Structure, Tie Persistence and Event Detection in Large Phone and SMS Networks Leman Akoglu and Bhavana Dalvi {lakoglu, 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 AttributesNode 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 How are these attributes correlated to each other and to TP and UP ? Delta_CDelta_KDelta_rRTOTP Delta_C Delta_K Delta_r R TO10.22 TP1 CKrUP C K r10.39 UP1 If A calls/texts B n times, can we say anything about how many times B calls/texts A? Are a node’s degree and its neighbors’ degrees correlated? How does the total duration or the number of phonecalls and SMSs grow by the number of contacts a user has? Does tie strength of i and j depend on their neighborhood overlap? Reciprocity patterns can be used to spot outliers. Deg of node & avg deg of its neighbors exhibit assortative mixing Total node strength grows super- linearly by increasing degree. Tie strength increases by increasing neighborhood overlap on avg. Local network attributes do help to predict tie persistence. Using both tie attributes and node attributes improve prediction accuracy Regression techniques give better accuracy than rule based techniques. Tie Persistence Event Detection At which points in time does the behavior of the customers change considerably? Can the detected change-points be attributed to a set of nodes, i.e. can we characterize which customer(s) cause most of the change? 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. Large change in users’ “eigen-behaviors” is flagged as change- points (events) in time. Our method detected “events” that coincide with major holidays and festivals in our data set. These results can be used to spot top users who contributes most to detected changes. 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/SMS 6 months data Tie strength based on (a) # SMS (b) # Phone calls (c) Duration of phone calls