Machine Learning/Kaggle Social Network Contest/Network Description: Difference between revisions
(→Conectivity: effect of adding test data on clusters) |
|||
Line 9: | Line 9: | ||
"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] | "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 Graph is '''not''' weakly connected | * 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. | * 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] | ** c.f. [http://cneurocvs.rmki.kfki.hu/igraph/doc/R/clusters.html igraph clustering] | ||
Line 38: | Line 38: | ||
| 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. | |||
* 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 | * 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 |
Revision as of 00:53, 24 November 2010
Here we can put the descriptive statistics of the network:
- Number of fully sampled nodes: 37,689
- ie the unique "outnodes" in the edge list
- Total number of nodes: 1,133,547
- number of edges: 7,237,983
Conectivity
"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." 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. 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
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.
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.
- 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
- R igraph
- diameter (dg, directed = TRUE, unconnected = TRUE)
- Was taking forever so I aborted (after 34 minutes...)
- Total number of direct neighbours out: 7 275 672, in: 508 688, all: 7 473 273
- For each of our 38k I calculated the number of outbound neighbours and summed it
- R igraph:
- sum(neighborhood.size(dg, 1, nodes=myGuys, mode="out"))
- mode = "in", "out" or "all"