Editing Machine Learning/Kaggle Social Network Contest/Network Description

Jump to navigation Jump to search
Warning: You are not logged in. Your IP address will be publicly visible if you make any edits. If you log in or create an account, your edits will be attributed to your username, along with other benefits.

The edit can be undone. Please check the comparison below to verify that this is what you want to do, and then publish the changes below to finish undoing the edit.

Latest revision Your text
Line 6: Line 6:
* number of edges: 7,237,983
* number of edges: 7,237,983


== Conectivity ==
* Diameter of the directed graph
"A digraph is strongly connected if every vertex is reachable from every other following the directions of the arcs. On the contrary, a digraph is weakly connected if its underlying undirected graph is connected. A weakly connected graph can be thought of as a digraph in which every vertex is "reachable" from every other but not necessarily following the directions of the arcs. A strong orientation is an orientation that produces a strongly connected digraph." [http://en.wikipedia.org/wiki/Glossary_of_graph_theory wikipedia]
 
* The Training Graph is '''not''' weakly connected
* It contains 27 subgraphs This means that it can be broken down into at least two discrete subgraphs.
** c.f. [http://cneurocvs.rmki.kfki.hu/igraph/doc/R/clusters.html igraph clustering]
** There is one very large cluster containing all but 154 verticies, then 4 with size 10 - 37, 8 sized 3 - 7 and 13 size 2
** note that igraph seems to create a vertex labelled 0 but the labels in the traindata file range from 1 to 1133547
 
* I also grabbed the number of strongly connected subgraphs
{| border="1"
|-
!| Cluster Size
| 1 
|  2 
|  3 
|  4 
|  5   
|  9 
| 10
| 32464
|-
!| freq
|1100647   
| 162   
| 18   
|5 
|4   
|  1 
|    1 
|    1
|}
 
When I added all of the test data to the graph and then re-ran the cluster analysis it found 22 clusters instead of 27. The largest cluster grew by 72 vertices.
{| border="1"
|-
!| Cluster Size
| 1 
|  2 
|  3 
|  4 
|  5   
|  7 
| 10
| 23
| 37
| 1133394
| 1133466
|-
!| Train
| 1
| 13
| 3
| 2
| 2
| 1
| 1
| 2
| 1
| 1
| 0
|-   
!| Train + Test
| 1
| 13
| 2
| 1
| 1
| 1
| 1
| 1
| 0
| 0
| 1
|}
 
Is it more likely that clusters were created by removing nodes or that they merged due to randomly adding nodes?
* TODO: figure out probs of adding and removing nodes under different sampling hypotheses.
* TODO: identify the edges which are merging the clusters
* I'm guessing that the chances of a randomly generated edge joins the small clusters is very low.
 
* Diameter of the directed graph is 14
** This is the longest of the shortest directed paths between two nodes
** This is the longest of the shortest directed paths between two nodes
** R igraph
** R igraph
Line 97: Line 16:
*** sum([http://cneurocvs.rmki.kfki.hu/igraph/doc/R/neighborhood.html neighborhood.size](dg, 1, nodes=myGuys, mode="out"))
*** sum([http://cneurocvs.rmki.kfki.hu/igraph/doc/R/neighborhood.html neighborhood.size](dg, 1, nodes=myGuys, mode="out"))
*** mode = "in", "out" or "all"
*** mode = "in", "out" or "all"
==How the test set was created ==
The test set seems to have been generated by randomly picking out nodes from the the outnode column and in nodes from the in node column. ie Not just randomly creating edges between any nodes.
* All test out nodes are in the training out node column
* All but 13 test in nodes are in the training in node column
Please note that all contributions to Noisebridge are considered to be released under the Creative Commons Attribution-NonCommercial-ShareAlike (see Noisebridge:Copyrights for details). If you do not want your writing to be edited mercilessly and redistributed at will, then do not submit it here.
You are also promising us that you wrote this yourself, or copied it from a public domain or similar free resource. Do not submit copyrighted work without permission!

To protect the wiki against automated edit spam, we kindly ask you to solve the following CAPTCHA:

Cancel Editing help (opens in new window)
Retrieved from "https://www.noisebridge.net/wiki/Machine_Learning/Kaggle_Social_Network_Contest/Network_Description"