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#LyX 2.0 created this file. For more info see http://www.lyx.org/
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\begin_body
\begin_layout Section
Definitions
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\begin_layout Subsection
Friendship:
\end_layout
\begin_layout Standard
Defined as having met another node at least twice after 5 PM or having met
another node at least twice in a context that is not
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university.
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\begin_layout Subsection
Personalized Page Rank
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\begin_layout Itemize
Briefly, a personalized PageRank is like standard PageRank, except that
when randomly teleporting to a new node, the surfer always teleports back
to the given source node being personalized (rather than to a node chosen
uniformly at random, as in the classic PageRank algorithm).
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That is, the random surfer in the personalized PageRank model works as follows:
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He starts at the source node X that we want to calculate a personalized
PageRank around.
At step i: with probability p, the surfer moves to a neighboring node chosen
uniformly at random; with probability 1−p, the surfer instead teleports
back to the original source node X.
The limiting probability that the surfer is at node N is then the personalized
PageRank score of node N around X.
\end_layout
\begin_layout Subsection
Mean Average Precision
\end_layout
\begin_layout Standard
Some simplification of the Mean Average Precision measure is used to score
the predictions.
At the moment though order doesn't matter.
\end_layout
\begin_layout Section
Data
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\begin_layout Standard
I split the whole observation period into bins of roughly 2 months (58.1538461538
4615 days).
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Some statistics for the networks are:
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\begin_layout Section
Models
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Goal
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The goal of the models is to see whether given a set of feature at t
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0
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\end_inset
you can predict whether there will be an edge (in this case a friendship)
between nodes at point t
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1
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.
\end_layout
\begin_layout Subsection
General approach
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In order to run a machine learning algorithm to recommend edges (which would
take two nodes, a source and a candidate destination, and generate a score
measuring the likelihood that the source would follow the destination),
it’s necessary to prune the set of candidates to run the algorithm on.
The approach was to calculate a personalized PageRank around each source
node.
\end_layout
\begin_layout Standard
I then only considered the 25 highest scoring candidate nodes for the next
step.
After pruning the set of candidate destination nodes to a more feasible
level, I fed pairs of (source, destination) nodes into a machine learning
model.
In this case a random forest model.
\end_layout
\begin_layout Subsection
Base
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Features:
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\begin_layout Itemize
Time spent together with another node
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To add:
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Adamic Adar scores
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Network similarity measures
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\begin_layout Subsection
Social
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Base model + additional features:
\end_layout
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Spatial-triadic closure
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\begin_layout Itemize
Potential spatial-triadic closure
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Number of other people present
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Time
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Base model + additional features:
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Mode of the hour of the day
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Mode of the day of the week
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\begin_layout Itemize
Mode of the hour of the week
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\begin_layout Subsection
Place
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Base model + additional features:
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Met at home
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Met at university
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Met at third place
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\begin_layout Subsection
Social & Time
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Features: Combination of social and time model
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\begin_layout Subsection
Place & Time
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\begin_layout Standard
Features: Combination of place and time model
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\begin_layout Subsection
Social & Place
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\begin_layout Standard
Features: Combination of social and place model
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\begin_layout Subsection
Social & Place & Time
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Features: Combination of all features
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\begin_layout Section
Outcomes
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At the moment I split the data into 10 bins and use 9 bins to train a random
forest model and test it on the 10th bin.
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As a measure the Mean Average Precision of the predicted links was used.
The outcomes for the first time-step are as follows:
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Next steps
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Do the analysis for all time steps
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Add additional features
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\begin_layout Itemize
Assess the importance of the features
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\begin_layout Itemize
Update MAP measure
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\begin_layout Itemize
Make sure the
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met at home
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metric works
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\begin_layout Section
Open questions
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How to best define friendship?
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\begin_layout Itemize
How many bins for testing?
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\begin_layout Itemize
What time periods to consider? All or just the first few as they are densest?
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\begin_layout Itemize
What to do with people that are singletons?
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\end_body
\end_document