most recent 30 from http://mathoverflow.net 2013-06-19T06:18:22Z http://mathoverflow.net/feeds/user/31666 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/128973/toolbox-for-directed-graphs Fatime 2013-04-28T01:19:14Z 2013-04-28T03:25:14Z

<p>Is there any toolbox to analyze directed graphs(especially Matlab toolbox)? Now, I want to generate some standard synthetic data, for example directed graph with modular structure(with some clusters) to test different clustering methods. I find some nice toolbox for undirected graphs that analyze statistic properties very well but I don't find for directed one.</p> <p>Thanks</p>

http://mathoverflow.net/questions/126888/global-solution-for-spectral-clustering Fatime 2013-04-08T18:06:20Z 2013-04-10T13:49:09Z

<p>I used spectral clustering for directed graphs suggested by Dengyong Zhou <a href="http://www.machinelearning.org/proceedings/icml2005/papers/131_LabeledUnlabeledGraph_ZhouEtAl.pdf" rel="nofollow">paper</a> to partition the graph.I selected the eigen vectors corresponding to k largest eigen values and then I use kmeans or FCM to partition them.For real data, I don't know the structure or pattern of the graph (the number of clusters, the diameters of the clusters, etc.).When I partition the graph into 2 clusters(by the sign of the eigenvector corresponding to second largest eigenvalue and without using kmeans or FCM) the result seems to be ok (the connections inside the cluster are strong) and it is natural because it is the global optimum, but for more than 2 I don't know how to determine if the result is good or not. Is there any optimum global solution for more than 2 clusters? How can I obtain the best result(with some mathematical reasoning)? any suggestion? I also ask similar question in <a href="http://math.stackexchange.com/questions/354919/global-solution-for-spectral-clustering" rel="nofollow">math.st</a></p> <p>Thanks.</p>

http://mathoverflow.net/questions/122779/stationary-distribution-for-different-types-of-graph Fatime 2013-02-24T05:43:42Z 2013-02-24T19:55:54Z

<p>This is a follow-up question to posts:</p> <p><a href="http://math.stackexchange.com/questions/311147/stationary-distribution-for-directed-graph" rel="nofollow">Stationary distribution for directed graph</a></p> <p><a href="http://math.stackexchange.com/questions/312626/stationary-distribution-for-different-types-of-graph/313201#313201" rel="nofollow">Stationary distribution for different types of graph</a></p> <p>The definition of stationary distribution in wikipedia:<a href="http://en.wikipedia.org/wiki/Markov_chain#Steady-state_analysis_and_limiting_distributions" rel="nofollow">Steady-state analysis and limiting distributions</a></p> <p>Are stationary distributions of graphs with every property(for example directed or undirected, strongly connected or sparse, periodic or aperiodic)proportional to eigenvector corresponding to eigenvalue 1 ?</p> <p>If not, what is the difference for each case?</p> <p>I know when the graph is undirected strongly connected and aperiodic, there is a unique stationary distribution equal to the degree of the vertex divided by the overall degree of nodes.But I don't Know how is it for other type of graph.</p> <p>Thanks</p>

http://mathoverflow.net/questions/122632/stationary-distribution-for-directed-graph Fatime 2013-02-22T14:42:32Z 2013-02-22T15:30:05Z

<p>I want to implement the algorithm of graph partitioning of sparse directed graph. In this algorithm after computing the transition matrix ,we should compute the stationary distribution of the random walk. I don't know how to compute the stationary distribution of random walk in such sparse directed graph.Is there any suggestion?</p>

http://mathoverflow.net/questions/132094/finding-optimum-point-of-parameters Fatime 2013-05-29T06:01:47Z 2013-05-29T06:01:47Z

@Christopher Thanks a lot for comment.I wait for any answer to help but there are a little attempt to my question.Is the question not clear?Whats the problem ? Do I select bad tags? The equation is linear combination of this three parameter ar1g1+a2g2+a3g3 and g1, g2 and g3 are some known constant and a1+a2+a3=1, if I use kfold test to find the optimum point the space of search is very large because of large dataset. Is there any test method for such cases?

http://mathoverflow.net/questions/128973/toolbox-for-directed-graphs Fatime 2013-04-28T05:09:08Z 2013-04-28T05:09:08Z

@ S. Sra Thanks for comment Why wrong? Is there low probability that the specialist work on like this toolbox?

http://mathoverflow.net/questions/126888/global-solution-for-spectral-clustering Fatime 2013-04-10T15:30:52Z 2013-04-10T15:30:52Z

@Federico I just like to receive answer as soon as possible and to consult different researchers.I also link to my question to if I accept the answer.What's the problem?By the way, I'm newcomer :) and I'll be happy if you mention any point I don't know.

http://mathoverflow.net/questions/122779/stationary-distribution-for-different-types-of-graph Fatime 2013-02-24T17:40:09Z 2013-02-24T17:40:09Z

@Ori Thanks for comment. I think this property is only satisfied for unique stationary distribution.Are you sure it is satisfied for each graph? – FatimeRahman 5 hours ago

http://mathoverflow.net/questions/122632/stationary-distribution-for-directed-graph/122638#122638 Fatime 2013-02-24T05:04:55Z 2013-02-24T05:04:55Z

Thanks a lot for your answer :) .Does this property(I mean the stationary distribution is proportional to left o right eigenvector corresponding to eigenvalue 1 ) true for every type of graph such as directed or undirected,strongly connected or sparse, periodic or aperiodic?