Edge Principal Components and Squash Clustering: Using the Special Structure of Phylogenetic Placement Data for Sample Comparison
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{"title"=>"Edge Principal Components and Squash Clustering: Using the Special Structure of Phylogenetic Placement Data for Sample Comparison", "type"=>"journal", "authors"=>[{"first_name"=>"Frederick A.", "last_name"=>"Matsen IV", "scopus_author_id"=>"55620556600"}, {"first_name"=>"Steven N.", "last_name"=>"Evans", "scopus_author_id"=>"55214872900"}], "year"=>2013, "source"=>"PLoS ONE", "identifiers"=>{"pui"=>"368506814", "arxiv"=>"1107.5095", "issn"=>"19326203", "isbn"=>"1932-6203 (Electronic)\\n1932-6203 (Linking)", "doi"=>"10.1371/journal.pone.0056859", "scopus"=>"2-s2.0-84874882695", "pmid"=>"23505415", "sgr"=>"84874882695"}, "id"=>"a4ce2bae-00eb-3f0f-a768-9c6195bec0b4", "abstract"=>"Principal components (PCA) and hierarchical clustering are two of the most heavily used techniques for analyzing the differences between nucleic acid sequence samples sampled from a given environment. However, a classical application of these techniques to distances computed between samples can lack transparency because there is no ready interpretation of the axes of classical PCA plots, and it is difficult to assign any clear intuitive meaning to either the internal nodes or the edge lengths of trees produced by distance-based hierarchical clustering methods such as UPGMA. We show that more interesting and interpretable results are produced by two new methods that leverage the special structure of phylogenetic placement data. Edge principal components analysis enables the detection of important differences between samples that contain closely related taxa. Each principal component axis is simply a collection of signed weights on the edges of the phylogenetic tree, and these weights are easily visualized by a suitable thickening and coloring of the edges. Squash clustering outputs a (rooted) clustering tree in which each internal node corresponds to an appropriate \"average\" of the original samples at the leaves below the node. Moreover, the length of an edge is a suitably defined distance between the averaged samples associated with the two incident nodes, rather than the less interpretable average of distances produced by UPGMA. We present these methods and illustrate their use with data from the microbiome of the human vagina.", "link"=>"http://www.mendeley.com/research/edge-principal-components-squash-clustering-using-special-structure-phylogenetic-placement-data-samp", "reader_count"=>164, "reader_count_by_academic_status"=>{"Unspecified"=>7, "Professor > Associate Professor"=>3, "Researcher"=>48, "Student > Doctoral Student"=>5, "Student > Ph. D. Student"=>64, "Student > Postgraduate"=>2, "Student > Master"=>16, "Other"=>4, "Student > Bachelor"=>6, "Lecturer"=>1, "Professor"=>8}, "reader_count_by_user_role"=>{"Unspecified"=>7, "Professor > Associate Professor"=>3, "Researcher"=>48, "Student > Doctoral Student"=>5, "Student > Ph. D. Student"=>64, "Student > Postgraduate"=>2, "Student > Master"=>16, "Other"=>4, "Student > Bachelor"=>6, "Lecturer"=>1, "Professor"=>8}, "reader_count_by_subject_area"=>{"Unspecified"=>9, "Agricultural and Biological Sciences"=>102, "Arts and Humanities"=>1, "Computer Science"=>10, "Earth and Planetary Sciences"=>1, "Engineering"=>2, "Environmental Science"=>13, "Biochemistry, Genetics and Molecular Biology"=>11, "Mathematics"=>7, "Medicine and Dentistry"=>3, "Neuroscience"=>2, "Physics and Astronomy"=>1, "Immunology and Microbiology"=>2}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>3}, "Physics and Astronomy"=>{"Physics and Astronomy"=>1}, "Mathematics"=>{"Mathematics"=>7}, "Unspecified"=>{"Unspecified"=>9}, "Environmental Science"=>{"Environmental Science"=>13}, "Arts and Humanities"=>{"Arts and Humanities"=>1}, "Engineering"=>{"Engineering"=>2}, "Neuroscience"=>{"Neuroscience"=>2}, "Earth and Planetary Sciences"=>{"Earth and Planetary Sciences"=>1}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>2}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>102}, "Computer Science"=>{"Computer Science"=>10}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>11}}, "reader_count_by_country"=>{"Canada"=>4, "Sweden"=>5, "United States"=>24, "Japan"=>1, "United Kingdom"=>2, "France"=>3, "Switzerland"=>1, "Germany"=>2, "Estonia"=>2}, "group_count"=>6}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/983653"], "description"=>"<p>The axes for the edge principal components plot are described in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0056859#pone-0056859-g004\" target=\"_blank\">Figures 4</a> (-axis) and 5 (-axis). The Nugent score is a diagnostic score for bacterial vaginosis, with high score indicating bacterial vaginosis.</p>", "links"=>[], "tags"=>["components", "applied", "forney", "fredricks", "plotted"], "article_id"=>649502, "categories"=>["Information And Computing Sciences", "Mathematics", "Genetics", "Evolutionary Biology"], "users"=>["Frederick A. Matsen IV", "Steven N. Evans"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0056859.g006", "stats"=>{"downloads"=>0, "page_views"=>13, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Edge_principal_components_analysis_edge_PCA_applied_to_the_combined_Forney_and_Fredricks_data_set_and_plotted_separately_/649502", "title"=>"Edge principal components analysis (edge PCA) applied to the combined Forney and Fredricks data set and plotted separately.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-12 08:03:34"}
  • {"files"=>["https://ndownloader.figshare.com/files/983650"], "description"=>"<p>Low-weight regions of the tree are excluded from the figure. The edges across which maximal between-sample heterogeneity is found are those between two different <i>Lactobacillus</i> clades: <i>L. iners</i> and <i>L. crispatus</i>. Thus, the second important “axis” appears to correspond to the relative levels of these two species.</p>", "links"=>[], "tags"=>["vaginal", "24", "percent"], "article_id"=>649499, "categories"=>["Information And Computing Sciences", "Mathematics", "Genetics", "Evolutionary Biology"], "users"=>["Frederick A. Matsen IV", "Steven N. Evans"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0056859.g005", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_second_principal_component_for_the_combined_vaginal_data_representing_about_24_percent_of_the_variance_/649499", "title"=>"The second principal component for the combined vaginal data, representing about 24 percent of the variance.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-12 08:03:14"}
  • {"files"=>["https://ndownloader.figshare.com/files/983663", "https://ndownloader.figshare.com/files/983664"], "description"=>"<div><p>Principal components analysis (PCA) and hierarchical clustering are two of the most heavily used techniques for analyzing the differences between nucleic acid sequence samples taken from a given environment. They have led to many insights regarding the structure of microbial communities. We have developed two new complementary methods that leverage how this microbial community data sits on a phylogenetic tree. <i>Edge principal components analysis</i> enables the detection of important differences between samples that contain closely related taxa. Each principal component axis is a collection of signed weights on the edges of the phylogenetic tree, and these weights are easily visualized by a suitable thickening and coloring of the edges. <i>Squash clustering</i> outputs a (rooted) clustering tree in which each internal node corresponds to an appropriate “average” of the original samples at the leaves below the node. Moreover, the length of an edge is a suitably defined distance between the averaged samples associated with the two incident nodes, rather than the less interpretable average of distances produced by UPGMA, the most widely used hierarchical clustering method in this context. We present these methods and illustrate their use with data from the human microbiome.</p> </div>", "links"=>[], "tags"=>["components", "squash", "phylogenetic", "comparison"], "article_id"=>649512, "categories"=>["Information And Computing Sciences", "Mathematics", "Genetics", "Evolutionary Biology"], "users"=>["Frederick A. Matsen IV", "Steven N. Evans"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0056859.s001", "https://dx.doi.org/10.1371/journal.pone.0056859.s002"], "stats"=>{"downloads"=>5, "page_views"=>16, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Edge_Principal_Components_and_Squash_Clustering_Using_the_Special_Structure_of_Phylogenetic_Placement_Data_for_Sample_Comparison__/649512", "title"=>"Edge Principal Components and Squash Clustering: Using the Special Structure of Phylogenetic Placement Data for Sample Comparison", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2013-03-12 08:04:26"}
  • {"files"=>["https://ndownloader.figshare.com/files/983644"], "description"=>"<p>When two clusters are merged, their mass distributions are combined according to a weighted average. The edges of the reference tree in this figure are thickened in proportion to the mass distribution (for simplicity, just a subtree of the reference tree is shown here). In this example, the lower mass distribution is an equal-proportion average of the upper two mass distributions. Similarities between mass distributions, such as the similarity seen between the two clusters for the <i>G. vaginalis</i> clade shown here, are what cause clusters to be merged. Such similarities between internal nodes can be visualized for the squash clustering algorithm; the software implementation produces such a visualization for every internal node of the clustering tree. Note that in this figure only the number of reads placed on each edge is shown, although each placement has an associated location on each edge when performing computation.</p>", "links"=>[], "tags"=>["depiction", "squash", "clustering"], "article_id"=>649493, "categories"=>["Information And Computing Sciences", "Mathematics", "Genetics", "Evolutionary Biology"], "users"=>["Frederick A. Matsen IV", "Steven N. Evans"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0056859.g002", "stats"=>{"downloads"=>3, "page_views"=>14, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_visual_depiction_of_the_squash_clustering_algorithm_/649493", "title"=>"A visual depiction of the squash clustering algorithm.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-12 08:02:50"}
  • {"files"=>["https://ndownloader.figshare.com/files/983657"], "description"=>"<p>The labels are not shown and they do not appear in the same order on the two trees. For a comparison of labeled trees, see Supplementary Figure S1.</p>", "links"=>[], "tags"=>["squash", "clustering", "upgma", "applied", "vaginal"], "article_id"=>649506, "categories"=>["Information And Computing Sciences", "Mathematics", "Genetics", "Evolutionary Biology"], "users"=>["Frederick A. Matsen IV", "Steven N. Evans"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0056859.g008", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_results_of_a_squash_clustering_and_b_UPGMA_as_applied_to_the_vaginal_data_/649506", "title"=>"The results of (a) squash clustering and (b) UPGMA as applied to the vaginal data.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-12 08:03:55"}
  • {"files"=>["https://ndownloader.figshare.com/files/983648"], "description"=>"<p>The reference tree is colored by principal component sign (positive colored orange, negative colored green) and thickened proportional to magnitude. The edges across which maximal between-sample heterogeneity is found are those leading to the <i>Lactobacillus</i> clade and those leading to the <i>Sneathia</i> and <i>Prevotella</i> clade. This axis corresponds to taxa that are important in the diagnosis of bacterial vaginosis, as <i>Sneathia</i> and <i>Prevotella</i> are associated with bacterial vaginosis, while <i>Lactobacillus</i> is associated with a healthy microbiome.</p>", "links"=>[], "tags"=>["vaginal", "56", "percent"], "article_id"=>649497, "categories"=>["Information And Computing Sciences", "Mathematics", "Genetics", "Evolutionary Biology"], "users"=>["Frederick A. Matsen IV", "Steven N. Evans"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0056859.g004", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_first_principal_component_for_the_combined_vaginal_data_representing_about_56_percent_of_the_variance_/649497", "title"=>"The first principal component for the combined vaginal data, representing about 56 percent of the variance.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-12 08:03:11"}
  • {"files"=>["https://ndownloader.figshare.com/files/983647"], "description"=>"<p>(a) For every edge of the tree, the difference is taken between the number of reads on the non-root side the number of reads on the root side (root marked with a star). (b) The results of this are put into a matrix corresponding to the sample number (row) and the edge number (column). (c) The standard PCA algorithm is then applied, resulting in a collection of eigenvectors (the principal components) and eigenvalues. (d) These eigenvectors are indexed by the edges of the tree, and hence they can be mapped back onto the tree.</p>", "links"=>[], "tags"=>["pca", "algorithm"], "article_id"=>649496, "categories"=>["Information And Computing Sciences", "Mathematics", "Genetics", "Evolutionary Biology"], "users"=>["Frederick A. Matsen IV", "Steven N. Evans"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0056859.g003", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_How_the_edge_PCA_algorithm_works_/649496", "title"=>"How the edge PCA algorithm works.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-12 08:03:05"}
  • {"files"=>["https://ndownloader.figshare.com/files/983659"], "description"=>"<p>This graphic shows very similar levels of topological accuracy for squash clustering and UPGMA, as well as high similarity between the topology returned by the two methods. The figure is divided into panels by the level of reconstructability parameter as described in the text (a larger implies easier reconstruction). The -axis is the value of for the distance as described in (1). The -axis is the rooted Robinson-Foulds distance: for the “squash” and “UPGMA” lines it is the distance between the reconstructed tree and the original tree using these two algorithms (lower is more accurate), while the “between” line shows the distance between the result for the two clustering algorithms (lower is more similar). Note that the maximum rooted RF distance between two trees with six taxa is four.</p>", "links"=>[], "tags"=>["simulation", "rooted", "robinson-foulds"], "article_id"=>649508, "categories"=>["Information And Computing Sciences", "Mathematics", "Genetics", "Evolutionary Biology"], "users"=>["Frederick A. Matsen IV", "Steven N. Evans"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0056859.g009", "stats"=>{"downloads"=>3, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_results_of_the_cluster_accuracy_simulation_experiment_using_the_rooted_Robinson_Foulds_RF_metric_/649508", "title"=>"The results of the cluster accuracy simulation experiment using the rooted Robinson-Foulds (RF) metric.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-12 08:04:08"}
  • {"files"=>["https://ndownloader.figshare.com/files/983656"], "description"=>"<p>Principal coordinates analysis applied to the Fredricks vaginal data set.</p>", "links"=>[], "tags"=>["coordinates", "applied", "fredricks", "vaginal"], "article_id"=>649505, "categories"=>["Information And Computing Sciences", "Mathematics", "Genetics", "Evolutionary Biology"], "users"=>["Frederick A. Matsen IV", "Steven N. Evans"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0056859.g007", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Principal_coordinates_analysis_applied_to_the_Fredricks_vaginal_data_set_/649505", "title"=>"Principal coordinates analysis applied to the Fredricks vaginal data set.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-12 08:03:50"}
  • {"files"=>["https://ndownloader.figshare.com/files/983641"], "description"=>"<p>The phylogenetic distribution of reads for a given sample determines its position in the principal components projection. For the first axis, reads that fall below edges with positive coefficients on that axis' tree (marked in orange on the tree) move the corresponding sample point to the right, while reads that land on edges with negative coefficients (marked in green on the tree) move the corresponding sample point to the left. The second axis is labeled with a subtree of the first tree (the position of which is marked with a star on the first principal component tree): reads below edges with positive coefficients move sample points up, while reads below edges with negative coefficients move sample points down. The principal components shown here are the actual principal components for the example shown in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0056859#pone-0056859-g004\" target=\"_blank\">Figures 4</a>, <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0056859#pone-0056859-g005\" target=\"_blank\">5</a>, and <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0056859#pone-0056859-g006\" target=\"_blank\">6</a>.</p>", "links"=>[], "tags"=>["graphical", "components"], "article_id"=>649490, "categories"=>["Information And Computing Sciences", "Mathematics", "Genetics", "Evolutionary Biology"], "users"=>["Frederick A. Matsen IV", "Steven N. Evans"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0056859.g001", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_graphical_representation_of_the_operation_of_edge_principal_components_analysis_edge_PCA_/649490", "title"=>"A graphical representation of the operation of edge principal components analysis (edge PCA).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-03-12 08:02:43"}

PMC Usage Stats | Further Information

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Relative Metric

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