# Machine Learning/Kaggle Social Network Contest/Features

From Noisebridge

## TODO

- Precisely define the listed features

## Possible Features

- Node Features
- nodeid
- outdegree
- indegree
- local clustering coefficient
- reciprocation of inbound probability (num of edges returned / num of inbound edges)
- reciprocation of outbound probability (num of edges returned / num of outbound edges)

- Edge Features
- nodetofollowid
- shortest distance nodeid to nodetofollowid
- density? (
~~median path length~~) - does reverse edge exist? (aka is nodetofollowid following nodeid?)
- number of common friends
- indegrees & outdegrees of nodetofollowid

- Network features
- unweighted random walk score
- global clustering coefficient
- Adamic-Adar score
- see original paper
- R igraph: similarity.invlogweighted

- Clustering
- membership of the same strongly connected cluster
- using igraph clusters

- membership of the same strongly connected cluster

The response variable is the probability that the nodeid to nodetofollowid edge will be created in the future

## Joe's attempt

I'm planning on collecting features based on an edge. Then sample the features over existing and randomly created edges and fit a logistic regression model to it.

For an edge from node s to node t I will calculate:

- the in-degree of s
- the out-degree of s
- the in-degree of t
- the out-degree of t
- RLD
_{-1}(s) - RLD
_{1}(s) - RLD
_{0}(s) - RLD
_{-1}(t) - RLD
_{1}(t) - RLD
_{0}(t) - AA
_{0}^{1}(s,t) - AA
_{0}^{1.5}(s,t) - AA
_{0}^{2}(s,t) - AA
_{-1}^{1}(s,t) - AA
_{-1}^{1.5}(s,t) - AA
_{-1}^{2}(s,t) - AA
_{1}^{1}(s,t) - AA
_{1}^{1.5}(s,t) - AA
_{1}^{2}(s,t)

where

- RLD
_{x}(n) is 1 / log(0.1 + the x-degree of node n), where -1 = in, 1 = out and 0 = any. (RLD = reciprocal log of degree )- note that I add 0.1 so that nodes with degree 1 have a score of 1/log(1.1) = 10.49 rather than1/log(1) which is a divide by zero
- logs are taken to base e

I define N_{x}^{h}(n) to be the nodes reachable from *n* in *h* hops along either any edge (x = 0), edges from t towards s (x = -1) or edges from s towards t (x = 1).

I define C_{x}^{h}(s,t) as the set of common neighbours of s and t a distance of h hops from s and t, excluding nodes in a closer common neighbourhood ie

- C
_{x}^{h}(s,t) = (N_{x}^{h}(s) ∩ N_{-x}^{h}(t)) \ ∪_{h' < h }(N_{x}^{h'}(s) ∩ N_{-x}^{h'}(t))- h = 1.5 corresponds to nodes which are one hop from either s or t and two hops from either t or s

- The sets C
_{x}^{h}(s,t) are distinct for different h. - It is directional, ie sometimes C
_{x}^{h}(s,t)≠C_{x}^{h}(t,s) - AA is the Adamic-Adar score calculated over different common neighbourhoods.
- the subscript 0, -1, 1 referes to neighbours reachable be following any, in or out node respectively
- the superscript 1, 1.5 and 2 refer to the the number of hops from a focal node the neighbour is.

- AA
_{x}^{h}(s,t) = sum_{n ∈ Cxh(s,t)}RLD_{0}(n)