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Mining Event Periodicity from Incomplete Observations Zhenhui (Jessie) Li*, Jingjing Wang, Jiawei Han University of Illinois at Urbana-Champaign *Now at Penn State University KDD 2012 Beijing, China 1Zhenhui Jessie Li

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Prologue: Detect Periodicity in Movements [Li et al., KDD’10] 2Zhenhui Jessie Li Problem: What is the periodicity of the movement? Bee example: 8 hours in hive 16 hours fly nearby

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Prologue: Detect Periodicity in Movements [Li et al., KDD’10] Observe the in-and-out movements from the reference spot (i.e., hive). in hive outside hive time 3Zhenhui Jessie Li Two-Dimensional Movement One-Dimensional Binary Sequence Easy to see the periodicity.

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Challenge: Periodicity Detection for Incomplete Observations Two factors result in incomplete observations: inconsistent + low sampling rate Movement data collection in real scenarios: – Human movements data collected from cellphones: only report locations when making calls – Animal movement data: 2~3 locations in 3~5 days Zhenhui Jessie Li :03 in :30 out :12 in :03 in :14 out :15 in … in hive outside hive Complete ObservationsIncomplete Observations

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A Challenging Case of Detecting Periodicity for Incomplete Observations Zhenhui Jessie Li :03 in :30 out :12 in :03 in :14 out :15 in … Sparse Raw Data inoutin Any periodicity in the above sequence?

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Mining Periodicity in Incomplete Data Zhenhui Jessie Li6 Event has a period of 20 Occurrences of the event happen between 20k+5 to 20k+10

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A Probabilistic Model for Periodic Event Zhenhui Jessie Li7 Example: Human daily periodicity visiting office Period as 24 Visiting office at 10-11am, 14-16pm

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A Probabilistic Model for Periodic Event with Random Observation Zhenhui Jessie Li8 generate x(5)=1 x(62)=0

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Periodicity Detection by Overlaying Observations Zhenhui Jessie Li9 Skewed distribution Even distribution True period Wrong period

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Relationship between Observation Ratio and Probabilistic Model Zhenhui Jessie Li10 Pos/Neg RatioPeriodic Distribution Vector

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Discrepancy Score to Measure Periodicity Zhenhui Jessie Li11 If T (=24) is the correct period, the discrepancy score should be large for certain set of timestamps If T (=23) is the wrong period, the discrepancy scores are likely to be zero for any set of timestamps

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Periodicity Measure Zhenhui Jessie Li12

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Performance Comparisons Zhenhui Jessie Li13 Sampling rate (Ratio of observed points in the complete sequence)

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Experiment on Real Human Data Zhenhui Jessie Li14 One person’s visits to a specific location Sampling rate: 20min Sampling rate: 1hour

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Problems with Using Fourier Transform to Detect Periodicity Zhenhui Jessie Li15 T=4 T=16

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Summary: Mining Event Periodicity from Incomplete Observations Motivation – Challenge of the real data: incomplete observations (inconsistent + low sampling rate) Method – Overlay the segments and measure the “skewness” of the distribution – Theoretically prove the correctness of the method Application – Location prediction – 2 nd place in Nokia Mobile Data Challenge 2012 – Periodicity-based feature + SVM Zhenhui Jessie Li16 Thanks! Questions?

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