Support Vector Machines and Kernels for Computational Biology
Publication Date
October 31, 2008
Journal
PLOS Computational Biology
Authors
Asa Ben Hur, Cheng Soon Ong, Sören Sonnenburg, Bernhard Schölkopf, et al
Volume
4
Issue
10
Pages
e1000173
DOI
http://doi.org/10.1371/journal.pcbi.1000173
Publisher URL
http://journals.plos.org/ploscompbiol/article?id=10.1371%2Fjournal.pcbi.1000173
PubMed
http://www.ncbi.nlm.nih.gov/pubmed/18974822
PubMed Central
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2547983
Europe PMC
http://europepmc.org/abstract/MED/18974822
Web of Science
000261480700002
Scopus
55449125185
Mendeley
http://www.mendeley.com/research/support-vector-machines-kernels-computational-biology-9
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Figshare

  • {"files"=>["https://ndownloader.figshare.com/files/917051"], "description"=>"<p>The area under the ROC curve (auROC) of SVMs with the spectrum, mixed spectrum, and weighted degree kernels on the acceptor splice site recognition task for different substring lengths ℓ.</p>", "links"=>[], "tags"=>["roc", "svms", "weighted", "kernels", "acceptor", "splice", "substring", "lengths"], "article_id"=>587501, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Infectious Diseases", "Genetics"], "users"=>["Asa Ben-Hur", "Cheng Soon Ong", "Sören Sonnenburg", "Bernhard Schölkopf", "Gunnar Rätsch"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000173.t002", "stats"=>{"downloads"=>0, "page_views"=>6, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_area_under_the_ROC_curve_auROC_of_SVMs_with_the_spectrum_mixed_spectrum_and_weighted_degree_kernels_on_the_acceptor_splice_site_recognition_task_for_different_substring_lengths_8467_/587501", "title"=>"The area under the ROC curve (auROC) of SVMs with the spectrum, mixed spectrum, and weighted degree kernels on the acceptor splice site recognition task for different substring lengths ℓ.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-21 07:42:31"}
  • {"files"=>["https://ndownloader.figshare.com/files/916909"], "description"=>"<p>The polynomial kernel of degree 1 leads to a linear separation (A). Higher-degree polynomial kernels allow a more flexible decision boundary (B,C). The style follows that of <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000173#pcbi-1000173-g003\" target=\"_blank\">Figure 3</a>.</p>", "links"=>[], "tags"=>["polynomial"], "article_id"=>587367, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Infectious Diseases", "Genetics"], "users"=>["Asa Ben-Hur", "Cheng Soon Ong", "Sören Sonnenburg", "Bernhard Schölkopf", "Gunnar Rätsch"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000173.g006", "stats"=>{"downloads"=>0, "page_views"=>3, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_effect_of_the_degree_of_a_polynomial_kernel_/587367", "title"=>"The effect of the degree of a polynomial kernel.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:41:47"}
  • {"files"=>["https://ndownloader.figshare.com/files/916984"], "description"=>"<p>For large values of <i>σ</i> (A), the decision boundary is nearly linear. As <i>σ</i> decreases, the flexibility of the decision boundary increases (B). Small values of <i>σ</i> lead to overfitting (C). The figure style follows that of <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000173#pcbi-1000173-g003\" target=\"_blank\">Figure 3</a>.</p>", "links"=>[], "tags"=>["width", "parameter", "gaussian", "kernel", "soft-margin"], "article_id"=>587441, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Infectious Diseases", "Genetics"], "users"=>["Asa Ben-Hur", "Cheng Soon Ong", "Sören Sonnenburg", "Bernhard Schölkopf", "Gunnar Rätsch"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000173.g007", "stats"=>{"downloads"=>1, "page_views"=>9, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_effect_of_the_width_parameter_of_the_Gaussian_kernel_963_for_a_fixed_value_of_the_soft_margin_constant_/587441", "title"=>"The effect of the width parameter of the Gaussian kernel (<i>σ</i>) for a fixed value of the soft-margin constant.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:42:09"}
  • {"files"=>["https://ndownloader.figshare.com/files/916760"], "description"=>"<p>In the post-processing step, the pre-mRNA is transformed into mRNA. One necessary step in the process of obtaining mature mRNA is called <i>splicing</i>. The mRNA sequence of a eukaryotic gene is “interrupted” by noncoding regions called <i>introns</i>. A gene starts with an exon and may then be interrupted by an intron, followed by another exon, intron, and so on until it ends in an exon. In the splicing process, the introns are removed. There are two different splice sites: the exon–intron boundary, referred to as the donor site or 5′ site (of the intron), and the intron–exon boundary, that is, the acceptor or 3′ site. Splice sites have quite strong consensus sequences, i.e., almost every position in a small window around the splice site is representative of the most frequently occurring nucleotide when many existing sequences are compared in an alignment (cf. <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000173#pcbi-1000173-g005\" target=\"_blank\">Figure 5</a>). (The caption text appeared similarly in <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000173#pcbi.1000173-Rtsch1\" target=\"_blank\">[30]</a>, the idea for this figure is from <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000173#pcbi.1000173-Lewin1\" target=\"_blank\">[11]</a>.)</p>", "links"=>[], "tags"=>["steps"], "article_id"=>587216, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Infectious Diseases", "Genetics"], "users"=>["Asa Ben-Hur", "Cheng Soon Ong", "Sören Sonnenburg", "Bernhard Schölkopf", "Gunnar Rätsch"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000173.g004", "stats"=>{"downloads"=>0, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_major_steps_in_protein_synthesis_transcription_post_processing_and_translation_/587216", "title"=>"The major steps in protein synthesis: transcription, post-processing, and translation.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:40:53"}
  • {"files"=>["https://ndownloader.figshare.com/files/916583"], "description"=>"<p>The decision boundary divides the space into two sets depending on the sign of <i>f</i>(<b>x</b>) = 〈<b>w,x</b>〉+<i>b</i>. The grayscale level represents the value of the discriminant function <i>f</i>(<b>x</b>): dark for low values and a light shade for high values.</p>", "links"=>[], "tags"=>["linear", "classifier", "separating", "classes", "points"], "article_id"=>587037, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Infectious Diseases", "Genetics"], "users"=>["Asa Ben-Hur", "Cheng Soon Ong", "Sören Sonnenburg", "Bernhard Schölkopf", "Gunnar Rätsch"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000173.g001", "stats"=>{"downloads"=>1, "page_views"=>16, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_A_linear_classifier_separating_two_classes_of_points_squares_and_circles_in_two_dimensions_/587037", "title"=>"A linear classifier separating two classes of points (squares and circles) in two dimensions.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:39:50"}
  • {"files"=>["https://ndownloader.figshare.com/files/916700"], "description"=>"<p>We modified the toy dataset by moving the point shaded in gray to a new position indicated by an arrow, which significantly reduces the margin with which a hard-margin SVM can separate the data. (A) We show the margin and decision boundary for an SVM with a very high value of <i>C</i>, which mimics the behavior of the hard-margin SVM since it implies that the slack variables <i>ξ<sub>i</sub></i> (and hence training mistakes) have very high cost. (B) A smaller value of <i>C</i> allows us to ignore points close to the boundary, and increases the margin. The decision boundary between negative examples and positive examples is shown as a thick line. The thin lines are on the margin (discriminant value equal to −1 or +1).</p>", "links"=>[], "tags"=>["soft-margin"], "article_id"=>587161, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Infectious Diseases", "Genetics"], "users"=>["Asa Ben-Hur", "Cheng Soon Ong", "Sören Sonnenburg", "Bernhard Schölkopf", "Gunnar Rätsch"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000173.g003", "stats"=>{"downloads"=>2, "page_views"=>217, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_effect_of_the_soft_margin_constant_C_on_the_decision_boundary_/587161", "title"=>"The effect of the soft-margin constant, <i>C</i>, on the decision boundary.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:40:34"}
  • {"files"=>["https://ndownloader.figshare.com/files/916634"], "description"=>"<p>The region between the two thin lines defines the <i>margin area</i> with −1≤〈<b>w,x</b>〉+<i>b</i>≤1. The data points highlighted with black centers are the <i>support vectors</i>: the examples that are closest to the decision boundary. They determine the margin by which the two classes are separated. Here, there are three support vectors on the edge of the margin area (<i>f</i>(<b>x</b>) = −1 or <i>f</i>(<b>x</b>) = +1).</p>", "links"=>[], "tags"=>["computed", "linear"], "article_id"=>587095, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Infectious Diseases", "Genetics"], "users"=>["Asa Ben-Hur", "Cheng Soon Ong", "Sören Sonnenburg", "Bernhard Schölkopf", "Gunnar Rätsch"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000173.g002", "stats"=>{"downloads"=>3, "page_views"=>12, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_The_maximum_margin_boundary_computed_by_a_linear_SVM_/587095", "title"=>"The maximum margin boundary computed by a linear SVM.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:40:13"}
  • {"files"=>["https://ndownloader.figshare.com/files/916869"], "description"=>"<p>The sequence logo <a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000173#pcbi.1000173-Schneider1\" target=\"_blank\">[72]</a>,<a href=\"http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000173#pcbi.1000173-Crooks1\" target=\"_blank\">[73]</a> shows the region around the intron/exon boundary—the acceptor splice site. In the running example, we use the region up to 40 nt upstream and downstream of the consensus site AG.</p>", "links"=>[], "tags"=>["logo", "acceptor", "splice", "sites", "occurring", "nucleotide", "sequences", "compared"], "article_id"=>587318, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Infectious Diseases", "Genetics"], "users"=>["Asa Ben-Hur", "Cheng Soon Ong", "Sören Sonnenburg", "Bernhard Schölkopf", "Gunnar Rätsch"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000173.g005", "stats"=>{"downloads"=>2, "page_views"=>16, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_Sequence_logo_for_acceptor_splice_sites_splice_sites_have_quite_strong_consensus_sequences_i_e_almost_every_position_in_a_small_window_around_the_splice_site_is_representative_of_the_most_frequently_occurring_nucleotide_when_many_existing_sequences_are_c/587318", "title"=>"Sequence logo for acceptor splice sites: splice sites have quite strong consensus sequences, i.e., almost every position in a small window around the splice site is representative of the most frequently occurring nucleotide when many existing sequences are compared in an alignment.", "pos_in_sequence"=>0, "defined_type"=>1, "published_date"=>"2013-02-21 07:41:26"}
  • {"files"=>["https://ndownloader.figshare.com/files/917084"], "description"=>"<p>Accuracy is measured using the area under the ROC curve (auROC) and is computed using 5-fold cross-validation (cf. the section Running Example: Splice Site Recognition for details).</p>", "links"=>[], "tags"=>["acceptor", "polynomial", "gaussian", "kernels", "degrees", "widths"], "article_id"=>587536, "categories"=>["Information And Computing Sciences", "Biological Sciences", "Infectious Diseases", "Genetics"], "users"=>["Asa Ben-Hur", "Cheng Soon Ong", "Sören Sonnenburg", "Bernhard Schölkopf", "Gunnar Rätsch"], "doi"=>"https://dx.doi.org/10.1371/journal.pcbi.1000173.t001", "stats"=>{"downloads"=>4, "page_views"=>5, "likes"=>0}, "figshare_url"=>"https://figshare.com/articles/_SVM_accuracy_on_the_task_of_acceptor_site_recognition_using_polynomial_and_Gaussian_kernels_with_different_degrees_d_and_widths_963_/587536", "title"=>"SVM accuracy on the task of acceptor site recognition using polynomial and Gaussian kernels with different degrees <i>d</i> and widths <i>σ</i>.", "pos_in_sequence"=>0, "defined_type"=>3, "published_date"=>"2013-02-21 07:42:45"}

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