Structure, Tie Persistence and Event Detection in Large Phone and SMS Networks

Leman Akoglu and Bhavana Dalvi{lakoglu , bbd} @cs.cmu.edu

Carnegie Mellon University and iLab

Dataset used for this work was provided by iLab at Carnegie Mellon University.

• Tie Persistence (TP) : It is the stability of ties across time as number of time-ticks in which a link is observed, over the total number P of time-ticks.

• User Perseverance (UP) : Perseverance of a user is defined as the average of the persistence of all his/her ties.

Tie Persistence

(2) Event Detection: • Define a sliding window of size W (set to 5 days) • Generate a correlation matrix C, with Cij being Pearson’s correlation

between the time series of pair (i,j)over window W. • Largest eigenvector of C give the “activity” of each node. • Compare “activity” vectors over time by taking dot product score Z (1 if same, 0 if perpendicular –flag for small Z)

Structure Analysis

Phone and SMS network

Tie Attributes Node Attributes

Reciprocity (R) : 1 if the tie is reciprocal in time tick

Degree (K)

Topological Overlap (TO) : Cluster Coefficient (C) :

User reciprocity (r) : Faction of ties containing both incoming and outgoing calls

# common neighbours

Node degree

# triads in which node is involved

Tie Persistence Event Detection

Methodology(1) Feature extraction: • Characterize nodes

with 12 network-features F: degree (number of contacts), total weight (phone call duration), …

• One TxN time-series matrix per feature, T=183 days N=1,8M users

(left) Z score vs time with W=5 and F=inweight (number of calls received).Top 10 days with the largest Z score is highlighted in red bars. (middle) u(t) vs r(t-1) for each node at T=Dec 26th. Top 5 nodes with the largest change is marked with red stars. (right) inweight vs time for the top 5 nodes marked –notice the change in calling behavior during the Christmas week.

• How to predict whether a link will persist in the future?

• Which link and node attributes are important in prediction?

Around 2M users, 50M edges, 500M phone

calls/SMS6 months data

Tie strength based on (a) # SMS (b) # Phone calls (c) Duration of phone calls