Discriminating Different Classes of Biological Networks by Analyzing the Graphs Spectra Distribution
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{"title"=>"Discriminating Different Classes of Biological Networks by Analyzing the Graphs Spectra Distribution", "type"=>"journal", "authors"=>[{"first_name"=>"Daniel Yasumasa", "last_name"=>"Takahashi", "scopus_author_id"=>"8241472000"}, {"first_name"=>"João Ricardo", "last_name"=>"Sato", "scopus_author_id"=>"56668321500"}, {"first_name"=>"Carlos Eduardo", "last_name"=>"Ferreira", "scopus_author_id"=>"35584668200"}, {"first_name"=>"André", "last_name"=>"Fujita", "scopus_author_id"=>"17433835800"}], "year"=>2012, "source"=>"PLoS ONE", "identifiers"=>{"pui"=>"366299792", "doi"=>"10.1371/journal.pone.0049949", "isbn"=>"1932-6203 (Electronic)\\r1932-6203 (Linking)", "pmid"=>"23284629", "issn"=>"19326203", "scopus"=>"2-s2.0-84871334644", "arxiv"=>"1208.2976", "sgr"=>"84871334644"}, "id"=>"9716017c-d04f-3dfa-a05b-5bb42e6c6d0b", "abstract"=>"The brain's structural and functional systems, protein-protein interaction, and gene networks are examples of biological systems that share some features of complex networks, such as highly connected nodes, modularity, and small-world topology. Recent studies indicate that some pathologies present topological network alterations relative to norms seen in the general population. Therefore, methods to discriminate the processes that generate the different classes of networks (e.g., normal and disease) might be crucial for the diagnosis, prognosis, and treatment of the disease. It is known that several topological properties of a network (graph) can be described by the distribution of the spectrum of its adjacency matrix. Moreover, large networks generated by the same random process have the same spectrum distribution, allowing us to use it as a \"fingerprint\". Based on this relationship, we introduce and propose the entropy of a graph spectrum to measure the \"uncertainty\" of a random graph and the Kullback-Leibler and Jensen-Shannon divergences between graph spectra to compare networks. We also introduce general methods for model selection and network model parameter estimation, as well as a statistical procedure to test the nullity of divergence between two classes of complex networks. Finally, we demonstrate the usefulness of the proposed methods by applying them to (1) protein-protein interaction networks of different species and (2) on networks derived from children diagnosed with Attention Deficit Hyperactivity Disorder (ADHD) and typically developing children. We conclude that scale-free networks best describe all the protein-protein interactions. Also, we show that our proposed measures succeeded in the identification of topological changes in the network while other commonly used measures (number of edges, clustering coefficient, average path length) failed.", "link"=>"http://www.mendeley.com/research/discriminating-different-classes-biological-networks-analyzing-graphs-spectra-distribution", "reader_count"=>42, "reader_count_by_academic_status"=>{"Professor > Associate Professor"=>6, "Librarian"=>1, "Researcher"=>14, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>6, "Student > Postgraduate"=>2, "Student > Master"=>4, "Other"=>2, "Student > Bachelor"=>3, "Professor"=>2, "Unspecified"=>1}, "reader_count_by_user_role"=>{"Professor > Associate Professor"=>6, "Librarian"=>1, "Researcher"=>14, "Student > Doctoral Student"=>1, "Student > Ph. D. Student"=>6, "Student > Postgraduate"=>2, "Student > Master"=>4, "Other"=>2, "Student > Bachelor"=>3, "Professor"=>2, "Unspecified"=>1}, "reader_count_by_subject_area"=>{"Unspecified"=>3, "Biochemistry, Genetics and Molecular Biology"=>1, "Nursing and Health Professions"=>1, "Agricultural and Biological Sciences"=>12, "Medicine and Dentistry"=>3, "Neuroscience"=>4, "Business, Management and Accounting"=>1, "Physics and Astronomy"=>7, "Psychology"=>3, "Social Sciences"=>1, "Computer Science"=>5, "Earth and Planetary Sciences"=>1}, "reader_count_by_subdiscipline"=>{"Medicine and Dentistry"=>{"Medicine and Dentistry"=>3}, "Neuroscience"=>{"Neuroscience"=>4}, "Social Sciences"=>{"Social Sciences"=>1}, "Physics and Astronomy"=>{"Physics and Astronomy"=>7}, "Psychology"=>{"Psychology"=>3}, "Earth and Planetary Sciences"=>{"Earth and Planetary Sciences"=>1}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>12}, "Computer Science"=>{"Computer Science"=>5}, "Nursing and Health Professions"=>{"Nursing and Health Professions"=>1}, "Business, Management and Accounting"=>{"Business, Management and Accounting"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>1}, "Unspecified"=>{"Unspecified"=>3}}, "reader_count_by_country"=>{"Republic of Singapore"=>1, "United States"=>3, "Finland"=>1, "Brazil"=>2, "United Kingdom"=>1}, "group_count"=>2}

Scopus | Further Information

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/522342"], "description"=>"<p>(<b>A</b>) Erdös-Rényi; (<b>B</b>) Scale-free; and (<b>C</b>) Small-world and their respective spectra, degree distributions, and entropies, in this order from top to bottom. The estimated entropies are computed for the respective graph type for the respective parameters (probability for the Erdös-Rényi, scaling exponent for the scale-free, and probability for the small-world random graphs). In (<b>A</b>) the entropy values estimated from the simulation data is depicted by a solid line and the theoretical value of the entropy computed using <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0049949#pone.0049949.e058\" target=\"_blank\">equation 4</a> is indicated by a dashed line.</p>", "links"=>[], "tags"=>["neuroscience", "pediatrics and child health", "neurological disorders", "mathematics"], "article_id"=>192832, "categories"=>["Mathematics", "Neuroscience", "Medicine"], "users"=>["Daniel Yasumasa Takahashi", "João Ricardo Sato", "Carlos Eduardo Ferreira", "André Fujita"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0049949.g001", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Illustrative_figure_of_the_three_different_complex_network_models_/192832", "title"=>"Illustrative figure of the three different complex network models.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 18:26:06"}
  • {"files"=>["https://ndownloader.figshare.com/files/522526"], "description"=>"<p>(<b>A</b>) Erdös-Rényi graphs; (<b>B</b>) scale-free graphs, and (<b>C</b>) small-world graphs. For the ROC curves, the x-axis represents the 1-specificity and the y-axis the sensitivity. Both ROC curves and p-value distributions were constructed by analyzing 10,000 experiments. Solid and dashed lines represent the test based on the spectral and degree distributions, respectively.</p>", "links"=>[], "tags"=>["p-value", "null"], "article_id"=>193022, "categories"=>["Mathematics", "Neuroscience", "Medicine"], "users"=>["Daniel Yasumasa Takahashi", "João Ricardo Sato", "Carlos Eduardo Ferreira", "André Fujita"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0049949.g003", "stats"=>{"downloads"=>0, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_ROC_curve_under_the_alternative_hypothesis_and_p_value_distribution_under_the_null_hypothesis_/193022", "title"=>"ROC curve under the alternative hypothesis and p-value distribution under the null hypothesis.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 18:27:06"}
  • {"files"=>["https://ndownloader.figshare.com/files/522863"], "description"=>"<p>The general characteristics of eight protein-protein interaction networks. For each network we indicate the number of nodes, the number of edges, the average degree, the diameter, the clustering coefficient and the average path length.</p>", "links"=>[], "tags"=>["characteristics", "protein-protein", "clustering", "coefficient"], "article_id"=>193356, "categories"=>["Mathematics", "Neuroscience", "Medicine"], "users"=>["Daniel Yasumasa Takahashi", "João Ricardo Sato", "Carlos Eduardo Ferreira", "André Fujita"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0049949.t002", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_general_characteristics_of_eight_protein_protein_interaction_networks_For_each_network_we_indicate_the_number_of_nodes_the_number_of_edges_the_average_degree_the_diameter_the_clustering_coefficient_and_the_average_path_length_/193356", "title"=>"The general characteristics of eight protein-protein interaction networks. For each network we indicate the number of nodes, the number of edges, the average degree, the diameter, the clustering coefficient and the average path length.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-19 18:28:52"}
  • {"files"=>["https://ndownloader.figshare.com/files/522797"], "description"=>"<p>\n <b>One standard deviation is indicated between brackets. Calculations were carried out for 50 repetitions. The parameters to be estimated for each graph model are: the probability </b><b> of connecting two nodes for Erdös-Rényi graphs, the power of the preferential attachment </b><b> for scale-free graphs, and the rewiring probability </b><b> for small-world graphs.</b></p>", "links"=>[], "tags"=>["parameters", "estimator", "kl", "divergence", "small-world"], "article_id"=>193290, "categories"=>["Mathematics", "Neuroscience", "Medicine"], "users"=>["Daniel Yasumasa Takahashi", "João Ricardo Sato", "Carlos Eduardo Ferreira", "André Fujita"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0049949.t001", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Average_parameters_estimated_by_minimum_distance_estimator_based_on_KL_divergence_for_Erd_246_s_R_233_nyi_random_scale_free_and_small_world_graphs_/193290", "title"=>"Average parameters estimated by minimum distance estimator based on KL divergence for Erdös-Rényi random, scale-free, and small-world graphs.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-19 18:28:28"}
  • {"files"=>["https://ndownloader.figshare.com/files/522829"], "description"=>"<p>The estimated Kullback-Leibler divergence between the eight species and the three random graph models. In bold are the lowest KL divergence values.</p>", "links"=>[], "tags"=>["kullback-leibler", "divergence", "graph", "lowest", "kl"], "article_id"=>193319, "categories"=>["Mathematics", "Neuroscience", "Medicine"], "users"=>["Daniel Yasumasa Takahashi", "João Ricardo Sato", "Carlos Eduardo Ferreira", "André Fujita"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0049949.t003", "stats"=>{"downloads"=>1, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_estimated_Kullback_Leibler_divergence_between_the_eight_species_and_the_three_random_graph_models_In_bold_are_the_lowest_KL_divergence_values_/193319", "title"=>"The estimated Kullback-Leibler divergence between the eight species and the three random graph models. In bold are the lowest KL divergence values.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-19 18:28:40"}
  • {"files"=>["https://ndownloader.figshare.com/files/522440"], "description"=>"<p>Given a graph belonging to (<b>A</b>) Erdös-Rényi with parameter , (<b>B</b>) scale-free with parameter , and (<b>C</b>) small-world with parameter  = 0.3, the solid, dashed, and dotted lines represent the proportion of graphs classified as Erdös-Rényi, scale-free, and small-world, respectively. Notice that the larger is the graph, the higher is the proportion of correct hits, showing that the model selection approach is consistent. For each graph size (10, 20, 30, 40, 50, 60, 70, 80, 90, 100, 110, 120 nodes), 1,000 repetitions were carried out.</p>", "links"=>[], "tags"=>["illustrating"], "article_id"=>192939, "categories"=>["Mathematics", "Neuroscience", "Medicine"], "users"=>["Daniel Yasumasa Takahashi", "João Ricardo Sato", "Carlos Eduardo Ferreira", "André Fujita"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0049949.g002", "stats"=>{"downloads"=>1, "page_views"=>10, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Figure_illustrating_the_performance_of_the_model_selection_approach_as_a_function_of_number_of_nodes_/192939", "title"=>"Figure illustrating the performance of the model selection approach as a function of number of nodes.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 18:26:42"}
  • {"files"=>["https://ndownloader.figshare.com/files/522733"], "description"=>"<p>Solid line represents the children with typical development. Dashed line represents children with combined type of ADHD (hyperactive-impulsive and inattentive).</p>", "links"=>[], "tags"=>["spectral", "distributions"], "article_id"=>193226, "categories"=>["Mathematics", "Neuroscience", "Medicine"], "users"=>["Daniel Yasumasa Takahashi", "João Ricardo Sato", "Carlos Eduardo Ferreira", "André Fujita"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0049949.g005", "stats"=>{"downloads"=>1, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_Spectral_and_B_degree_distributions_in_the_log_scale_/193226", "title"=>"(A) Spectral and (B) degree distributions in the log-scale.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 18:28:12"}
  • {"files"=>["https://ndownloader.figshare.com/files/522943"], "description"=>"<p>For number of edges, clustering coefficient and average path length, the Wilcoxon test was carried out. For degree and spectral distributions, the JS divergence with the bootstrap test was calculated.</p>", "links"=>[], "tags"=>["metrics", "graph", "discrepancy", "children", "adhd", "respective"], "article_id"=>193431, "categories"=>["Mathematics", "Neuroscience", "Medicine"], "users"=>["Daniel Yasumasa Takahashi", "João Ricardo Sato", "Carlos Eduardo Ferreira", "André Fujita"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0049949.t004", "stats"=>{"downloads"=>4, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Different_metrics_to_measure_graph_discrepancy_between_children_with_typical_development_and_children_with_combined_type_of_ADHD_hyperactive_impulsive_and_inattentive_and_their_respective_p_values_/193431", "title"=>"Different metrics to measure graph discrepancy between children with typical development and children with combined type of ADHD (hyperactive-impulsive and inattentive) and their respective p-values.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-19 18:29:14"}
  • {"files"=>["https://ndownloader.figshare.com/files/522906"], "description"=>"<p>The tests were carried out under the null hypothesis, i.e., in typical development children datasets of different laboratories. The laboratories were numbered from one to seven and the p-values are after Bonferroni correction for multiple tests.</p>", "links"=>[], "tags"=>["jensen-shannon", "divergence", "spectra", "distributions"], "article_id"=>193395, "categories"=>["Mathematics", "Neuroscience", "Medicine"], "users"=>["Daniel Yasumasa Takahashi", "João Ricardo Sato", "Carlos Eduardo Ferreira", "André Fujita"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0049949.t005", "stats"=>{"downloads"=>1, "page_views"=>16, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_P_values_obtained_by_testing_the_Jensen_Shannon_divergence_in_the_spectra_distributions_among_different_laboratories_/193395", "title"=>"P-values obtained by testing the Jensen-Shannon divergence in the spectra distributions among different laboratories.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-19 18:29:03"}
  • {"files"=>["https://ndownloader.figshare.com/files/522645"], "description"=>"<p>The frequency plot for the eigenvalues of the eight species (<i>H. pylori</i>, <i>R. norvegicus</i>, <i>M. musculus</i>, <i>E. coli</i>, <i>C. elegans</i>, <i>S. cerevisiae</i>, <i>H. sapiens</i>, <i>D. melanogaster</i>).</p>", "links"=>[], "tags"=>["neuroscience", "pediatrics and child health", "neurological disorders", "mathematics"], "article_id"=>193138, "categories"=>["Mathematics", "Neuroscience", "Medicine"], "users"=>["Daniel Yasumasa Takahashi", "João Ricardo Sato", "Carlos Eduardo Ferreira", "André Fujita"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0049949.g004", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_frequency_plots_/193138", "title"=>"The frequency plots.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-19 18:27:43"}

PMC Usage Stats | Further Information

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Relative Metric

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