis_of_data_from_the_San_Antonio_Family_Heart_Study_/569612", "title"=>"MMC analysis of data from the San Antonio Family Heart Study.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-05-08 02:40:12"}
  • {"files"=>["https://ndownloader.figshare.com/files/898894"], "description"=>"<p>Three measures of accuracy are reported for MMC as the number of observations ranges from 4 to 36 in the simulation study. Shown in red for each case is the percentage of simulations in which pairs of variables are correctly clustered. Shown in blue is the percentage of pairs correctly separated; the overall percentage correct is in black. Each point on the plot represents the results across 1,000 datasets. The scenario considered in <a href=\"http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1000479#pgen-1000479-t001\" target=\"_blank\">Table 1</a> (MMC default) is highlighted in gray.</p>", "links"=>[], "tags"=>["simulated"], "article_id"=>569361, "categories"=>["Genetics", "Medicine"], "users"=>["Eric A. Stone", "Julien F. Ayroles"], "doi"=>"https://dx.doi.org/10.1371/journal.pgen.1000479.g004", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_MMC_analysis_of_simulated_data_/569361", "title"=>"MMC analysis of simulated data.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-05-08 02:36:01"}
  • {"files"=>["https://ndownloader.figshare.com/files/898663"], "description"=>"<p>(A) A graph with 10 vertices and 22 edges. Thick black lines denote strong edges and thin dotted lines denote weak edges. The edge classes have been drawn so that the distinction between them is prominent: {1,2,3,4} and {5,6,7,8,9,10} are intuitive communities of connected vertices. (B) Ostensibly the same graph as in the previous panel, with the edge classes drawn to obscure the communities that were so prominent. (C) Depiction of the affinity matrix that corresponds to the graph in panel (A). Rows and columns denote vertices, and each (row,column) entry of the matrix is shaded to indicate the strength of its corresponding edge, if any. As drawn, the contrast between strong and weak edges is sufficient to reveal two communities as clusters of darkly shaded squares along the matrix main diagonal. (D) Depiction of the affinity matrix that corresponds to the graph in panel (B). With less contrast between edge classes, the pattern along the main diagonal is largely obscured.</p>", "links"=>[], "tags"=>["graphs", "affinity"], "article_id"=>569121, "categories"=>["Genetics", "Medicine"], "users"=>["Eric A. Stone", "Julien F. Ayroles"], "doi"=>"https://dx.doi.org/10.1371/journal.pgen.1000479.g001", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Community_structure_in_graphs_and_affinity_matrices_/569121", "title"=>"Community structure in graphs and affinity matrices.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-05-08 02:32:01"}
  • {"files"=>["https://ndownloader.figshare.com/files/898781"], "description"=>"<p>Panels (A)–(F) illustrate the method of modulated modularity clustering by example. (A) Example data consisting of nine observations on twelve variables drawn from a standard multivariate Normal distribution with variance-covariance matrix given by the correlation matrix from <a href=\"http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1000479#pgen-1000479-g002\" target=\"_blank\">Figure 2</a>. The variables have been permuted so that the block structure of the data will be obscured. (B) Heat map showing the pairwise correlations between variables (numbered 1 through 12 <i>after</i> permutation). The color scheme was introduced in <a href=\"http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1000479#pgen-1000479-g002\" target=\"_blank\">Figure 2</a>. (C) Surface plot of the maximum modularity attainable for a fixed number of clusters as varies. The 4,213,597 possible partitions of the twelve variables are grouped by number of parts (and hence clusters), and the maximum modularity found among these is shown on the plot for each . The surface appears convex and attains its maximum at (on a grid of step size 0.001) for a clustering of size 4. For larger examples, it is not possible to enumerate all partitions, and an approximate method is used to marginally maximize in . (D) The optimal defines the graph whose community structure is to be evaluated. The graph has affinity matrix with entries ; for illustration, these values have been shifted and linearly scaled so that the previously introduced heat map applies. To identify the partition of maximum modularity, we use a greedy forward search in which the initial graph is recursively bisected into subgraphs until the overall modularity can no longer increase. In the figure, each level (LEVEL 1, LEVEL 2) indicates a round of bisection, and each subgraph is represented by its corresponding section of the affinity matrix. There is no third level; subsequent to the second round, the overall modularity cannot be increased through further bisection. (E) The resulting clustering is used to reorder the affinity matrix by permutation of its rows and columns. Entries with colors other than dark blue have now been aggregated along the main diagonal. (F) Applying the same permutation to the correlation matrix reveals the four correlated clusters of variables ({1,9},{4,7,8,11},{2,6,12},{3,5,10}) hidden within the data.</p>", "links"=>[], "tags"=>["modularity"], "article_id"=>569245, "categories"=>["Genetics", "Medicine"], "users"=>["Eric A. Stone", "Julien F. Ayroles"], "doi"=>"https://dx.doi.org/10.1371/journal.pgen.1000479.g003", "stats"=>{"downloads"=>1, "page_views"=>22, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Modulated_modularity_clustering_/569245", "title"=>"Modulated modularity clustering.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-05-08 02:34:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/444955"], "description"=>"<div><p>In recent years, the advent of high-throughput assays, coupled with their diminishing cost, has facilitated a systems approach to biology. As a consequence, massive amounts of data are currently being generated, requiring efficient methodology aimed at the reduction of scale. Whole-genome transcriptional profiling is a standard component of systems-level analyses, and to reduce scale and improve inference clustering genes is common. Since clustering is often the first step toward generating hypotheses, cluster quality is critical. Conversely, because the validation of cluster-driven hypotheses is indirect, it is critical that quality clusters not be obtained by subjective means. In this paper, we present a new objective-based clustering method and demonstrate that it yields high-quality results. Our method, modulated modularity clustering (MMC), seeks community structure in graphical data. MMC modulates the connection strengths of edges in a weighted graph to maximize an objective function (called modularity) that quantifies community structure. The result of this maximization is a clustering through which tightly-connected groups of vertices emerge. Our application is to systems genetics, and we quantitatively compare MMC both to the hierarchical clustering method most commonly employed and to three popular spectral clustering approaches. We further validate MMC through analyses of human and <em>Drosophila melanogaster</em> expression data, demonstrating that the clusters we obtain are biologically meaningful. We show MMC to be effective and suitable to applications of large scale. In light of these features, we advocate MMC as a standard tool for exploration and hypothesis generation.</p></div>", "links"=>[], "tags"=>["modulated", "modularity", "clustering", "exploratory", "genomic", "inference"], "article_id"=>147694, "categories"=>["Genetics", "Medicine"], "users"=>["Eric A. Stone", "Julien F. Ayroles"], "doi"=>"https://dx.doi.org/10.1371/journal.pgen.1000479", "stats"=>{"downloads"=>1, "page_views"=>7, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Modulated_Modularity_Clustering_as_an_Exploratory_Tool_for_Functional_Genomic_Inference/147694", "title"=>"Modulated Modularity Clustering as an Exploratory Tool for Functional Genomic Inference", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2009-05-08 02:08:14"}
  • {"files"=>["https://ndownloader.figshare.com/files/899241"], "description"=>"<p>(A) Representation of the NK cell mediated cytotoxicity KEGG pathway. Genes in Module 5 associated with HDL-C variation are colored orange. (B) Relevance network representation of Module 5 after enforcing an absolute correlation threshold of 0.5. (C) Bar graphs of cell-specific expression patterns restricted to derivatives of whole blood. Grey bars indicate relative cell-specific expression levels across all 673 genes associated with HDL-C. Blue bars consider only the genes in Module 5.</p>", "links"=>[], "tags"=>["module-specific", "enrichment", "pathways"], "article_id"=>569707, "categories"=>["Genetics", "Medicine"], "users"=>["Eric A. Stone", "Julien F. Ayroles"], "doi"=>"https://dx.doi.org/10.1371/journal.pgen.1000479.g007", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Illustration_of_module_specific_enrichment_of_pathways_and_tissues_/569707", "title"=>"Illustration of module-specific enrichment of pathways and tissues.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-05-08 02:41:47"}
  • {"files"=>["https://ndownloader.figshare.com/files/898701"], "description"=>"<p>Twelve variables are correlated as shown in the figure. The heat map used to illustrate the pairwise correlations ranges from dark red (perfect correlation, ) through green (no correlation, ) to dark blue (perfect anticorrelation, ). On the diagonal are four correlated clusters of varying strength: {1,2} with an of 0.9, {3,4,5,6} with an of 0.7, {7,8,9} with an of 0.6, and {10,11,12} with an of 0.8. There are nonzero correlations between two pairs of clusters; members of {1,2} and {3,4,5,6} are positively correlated (), while members of {7,8,9} and {10,11,12} are negatively correlated ().</p>", "links"=>[], "tags"=>["simulated"], "article_id"=>569177, "categories"=>["Genetics", "Medicine"], "users"=>["Eric A. Stone", "Julien F. Ayroles"], "doi"=>"https://dx.doi.org/10.1371/journal.pgen.1000479.g002", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Correlation_structure_for_simulated_data_/569177", "title"=>"Correlation structure for simulated data.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-05-08 02:32:57"}
  • {"files"=>["https://ndownloader.figshare.com/files/899014"], "description"=>"<p>Panels (A)–(D) describe a systems genetic analysis of 414 <i>Drosophila melanogaster</i> genes associated with a competitive fitness phenotype. (A) The reordered matrix of pairwise genetic correlations between transcriptional profiles, in analogy to <a href=\"http://www.plosgenetics.org/article/info:doi/10.1371/journal.pgen.1000479#pgen-1000479-g003\" target=\"_blank\">Figure 3F</a>. The twenty clusters identified by MMC are numbered (Modules 1–20), color-coded (to the left and below), and emphasized with borders. From the upper left (Module 1) to lower right (Module 20), modules are ordered by decreasing average connectivity, defined here as average absolute pairwise correlation within the module. (B) Relevance network obtained from the 414 genes by enforcing an absolute correlation threshold of . The genes are numbered and color-coded as in (A) to indicate module membership. Only genes with at least one connection are shown. (C) Bar chart of the genes in Module 9 reporting for each one its relative expression level across eleven tissues. Genes are shown on the -axis, tissues are shown on the -axis, and relative expression is shown on the -axis. Expression in the ovary has been highlighted in red, and the genes featured in the next panel have been highlighted in blue. (D) Local alignment of five genes sharing the <i>dsx</i> motif in their 5′ UTRs. Above the alignment, a logo is shown to represent the profile of the 17 bp recognition sequence of <i>doublesex</i>.</p>", "links"=>[], "tags"=>["computational biology/systems biology", "genetics and genomics", "genetics and genomics/complex traits", "genetics and genomics/gene expression"], "article_id"=>569473, "categories"=>["Genetics", "Medicine"], "users"=>["Eric A. Stone", "Julien F. Ayroles"], "doi"=>"https://dx.doi.org/10.1371/journal.pgen.1000479.g005", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_MMC_analysis_of_Drosophila_melanogaster_data_/569473", "title"=>"MMC analysis of <i>Drosophila melanogaster</i> data.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2009-05-08 02:37:53"}

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