Visualization and Curve-Parameter Estimation Strategies for Efficient Exploration of Phenotype Microarray Kinetics
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{"title"=>"Visualization and curve-parameter estimation strategies for efficient exploration of phenotype microarray kinetics", "type"=>"journal", "authors"=>[{"first_name"=>"Lea A I", "last_name"=>"Vaas", "scopus_author_id"=>"37038632200"}, {"first_name"=>"Johannes", "last_name"=>"Sikorski", "scopus_author_id"=>"15846566700"}, {"first_name"=>"Victoria", "last_name"=>"Michael", "scopus_author_id"=>"55193606000"}, {"first_name"=>"Markus", "last_name"=>"Göker", "scopus_author_id"=>"6602789910"}, {"first_name"=>"Hans Peter", "last_name"=>"Klenk", "scopus_author_id"=>"55145833600"}], "year"=>2012, "source"=>"PLoS ONE", "identifiers"=>{"issn"=>"19326203", "scopus"=>"2-s2.0-84859982600", "pui"=>"364661754", "doi"=>"10.1371/journal.pone.0034846", "isbn"=>"1932-6203 (Electronic)\\r1932-6203 (Linking)", "sgr"=>"84859982600", "pmid"=>"22536335"}, "id"=>"15a41c03-f666-3ebf-aa7d-cf8386c96ee0", "abstract"=>"BACKGROUND: The Phenotype MicroArray (OmniLog(R) PM) system is able to simultaneously capture a large number of phenotypes by recording an organism's respiration over time on distinct substrates. This technique targets the object of natural selection itself, the phenotype, whereas previously addressed '-omics' techniques merely study components that finally contribute to it. The recording of respiration over time, however, adds a longitudinal dimension to the data. To optimally exploit this information, it must be extracted from the shapes of the recorded curves and displayed in analogy to conventional growth curves. METHODOLOGY: The free software environment R was explored for both visualizing and fitting of PM respiration curves. Approaches using either a model fit (and commonly applied growth models) or a smoothing spline were evaluated. Their reliability in inferring curve parameters and confidence intervals was compared to the native OmniLog(R) PM analysis software. We consider the post-processing of the estimated parameters, the optimal classification of curve shapes and the detection of significant differences between them, as well as practically relevant questions such as detecting the impact of cultivation times and the minimum required number of experimental repeats. CONCLUSIONS: We provide a comprehensive framework for data visualization and parameter estimation according to user choices. A flexible graphical representation strategy for displaying the results is proposed, including 95% confidence intervals for the estimated parameters. The spline approach is less prone to irregular curve shapes than fitting any of the considered models or using the native PM software for calculating both point estimates and confidence intervals. These can serve as a starting point for the automated post-processing of PM data, providing much more information than the strict dichotomization into positive and negative reactions. Our results form the basis for a freely available R package for the analysis of PM data.", "link"=>"http://www.mendeley.com/research/visualization-curveparameter-estimation-strategies-efficient-exploration-phenotype-microarray-kineti", "reader_count"=>88, "reader_count_by_academic_status"=>{"Unspecified"=>1, "Professor > Associate Professor"=>4, "Researcher"=>27, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>30, "Student > Postgraduate"=>6, "Student > Master"=>7, "Other"=>3, "Student > Bachelor"=>2, "Lecturer"=>1, "Professor"=>5}, "reader_count_by_user_role"=>{"Unspecified"=>1, "Professor > Associate Professor"=>4, "Researcher"=>27, "Student > Doctoral Student"=>2, "Student > Ph. D. Student"=>30, "Student > Postgraduate"=>6, "Student > Master"=>7, "Other"=>3, "Student > Bachelor"=>2, "Lecturer"=>1, "Professor"=>5}, "reader_count_by_subject_area"=>{"Engineering"=>4, "Unspecified"=>3, "Environmental Science"=>4, "Biochemistry, Genetics and Molecular Biology"=>5, "Mathematics"=>3, "Agricultural and Biological Sciences"=>58, "Neuroscience"=>1, "Psychology"=>1, "Social Sciences"=>2, "Computer Science"=>1, "Immunology and Microbiology"=>6}, "reader_count_by_subdiscipline"=>{"Engineering"=>{"Engineering"=>4}, "Neuroscience"=>{"Neuroscience"=>1}, "Social Sciences"=>{"Social Sciences"=>2}, "Psychology"=>{"Psychology"=>1}, "Immunology and Microbiology"=>{"Immunology and Microbiology"=>6}, "Agricultural and Biological Sciences"=>{"Agricultural and Biological Sciences"=>58}, "Computer Science"=>{"Computer Science"=>1}, "Biochemistry, Genetics and Molecular Biology"=>{"Biochemistry, Genetics and Molecular Biology"=>5}, "Mathematics"=>{"Mathematics"=>3}, "Unspecified"=>{"Unspecified"=>3}, "Environmental Science"=>{"Environmental Science"=>4}}, "reader_count_by_country"=>{"Canada"=>1, "United States"=>5, "Ireland"=>1, "South Africa"=>1, "Germany"=>1}, "group_count"=>4}

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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/649398"], "description"=>"<p>PM curves from a representative technical repetition from the first dataset were arranged according to the original 8×12 wells plate layout. The respective curves from all four strains are superimposed; the affiliation to each strain is indicated by color as follows: black, <i>E. coli</i> DSM 18039; red, <i>E. coli</i> DSM 30038<sup>T</sup>; green, <i>P. aeruginosa</i> DSM 1707; blue, <i>P. aeruginosa</i> 429SC. The x-axes show the measurement times in hours, the y-axes the curve heights in OmniLog® units. In the caption of each panel the corresponding coordinate of the well is shown. Details of the curves from wells G11 and H11 are examined in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0034846#pone-0034846-g003\" target=\"_blank\">Figs. 3</a> and <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0034846#pone-0034846-g004\" target=\"_blank\">4</a>.</p>", "links"=>[], "tags"=>["pm", "curves"], "article_id"=>319893, "categories"=>["Biotechnology", "Biological Sciences", "Genetics", "Microbiology"], "users"=>["Lea A. I. Vaas", "Johannes Sikorski", "Victoria Michael", "Markus Göker", "Hans-Peter Klenk"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0034846.g002", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Visualization_of_PM_curves_as_such_via_the_function_xyplot_/319893", "title"=>"Visualization of PM curves as such <i>via</i> the function <i>xyplot()</i>.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-04-20 02:44:53"}
  • {"files"=>["https://ndownloader.figshare.com/files/335263", "https://ndownloader.figshare.com/files/335287", "https://ndownloader.figshare.com/files/335309", "https://ndownloader.figshare.com/files/335442", "https://ndownloader.figshare.com/files/335709", "https://ndownloader.figshare.com/files/336016", "https://ndownloader.figshare.com/files/336405", "https://ndownloader.figshare.com/files/336454", "https://ndownloader.figshare.com/files/336500", "https://ndownloader.figshare.com/files/336634"], "description"=>"<div><h3>Background</h3><p>The Phenotype MicroArray (OmniLog® PM) system is able to simultaneously capture a large number of phenotypes by recording an organism's respiration over time on distinct substrates. This technique targets the object of natural selection itself, the phenotype, whereas previously addressed ‘-omics’ techniques merely study components that finally contribute to it. The recording of respiration over time, however, adds a longitudinal dimension to the data. To optimally exploit this information, it must be extracted from the shapes of the recorded curves and displayed in analogy to conventional growth curves.</p> <h3>Methodology</h3><p>The free software environment R was explored for both visualizing and fitting of PM respiration curves. Approaches using either a model fit (and commonly applied growth models) or a smoothing spline were evaluated. Their reliability in inferring curve parameters and confidence intervals was compared to the native OmniLog® PM analysis software. We consider the post-processing of the estimated parameters, the optimal classification of curve shapes and the detection of significant differences between them, as well as practically relevant questions such as detecting the impact of cultivation times and the minimum required number of experimental repeats.</p> <h3>Conclusions</h3><p>We provide a comprehensive framework for data visualization and parameter estimation according to user choices. A flexible graphical representation strategy for displaying the results is proposed, including 95% confidence intervals for the estimated parameters. The spline approach is less prone to irregular curve shapes than fitting any of the considered models or using the native PM software for calculating both point estimates and confidence intervals. These can serve as a starting point for the automated post-processing of PM data, providing much more information than the strict dichotomization into positive and negative reactions. Our results form the basis for a freely available R package for the analysis of PM data.</p> </div>", "links"=>[], "tags"=>["visualization", "curve-parameter", "estimation", "strategies", "phenotype", "microarray", "kinetics"], "article_id"=>126235, "categories"=>["Biotechnology", "Biological Sciences", "Genetics", "Microbiology"], "users"=>["Lea A. I. Vaas", "Johannes Sikorski", "Victoria Michael", "Markus Göker", "Hans-Peter Klenk"], "doi"=>["https://dx.doi.org/10.1371/journal.pone.0034846.s001", "https://dx.doi.org/10.1371/journal.pone.0034846.s002", "https://dx.doi.org/10.1371/journal.pone.0034846.s003", "https://dx.doi.org/10.1371/journal.pone.0034846.s004", "https://dx.doi.org/10.1371/journal.pone.0034846.s005", "https://dx.doi.org/10.1371/journal.pone.0034846.s006", "https://dx.doi.org/10.1371/journal.pone.0034846.s007", "https://dx.doi.org/10.1371/journal.pone.0034846.s008", "https://dx.doi.org/10.1371/journal.pone.0034846.s009", "https://dx.doi.org/10.1371/journal.pone.0034846.s010"], "stats"=>{"downloads"=>10, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/Visualization_and_Curve_Parameter_Estimation_Strategies_for_Efficient_Exploration_of_Phenotype_Microarray_Kinetics/126235", "title"=>"Visualization and Curve-Parameter Estimation Strategies for Efficient Exploration of Phenotype Microarray Kinetics", "pos_in_sequence"=>0, "defined_type"=>4, "published_date"=>"2012-04-20 01:43:55"}
  • {"files"=>["https://ndownloader.figshare.com/files/649551"], "description"=>"<p>Left, enlarged view of the curves from wells G11 and H11 as depicted in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0034846#pone-0034846-g002\" target=\"_blank\">Fig. 2</a>. As in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0034846#pone-0034846-g002\" target=\"_blank\">Fig. 2</a>, the affiliation to each strain is indicated by color as follows: black, <i>E. coli</i> DSM 18039; red, <i>E. coli</i> DSM 30038<sup>T</sup>; green, <i>P. aeruginosa</i> DSM 1707; blue, <i>P. aeruginosa</i> 429SC. Right, point estimates and 95% CIs for each of the four parameters lag phase (λ), slope (µ), maximum (A) and area under the curve (AUC) estimated from the eight curves depicted on the left using either the model-fitting (blue dots and CIs) or the spline approach (red dots and CIs). The gray stars are the respective point estimators inferred with the native OmniLog® software (which does not provide CIs). The colored circular areas refer to the colors of the curves in the left part of the figure.</p>", "links"=>[], "tags"=>["parameter", "ci", "estimates", "curves"], "article_id"=>320039, "categories"=>["Biotechnology", "Biological Sciences", "Genetics", "Microbiology"], "users"=>["Lea A. I. Vaas", "Johannes Sikorski", "Victoria Michael", "Markus Göker", "Hans-Peter Klenk"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0034846.g003", "stats"=>{"downloads"=>0, "page_views"=>0, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_parameter_and_CI_estimates_from_the_same_curves_using_three_distinct_approaches_/320039", "title"=>"Comparison of parameter and CI estimates from the same curves using three distinct approaches.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-04-20 00:00:39"}
  • {"files"=>["https://ndownloader.figshare.com/files/649729"], "description"=>"<p>Left, a plot of the raw respiration data illustrates their courses individually for each of the ten repetitions. The red curve (D12/4) was used as an exemplar for demonstrating the detection of significant differences via CIs. In the right panel, point estimates and 95% CIs for each of the four parameters from the spline approach are given for each replication. The blue lines highlight the position of the upper and lower limit of CIs from D12/4's parameters. A non-overlap of the CIs of different curves indicates a difference of a statistically detectable amount, and the distance between two intervals provides information about the expected minimum difference.</p>", "links"=>[], "tags"=>["curve-parameter", "estimates", "cis", "parameters", "lag", "repetitions", "respiration"], "article_id"=>320212, "categories"=>["Biotechnology", "Biological Sciences", "Genetics", "Microbiology"], "users"=>["Lea A. I. Vaas", "Johannes Sikorski", "Victoria Michael", "Markus Göker", "Hans-Peter Klenk"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0034846.g005", "stats"=>{"downloads"=>2, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_curve_parameter_point_estimates_and_their_95_CIs_for_each_of_the_four_parameters_lag_phase_955_slope_956_maximum_A_and_area_under_the_curve_AUC_estimated_for_ten_technical_repetitions_of_respiration_on_well_D12_/320212", "title"=>"Comparison of curve-parameter point estimates and their 95% CIs for each of the four parameters lag phase (λ), slope (μ), maximum (A) and area under the curve (AUC), estimated for ten technical repetitions of respiration on well D12.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-04-20 00:03:32"}
  • {"files"=>["https://ndownloader.figshare.com/files/649819"], "description"=>"<p>The upper panels show the plot of the respiration curves of <i>E. coli</i> DSM 18039 = K12 on well C08 when grown on solid LB medium for 16.75 h (t<sub>1</sub>), 18 h (t<sub>2</sub>), 19.33 (t<sub>3</sub>), 20.5 (t<sub>4</sub>), 21.92 (t<sub>5</sub>), 23.25 h (t<sub>6</sub>), 24.5 h (t<sub>7</sub>), 25.58 h (t<sub>8</sub>) or 40.33 h (t<sub>9</sub>), respectively, and subsequently measured on GEN III microplates™ in the PM modus over 91 h. The lower panels shows point estimates and 95% CIs for each of the four parameters from the spline approach. The blue lines highlight the position of the upper and lower limits of the CIs from repetition no. 4 at t<sub>5</sub>. A non-overlap of the CIs of different curves indicates a difference of a statistically detectable amount, and the distance between two intervals provides information about the expected minimum difference.</p>", "links"=>[], "tags"=>["estimates", "cis", "parameters", "lag", "replicates", "respiration", "cells", "additionally", "subjected", "pretreatments"], "article_id"=>320294, "categories"=>["Biotechnology", "Biological Sciences", "Genetics", "Microbiology"], "users"=>["Lea A. I. Vaas", "Johannes Sikorski", "Victoria Michael", "Markus Göker", "Hans-Peter Klenk"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0034846.g006", "stats"=>{"downloads"=>1, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Comparison_of_point_estimates_and_their_95_CIs_for_each_of_the_four_parameters_lag_phase_955_slope_956_maximum_A_and_area_under_the_curve_AUC_estimated_for_four_technical_replicates_of_respiration_on_well_C08_in_which_the_cells_were_additionally_subjecte/320294", "title"=>"Comparison of point estimates and their 95% CIs for each of the four parameters lag phase (λ), slope (μ), maximum (A) and area under the curve (AUC), estimated for four technical replicates of respiration on well C08, in which the cells were additionally subjected to distinct pretreatments (cultivation times).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-04-20 00:04:54"}
  • {"files"=>["https://ndownloader.figshare.com/files/649910"], "description"=>"<p>The upper panels show the results from the preliminary calculation, a simple calculation of group means of confidence limits and point estimators. The groups, here the distinct pretreatments (cultivation times t1 to t9), are given on the y-axis. For orientation, the blue lines highlight the position of upper and lower limit of CIs from repetition no. 4 at t<sub>5</sub>, in analogy to <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0034846#pone-0034846-g006\" target=\"_blank\">Fig. 6</a>. In the lower panels the 95% CIs for the differences of group means are represented. The set of user-defined comparisons was calculated for the point estimators of each of the four parameters lag phase (λ), slope (μ), maximum (A) and area under the curve (AUC). Since these are CIs for the differences between the means, a non-overlap with zero indicates a statistically detectable difference between the considered group means of the examined curve parameters.</p>", "links"=>[], "tags"=>["group-wise", "representations", "parameters", "lag"], "article_id"=>320404, "categories"=>["Biotechnology", "Biological Sciences", "Genetics", "Microbiology"], "users"=>["Lea A. I. Vaas", "Johannes Sikorski", "Victoria Michael", "Markus Göker", "Hans-Peter Klenk"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0034846.g007", "stats"=>{"downloads"=>1, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Visualization_of_group_wise_representations_of_the_four_curve_parameters_lag_phase_955_slope_956_maximum_A_and_area_under_the_curve_AUC_/320404", "title"=>"Visualization of group-wise representations of the four curve parameters lag phase (λ), slope (μ), maximum (A) and area under the curve (AUC).", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-04-20 00:06:44"}
  • {"files"=>["https://ndownloader.figshare.com/files/650151"], "description"=>"<p>Summary statistics from parameter estimation from the three dataset exemplars using both the model fitting and model-free spline fitting approach from the basic part of R's add-on package <i>grofit</i> (Kahm et al. 2010). Results with parameters ë<0 and A>400 indicate biologically unreasonable estimates; parameter estimates 0</p>", "links"=>[], "tags"=>["parameter"], "article_id"=>320651, "categories"=>["Biotechnology", "Biological Sciences", "Genetics", "Microbiology"], "users"=>["Lea A. I. Vaas", "Johannes Sikorski", "Victoria Michael", "Markus Göker", "Hans-Peter Klenk"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0034846.t001", "stats"=>{"downloads"=>0, "page_views"=>1, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Reliability_in_parameter_estimation_/320651", "title"=>"Reliability in parameter estimation.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2012-04-20 00:10:51"}
  • {"files"=>["https://ndownloader.figshare.com/files/649648"], "description"=>"<p>The raw colour intensities (black circles), measured over time (x-axis, hours) were fitted by both a parametric model (thick blue line) and a model-free spline (thick red line). The thin dashed lines indicate the maximum slope of each approach (thin dashed black line corresponds to the model fitting approach, the thin dashed red line to the spline, respectively). In the left panel the irregularity is better customized by the spline fit, whereas the model straightens it with the consequence of underestimating the maximum height (A). In case of (almost) no respiration (right panel), the fitted model apparently yielded biologically reasonable parameter estimates for µ but not for λ. In contrast, the spline approach exhibited overfitting and yielded overestimated µ and also overestimated, but biologically meaningful λ. Note the particularly broad CIs for these parameter estimates in <a href=\"http://www.plosone.org/article/info:doi/10.1371/journal.pone.0034846#pone-0034846-g003\" target=\"_blank\">Fig. 3</a>.</p>", "links"=>[], "tags"=>["parametric", "fitting", "model-free", "spline", "cases", "strains", "marked"], "article_id"=>320133, "categories"=>["Biotechnology", "Biological Sciences", "Genetics", "Microbiology"], "users"=>["Lea A. I. Vaas", "Johannes Sikorski", "Victoria Michael", "Markus Göker", "Hans-Peter Klenk"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0034846.g004", "stats"=>{"downloads"=>1, "page_views"=>4, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Visualization_of_parametric_fitting_and_model_free_spline_fitting_for_the_two_special_cases_from_G11_the_strains_marked_red_here_left_and_green_here_right_respectively_/320133", "title"=>"Visualization of parametric fitting and model-free spline fitting for the two special cases from G11, the strains marked red (here left) and green (here right), respectively.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-04-20 00:02:13"}
  • {"files"=>["https://ndownloader.figshare.com/files/650125"], "description"=>"<p>All-against-all correlations measured using Kendall's τ (above the diagonal) and Spearman's correlation index (below the diagonal) describe how the different curve parameters estimated using either model fitting or spline fit are associated with each other and with the corresponding parameters from the alternative fitting approach.</p>", "links"=>[], "tags"=>["between-method", "interdependence", "parameter"], "article_id"=>320613, "categories"=>["Biotechnology", "Biological Sciences", "Genetics", "Microbiology"], "users"=>["Lea A. I. Vaas", "Johannes Sikorski", "Victoria Michael", "Markus Göker", "Hans-Peter Klenk"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0034846.t002", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Within_method_and_between_method_interdependence_of_parameter_estimates_/320613", "title"=>"Within-method and between-method interdependence of parameter estimates.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2012-04-20 00:10:13"}
  • {"files"=>["https://ndownloader.figshare.com/files/649219"], "description"=>"<p>Each respiration curve is displayed as a thin horizontal line, in which the curve height as measured in OmniLog® units is represented by color intensity (darker parts indicate higher values). The x-axes correspond to the measurement time in hours. The upper part shows an overview of two plates. Here, the descriptions of the y axes (only visible if enlarged, but see below) list the names of the wells; the descriptions of the x axes list the measurement time in hours. The boxes below represent magnified parts of the upper panel to illustrate the color changes in the case of decreasing color intensities (regions surrounded by black ellipses) or technical problems such as short-term intermediate peaks (positions marked by eight-pointed stars).</p>", "links"=>[], "tags"=>["pm", "curves", "maps", "re-implementation", "jacobsen", "et"], "article_id"=>319699, "categories"=>["Biotechnology", "Biological Sciences", "Genetics", "Microbiology"], "users"=>["Lea A. I. Vaas", "Johannes Sikorski", "Victoria Michael", "Markus Göker", "Hans-Peter Klenk"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0034846.g001", "stats"=>{"downloads"=>0, "page_views"=>8, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Visualization_of_PM_curves_as_heat_maps_via_the_function_levelplot_as_a_re_implementation_of_the_approach_of_Jacobsen_et_al_2007_in_R_/319699", "title"=>"Visualization of PM curves as heat maps <i>via</i> the function <i>levelplot()</i> as a re-implementation of the approach of Jacobsen et al. (2007) in R.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-04-20 02:41:39"}
  • {"files"=>["https://ndownloader.figshare.com/files/650026"], "description"=>"<p>The outer figure is a scree plot in which the residual sums of squares (RSS, y-axis) are plotted against the corresponding predefined numbers of archetypes (x-axis). Apparently either four or five archetypes are optimal according to the “elbow criterion”. The insert (upper right) is a parallel coordinates plot showing the original measurements (gray lines) as well as the optimal archetypes (green, black, blue, violet and red lines) obtained if five archetypes are requested. On the x-axis, the names of the curve parameters are indicated. The minima and maxima of the four y-axes are also indicated. For an interpretation of the archetypes, see the main text.</p>", "links"=>[], "tags"=>["archetype", "parameters", "pm", "curves", "dataset", "smoothing"], "article_id"=>320513, "categories"=>["Biotechnology", "Biological Sciences", "Genetics", "Microbiology"], "users"=>["Lea A. I. Vaas", "Johannes Sikorski", "Victoria Michael", "Markus Göker", "Hans-Peter Klenk"], "doi"=>"https://dx.doi.org/10.1371/journal.pone.0034846.g008", "stats"=>{"downloads"=>4, "page_views"=>2, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Results_from_an_archetype_analysis_of_the_four_parameters_estimated_from_the_PM_curves_obtained_from_the_1_st_and_the_2_nd_dataset_using_the_smoothing_splines_/320513", "title"=>"Results from an archetype analysis of the four parameters estimated from the PM curves obtained from the 1<sup>st</sup> and the 2<sup>nd</sup> dataset using the smoothing splines.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2012-04-20 00:08:33"}

PMC Usage Stats | Further Information

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Relative Metric

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