Swarm: Mining Relaxed Temporal Moving

Mining Following Relationships in Movement DataZhenhui Jessie Li, Fei WuPennsylvania State UniversityICDM ConferenceDallas, TexasDecember 8, 20131

Margaret CrofootUC Davis1Booming Age of Spatial and Temporal Data2IDTimestampLocationPeter2010-04-02 13:1237.5, -122.5Peter2010-04-02 15:2237.2, -123.5

Advanced satellite, sensors, RFID, and wireless technologies:Prevalence of mobile devices such as smart phonesGPS embedded in carsSensors attached on animalsA trajectory: A sequence of timestamps and locations

Human movementAnimal movementZhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement DataMoving Object Relational Patterns3

Periodic patterns [KDD10, KDD12]: self relationship, repeated behaviorSwarm pattern [VLDB10]: moving object clustersFollower pattern: moving together but with time lagZhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement DataChallenges in Detecting Following Patterns1. The following time lag is varying- follow with lag 1 minute to 10 minutes2. Trajectories are highly dynamic- follower may take different routes3. Following only happens in a short period of time- 9 minutes following interval in an one-year tracking period4

Problem: Given two moving objects R=r1r2r3rn and S=s1s2s3sn, find the time intervals that R follows Sclick the image to play videoZhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement DataPrevious Work: Find Following Patterns Using Front Region5

Ss1s2s3s4s5Rr1r2r3r4r5in front regionnoyesnonoyess1s2s3s4s5r1r2r3r4r5Laube and Imfeld: REMO: Analyzing Relative Motion within Groups of Trackable Moving Point Objects. GIScience 2002Andersson, Gudmundsson, Laube, and Wolle: Reporting Leaders and Followers among Trajectories of Moving Point Objects. GeoInformatica 12(4) 2008Three parameters to define front region:Problem: Leader may not necessarily be in the front regionZhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement DataPrevious Work: Correlation-Based Method6

starting point itime window wtime lag lRS

Cross Correlation:A frequently used method in time series to measure the similarity between lagged time seriesProblem:Assume a constant time lagEnumerating three parameters will report many duplicate time intervals, cannot dig out the true intervalExpensive time: O(n4)Shirabe. "Correlation analysis of discrete motions." Geographic Information Science. 2006. Zhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement DataDynamic Time Warping Idea to Handle Varying Time Lags7

dmaxlmax = 3A following pair: ri follows sj(1) dist(ri, sj) dmax(2) 0< i-j lmax* green lines indicate following pairZhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement DataFind Following Intervals using Local Sequence Alignment (LSA)Find following time intervals = best local sequence alignmentDTW (minimize distances) LSA (maximize matchings)Use dynamic programming8

Optimal matching: R[3:14] match with S[1:13]Zhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement Datalocal sequence alignment to find local following intervals8

LSA Greedily Maximizes Alignment Score9

Optimal matching: R[3:14] match with S[1:13]R[12:14] moves with S[12:14]Problem with LSA: cannot differentiate following from moving together Zhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement DataLocal Minimizer to Differentiate Following from Moving Together10

* green line indicates local minimizer

if sj is the local minimizer for rij < i, f(i) = 1(ri follows sj)j i, f(i) = 0 (ri not follow sj)if ri has no local minimizer, f(i)=xsj is the Local Minimizer to ri(1) sj (j in [i-lmax, i+lmax]) is the closest point to ri(2) dist(ri, sj) dmaxZhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement DataSignificant Following Time Interval11

if sj is the local minimizer for rij < i, f(i) = 1(ri follows sj)j i, f(i) = 0 (ri not follow sj)if ri has no local minimizer, f(i)=xSignificant following time interval I should have higher following frequency than expected

Expected following frequency:

If R and S are moving together, we expect half following (1s) and half non-following (0s)

Following score (difference between actual and expected frequency):Zhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement Data

Significant Following Time Interval12R follows S from r3 to r11 and then moves together with S from r12 to r14

Interval with maximal score:Zhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement DataExperiments: Method for Comparison13

starting point itime window wtime lag lRS

REMO 2. Correlation-based method3. LSA: local sequence alignmentnot successfulnot successfulmoderately successfulZhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement DataSynthetic Dataset for Effectiveness Evaluation14

Synthetic data:Generate by Rayleigh flight model (random walk)Following time lag vary from 1 to 10Following distance: 8True following range: [100:250] and [700:800]R trajectoryS trajectoryfollowing locations

Zhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement DataCase Studies on Real Baboon Data1526 baboons tracked from 8/1-27, 2012 in Laikipia KenyaSampling rate: 1 secondParameter: dmax = 50 (meters), lmax = 60 (seconds)

http://faculty.ist.psu.edu/jessieli/icdm13/following.html

click the image to play videoVisit this webpage to see animationZhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement Data15REMO Reports Many Small Intervals16

[2969:3221]Case 3. 10:00-11:00 AM August 2, 2012

REMO breaks this interval into many small intervalsREMO reports many small non-following intervalsZhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement DataCorrelation-based Method Reports Many Duplicate intervals17

Case 3. 10:00-11:00 AM August 2, 2012

bold intervals: duplicate intervalsZhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement Data

LSA is Sensitive to Distance Parameter18Case 3. 10:00-11:00 AM August 2, 2012[2969:3221]

dmax = 50: treat this interval as moving togetherdmax = 25: break it into many small intervalsZhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement DataSummaryWe propose a simple but effective method to detect following time intervals between two moving objectslocal minimizer: find the closest locationtwo relaxed parameters: dmax and lmaxsignificant time intervals: followings more than expectedlinear complexity O(n)Our solutions addresses real challengesunknown and varying time lagsdynamics in trajectoriessubtle relationships19Zhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement DataFuture Work: Understand the Context20

Across the forestOn the roadZhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement DataFuture Work: From Pairs to Social Network21

Thanks! Questions?Zhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement Data22Mining Following Relationships in Movement Data23Supplementary slidesMining Following Relationships in Movement DataSignificant Following Time Interval24

if sj is the local minimizer for rij < i, f(i) = 1(ri follows sj)j i, f(i) = 0 (ri not follow sj)if ri has no local minimizer, f(i)=xSignificant following time interval I should have higher following frequency than expected

Expected following frequency:

If R and S are moving together, we expect half following (1s) and half non-following (0s)

Following score (difference between actual and expected frequency):Zhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement Data

Maximal Segment = the Following Time Intervals25

Maximal segment: [3,11]R follows S from r3 to r11 and then moves together with S from r12 to r14Zhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement DataReverse Test26Relationship symmetry: if ri follows sj, sj should lead ri

s7 is local minimizer for r8 r8 follows s7r8 is not the local minimizer for s7 s7 does not lead r8

s7 is local minimizer for r7 r7 follows s7r7 is the local minimizer for s7 s7 leads r7Satisfy symmetryNot satisfy symmetryZhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement DataReverse Test Modifies Following Score27

Not satisfy symmetry, value 1 becomes 0Value 1 remains if pass reverse testValue 1 becomes 0 if fail reverse testValue 0 becomes -1Then, same Maximal Segment method can be appliedZhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement DataCase Study for Method Comparison28

Zhenhui Jessie Li, Penn State UniversityMining Following Relationships in Movement Data