anomalous node detection in time series of mobile communication graphs leman akoglu january 28, 2010
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Anomalous Node Detection in Time Series of
Mobile Communication Graphs
Leman AkogluJanuary 28, 2010
Project Question
(1) In a given graph in which- edges are weighted- nodes are UNlabeled
which nodes to consider as “anomalous”?
(2) How about in a time-series of graphs?
Dataset: who-calls/texts-whom• 3 million customers interacting over 6 months
• + incoming/outgoing edges from/to out-of-network users
• Both SMS and phone-call
ego
4
egonetWhich nodes are anomalous?
Which nodes are anomalous?
5
Features to characterize nodes
Ni: number of neighbors (degree) of ego i
Ei: number of edges in egonet i
Wi: total weight of egonet i
Si: number of singleton neighbors of ego i with degree 1
max(di): average degree of i’s neighbors …
features nodes
M
“2-mode look” at the data as a matrix
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Which nodes are anomalous?
time
nodes
M
“3-mode look” at the data as a tensor
features
time
Mt
nodes
time
UVT∑
Preliminary objectives
• ICA? Robust PCA?• How to capture correlations between
features?• How to do evaluation? • Anomalous edges/groups of nodes?