PUMA publications for /author/Aaron%20Clausethttps://puma.uni-kassel.de/author/Aaron%20ClausetPUMA RSS feed for /author/Aaron%20Clauset2019-10-16T06:37:44+02:00Power-Law Distributions in Empirical Datahttps://puma.uni-kassel.de/bibtex/2c0097d202655474b1db6811ddea03410/stephandoerfelstephandoerfel2015-05-13T19:03:06+02:00clauset fit empirical powerLaw <span class="authorEditorList"><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Aaron Clauset" itemprop="url" href="/author/Aaron%20Clauset"><span itemprop="name">A. Clauset</span></a></span>, <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Cosma Rohilla Shalizi" itemprop="url" href="/author/Cosma%20Rohilla%20Shalizi"><span itemprop="name">C. Shalizi</span></a></span>, und <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="M. E. J. Newman" itemprop="url" href="/author/M.%20E.%20J.%20Newman"><span itemprop="name">M. Newman</span></a></span>. </span><span itemtype="http://schema.org/PublicationIssue" itemscope="itemscope" itemprop="isPartOf"><span itemtype="http://schema.org/Periodical" itemscope="itemscope" itemprop="isPartOf"><span itemprop="name"><em>SIAM Review</em></span></span> <em><span itemtype="http://schema.org/PublicationVolume" itemscope="itemscope" itemprop="isPartOf"><span itemprop="volumeNumber">51 </span></span>(<span itemprop="issueNumber">4</span>):
<span itemprop="pagination">661-703</span></em> </span>(<em><span>2009<meta content="2009" itemprop="datePublished"/></span></em>)Wed May 13 19:03:06 CEST 2015SIAM Review4661-703Power-Law Distributions in Empirical Data512009clauset fit empirical powerLaw Power-law distributions in empirical datahttps://puma.uni-kassel.de/bibtex/27da1624e601898dd74df839ce2daeb24/stummestumme2015-04-20T13:44:42+02:00distributions law distribution empirical power data powerlaw <span class="authorEditorList"><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Aaron Clauset" itemprop="url" href="/author/Aaron%20Clauset"><span itemprop="name">A. Clauset</span></a></span>, <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Cosma Rohilla Shalizi" itemprop="url" href="/author/Cosma%20Rohilla%20Shalizi"><span itemprop="name">C. Shalizi</span></a></span>, und <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="M. E. J. Newman" itemprop="url" href="/author/M.%20E.%20J.%20Newman"><span itemprop="name">M. Newman</span></a></span>. </span>(<em><span>2007<meta content="2007" itemprop="datePublished"/></span></em>)<em>cite arxiv:0706.1062Comment: 43 pages, 11 figures, 7 tables, 4 appendices; code available at http://www.santafe.edu/~aaronc/powerlaws/.</em>Mon Apr 20 13:44:42 CEST 2015cite arxiv:0706.1062Comment: 43 pages, 11 figures, 7 tables, 4 appendices; code available at http://www.santafe.edu/~aaronc/powerlaws/Power-law distributions in empirical data2007distributions law distribution empirical power data powerlaw Power-law distributions occur in many situations of scientific interest and
have significant consequences for our understanding of natural and man-made
phenomena. Unfortunately, the detection and characterization of power laws is
complicated by the large fluctuations that occur in the tail of the
distribution -- the part of the distribution representing large but rare events
-- and by the difficulty of identifying the range over which power-law behavior
holds. Commonly used methods for analyzing power-law data, such as
least-squares fitting, can produce substantially inaccurate estimates of
parameters for power-law distributions, and even in cases where such methods
return accurate answers they are still unsatisfactory because they give no
indication of whether the data obey a power law at all. Here we present a
principled statistical framework for discerning and quantifying power-law
behavior in empirical data. Our approach combines maximum-likelihood fitting
methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic
and likelihood ratios. We evaluate the effectiveness of the approach with tests
on synthetic data and give critical comparisons to previous approaches. We also
apply the proposed methods to twenty-four real-world data sets from a range of
different disciplines, each of which has been conjectured to follow a power-law
distribution. In some cases we find these conjectures to be consistent with the
data while in others the power law is ruled out.[0706.1062] Power-law distributions in empirical dataFinding community structure in very large networkshttps://puma.uni-kassel.de/bibtex/2458e03efb1ef50a5338907bb58c426f6/jpbajpba2014-10-17T20:01:34+02:002014 kde bachelorarbeit <span class="authorEditorList"><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Aaron Clauset" itemprop="url" href="/author/Aaron%20Clauset"><span itemprop="name">A. Clauset</span></a></span>, <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="M. E. J. Newman" itemprop="url" href="/author/M.%20E.%20J.%20Newman"><span itemprop="name">M. Newman</span></a></span>, und <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title=" and Cristopher Moore" itemprop="url" href="/author/null%20and%20Cristopher%20Moore"><span itemprop="name">and Cristopher Moore</span></a></span>. </span><span itemtype="http://schema.org/PublicationIssue" itemscope="itemscope" itemprop="isPartOf"><span itemtype="http://schema.org/Periodical" itemscope="itemscope" itemprop="isPartOf"><span itemprop="name"><em>Physical Review E</em></span></span> </span>(<em><span>2004<meta content="2004" itemprop="datePublished"/></span></em>)Fri Oct 17 20:01:34 CEST 2014Physical Review E1-- 6Finding community structure in very large networks20042014 kde bachelorarbeit Abstract: The discovery and analysis of community structure in networks is a topic of considerable recent interest within the physics community, but most methods proposed so far are unsuitable for very large networks because of their computational cost. Here we present a hierarchical agglomeration algorithm for detecting community structure which is faster than many competing algorithms: its running time on a network with n vertices and m edges is O(mdlog n) where d is the depth of the dendrogram describing the community structure. Many real-world networks are sparse and hierarchical, with m n and d log n, in which case our algorithm runs in essentially linear time, O(n log2 n). As an example of the application of this algorithm we use it to analyze a network of items for sale on the web-site of a large online retailer, items in the network being linked if they are frequently purchased by the same buyer. The network has more than 400 000 vertices and 2 million edges. We show that our algorithm can extract meaningful communities from this network, revealing large-scale patterns present in the purchasing habits of customers.Power-Law Distributions in Empirical Datahttps://puma.uni-kassel.de/bibtex/2c0097d202655474b1db6811ddea03410/stummestumme2012-03-16T10:24:55+01:00law power powerlaw <span class="authorEditorList"><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Aaron Clauset" itemprop="url" href="/author/Aaron%20Clauset"><span itemprop="name">A. Clauset</span></a></span>, <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Cosma Rohilla Shalizi" itemprop="url" href="/author/Cosma%20Rohilla%20Shalizi"><span itemprop="name">C. Shalizi</span></a></span>, und <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="M. E. J. Newman" itemprop="url" href="/author/M.%20E.%20J.%20Newman"><span itemprop="name">M. Newman</span></a></span>. </span><span itemtype="http://schema.org/PublicationIssue" itemscope="itemscope" itemprop="isPartOf"><span itemtype="http://schema.org/Periodical" itemscope="itemscope" itemprop="isPartOf"><span itemprop="name"><em>SIAM Review</em></span></span> <em><span itemtype="http://schema.org/PublicationVolume" itemscope="itemscope" itemprop="isPartOf"><span itemprop="volumeNumber">51 </span></span>(<span itemprop="issueNumber">4</span>):
<span itemprop="pagination">661--703</span></em> </span>(<em><span>2009<meta content="2009" itemprop="datePublished"/></span></em>)Fri Mar 16 10:24:55 CET 2012SIAM Review4661--703Power-Law Distributions in Empirical Data512009law power powerlaw Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution—the part of the distribution representing large but rare events—and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov–Smirnov (KS) statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data, while in others the power law is ruled out.Power-Law Distributions in Empirical Datahttps://puma.uni-kassel.de/bibtex/2c0097d202655474b1db6811ddea03410/jaeschkejaeschke2011-12-20T12:18:38+01:00power-law statistics analysis data <span class="authorEditorList"><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Aaron Clauset" itemprop="url" href="/author/Aaron%20Clauset"><span itemprop="name">A. Clauset</span></a></span>, <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Cosma Rohilla Shalizi" itemprop="url" href="/author/Cosma%20Rohilla%20Shalizi"><span itemprop="name">C. Shalizi</span></a></span>, und <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="M. E. J. Newman" itemprop="url" href="/author/M.%20E.%20J.%20Newman"><span itemprop="name">M. Newman</span></a></span>. </span><span itemtype="http://schema.org/PublicationIssue" itemscope="itemscope" itemprop="isPartOf"><span itemtype="http://schema.org/Periodical" itemscope="itemscope" itemprop="isPartOf"><span itemprop="name"><em>SIAM Review</em></span></span> <em><span itemtype="http://schema.org/PublicationVolume" itemscope="itemscope" itemprop="isPartOf"><span itemprop="volumeNumber">51 </span></span>(<span itemprop="issueNumber">4</span>):
<span itemprop="pagination">661--703</span></em> </span>(<em><span>2009<meta content="2009" itemprop="datePublished"/></span></em>)Tue Dec 20 12:18:38 CET 2011SIAM Review4661--703Power-Law Distributions in Empirical Data512009power-law statistics analysis data Power-law distributions occur in many situations of scientific interest and have significant consequences for our understanding of natural and man-made phenomena. Unfortunately, the detection and characterization of power laws is complicated by the large fluctuations that occur in the tail of the distribution—the part of the distribution representing large but rare events—and by the difficulty of identifying the range over which power-law behavior holds. Commonly used methods for analyzing power-law data, such as least-squares fitting, can produce substantially inaccurate estimates of parameters for power-law distributions, and even in cases where such methods return accurate answers they are still unsatisfactory because they give no indication of whether the data obey a power law at all. Here we present a principled statistical framework for discerning and quantifying power-law behavior in empirical data. Our approach combines maximum-likelihood fitting methods with goodness-of-fit tests based on the Kolmogorov–Smirnov (KS) statistic and likelihood ratios. We evaluate the effectiveness of the approach with tests on synthetic data and give critical comparisons to previous approaches. We also apply the proposed methods to twenty-four real-world data sets from a range of different disciplines, each of which has been conjectured to follow a power-law distribution. In some cases we find these conjectures to be consistent with the data, while in others the power law is ruled out.Power-law distributions in empirical datahttps://puma.uni-kassel.de/bibtex/27da1624e601898dd74df839ce2daeb24/folkefolke2010-05-04T08:55:46+02:00fit law analysis power data <span class="authorEditorList"><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Aaron Clauset" itemprop="url" href="/author/Aaron%20Clauset"><span itemprop="name">A. Clauset</span></a></span>, <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Cosma Rohilla Shalizi" itemprop="url" href="/author/Cosma%20Rohilla%20Shalizi"><span itemprop="name">C. Shalizi</span></a></span>, und <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="M. E. J. Newman" itemprop="url" href="/author/M.%20E.%20J.%20Newman"><span itemprop="name">M. Newman</span></a></span>. </span>(<em><span>2007<meta content="2007" itemprop="datePublished"/></span></em>)<em>cite arxiv:0706.1062
Comment: 43 pages, 11 figures, 7 tables, 4 appendices; code available at
http://www.santafe.edu/~aaronc/powerlaws/.</em>Tue May 04 08:55:46 CEST 2010cite arxiv:0706.1062
Comment: 43 pages, 11 figures, 7 tables, 4 appendices; code available at
http://www.santafe.edu/~aaronc/powerlaws/Power-law distributions in empirical data2007fit law analysis power data Power-law distributions occur in many situations of scientific interest and
have significant consequences for our understanding of natural and man-made
phenomena. Unfortunately, the detection and characterization of power laws is
complicated by the large fluctuations that occur in the tail of the
distribution -- the part of the distribution representing large but rare events
-- and by the difficulty of identifying the range over which power-law behavior
holds. Commonly used methods for analyzing power-law data, such as
least-squares fitting, can produce substantially inaccurate estimates of
parameters for power-law distributions, and even in cases where such methods
return accurate answers they are still unsatisfactory because they give no
indication of whether the data obey a power law at all. Here we present a
principled statistical framework for discerning and quantifying power-law
behavior in empirical data. Our approach combines maximum-likelihood fitting
methods with goodness-of-fit tests based on the Kolmogorov-Smirnov statistic
and likelihood ratios. We evaluate the effectiveness of the approach with tests
on synthetic data and give critical comparisons to previous approaches. We also
apply the proposed methods to twenty-four real-world data sets from a range of
different disciplines, each of which has been conjectured to follow a power-law
distribution. In some cases we find these conjectures to be consistent with the
data while in others the power law is ruled out.
Finding community structure in very large networkshttps://puma.uni-kassel.de/bibtex/20ea285bfc0f5a46ffec8a213e5133ba6/hothohotho2007-05-25T16:30:51+02:00networks clustering large community toread <span class="authorEditorList"><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Aaron Clauset" itemprop="url" href="/author/Aaron%20Clauset"><span itemprop="name">A. Clauset</span></a></span>, <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="M. E. J. Newman" itemprop="url" href="/author/M.%20E.%20J.%20Newman"><span itemprop="name">M. Newman</span></a></span>, und <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Cristopher Moore" itemprop="url" href="/author/Cristopher%20Moore"><span itemprop="name">C. Moore</span></a></span>. </span><span itemtype="http://schema.org/PublicationIssue" itemscope="itemscope" itemprop="isPartOf"><span itemtype="http://schema.org/Periodical" itemscope="itemscope" itemprop="isPartOf"><span itemprop="name"><em>Physical Review E</em></span></span> </span>(<em><span>2004<meta content="2004" itemprop="datePublished"/></span></em>)Fri May 25 16:30:51 CEST 2007Physical Review E066111Finding community structure in very large networks702004networks clustering large community toread [cond-mat/0408187] Finding community structure in very large networksFinding community structure in very large networkshttps://puma.uni-kassel.de/bibtex/2a35d69f1d41a6cdd0632c5e1cadb4d44/jaeschkejaeschke2006-05-15T16:42:47+02:00detection newman large community network structure gn <span class="authorEditorList"><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Aaron Clauset" itemprop="url" href="/author/Aaron%20Clauset"><span itemprop="name">A. Clauset</span></a></span>, <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="M.E.J. Newman" itemprop="url" href="/author/M.E.J.%20Newman"><span itemprop="name">M. Newman</span></a></span>, und <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Cristopher Moore" itemprop="url" href="/author/Cristopher%20Moore"><span itemprop="name">C. Moore</span></a></span>. </span><span itemtype="http://schema.org/PublicationIssue" itemscope="itemscope" itemprop="isPartOf"><span itemtype="http://schema.org/Periodical" itemscope="itemscope" itemprop="isPartOf"><span itemprop="name"><em>Physical Review E</em></span></span> </span>(<em><span>2004<meta content="2004" itemprop="datePublished"/></span></em>)Mon May 15 16:42:47 CEST 2006Physical Review E066111Finding community structure in very large networks702004detection newman large community network structure gn Finding community structure in very large networkshttps://puma.uni-kassel.de/bibtex/2f9a12630a6d31d576ea5222219a4cf0b/hothohotho2006-02-15T08:00:29+01:00clustering large community network <span class="authorEditorList"><span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Aaron Clauset" itemprop="url" href="/author/Aaron%20Clauset"><span itemprop="name">A. Clauset</span></a></span>, <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="M. E. J. Newman" itemprop="url" href="/author/M.%20E.%20J.%20Newman"><span itemprop="name">M. Newman</span></a></span>, und <span itemtype="http://schema.org/Person" itemscope="itemscope" itemprop="author"><a title="Cristopher Moore" itemprop="url" href="/author/Cristopher%20Moore"><span itemprop="name">C. Moore</span></a></span>. </span>(<em><span>August 2004<meta content="August 2004" itemprop="datePublished"/></span></em>)Wed Feb 15 08:00:29 CET 2006AugustFinding community structure in very large networks2004clustering large community network The discovery and analysis of community structure in networks is a topic of
considerable recent interest within the physics community, but most methods
proposed so far are unsuitable for very large networks because of their
computational cost. Here we present a hierarchical agglomeration algorithm for
detecting community structure which is faster than many competing algorithms:
its running time on a network with n vertices and m edges is O(m d log n) where
d is the depth of the dendrogram describing the community structure. Many
real-world networks are sparse and hierarchical, with m ~ n and d ~ log n, in
which case our algorithm runs in essentially linear time, O(n log^2 n). As an
example of the application of this algorithm we use it to analyze a network of
items for sale on the web-site of a large online retailer, items in the network
being linked if they are frequently purchased by the same buyer. The network
has more than 400,000 vertices and 2 million edges. We show that our algorithm
can extract meaningful communities from this network, revealing large-scale
patterns present in the purchasing habits of customers.