When And Where Next: Individual Mobility Prediction

1. When And Where Next: Individual Mobility Prediction GyözöGidofalvi and Fang Dong Geodesy and Geoinformatics KTH – Royal InstituteofTechnology

2. Outline Motivation Related work Problem definition Inhomogeneous Continuous-Time Markov (ICTM) model for temporal and spatial mobility prediction Empirical evaluation Conclusions and future work MobiGIS 2012, Redondo Beach, CA

3. Motivation Increasing adoption of location-aware mobile devices • Capable of observing and processing the movement information of the individual mobile user • Cons of mobile computing: distributed processing and privacy-preservation Increasing adoption of Location-Based Services (LBS) • Most services still only focus on current location of the user Movement of an individual contains a high degree of regularity • Trajectory of an individual exhibits a 93% potential predictability [Barabasi et. al] • Regularity can be temporal, periodic and sequential Broad applications of movement prediction • Transport • Urban planning • Mobile communication network optimization • Prefetching for LBS MobiGIS 2012, Redondo Beach, CA

4. Outline Motivation Related work Problem definition Inhomogeneous Continuous-Time Markov (ICTM) model for temporal and spatial mobility prediction Empirical evaluation Conclusions and future work MobiGIS 2012, Redondo Beach, CA

5. Related Work Movement prediction approaches that have been proposed in the last 10 years can be classified along 4 major dimensions: Prediction model: • Discrete-time Markov model based vs. sequential rule / trajectory pattern based Model basis / generality: • General model for all objects vs type-base model for similar (type of) objects vs. specific model for each individual object Definition of Regions Of Interest (ROI) for prediction: • Applicationspecific ROIs vs. density-based ROIs vs. grid-based ROIs Prediction provision: • Sequential spatial prediction (loc. of next ROI) vs. spatio-temporalprediction MobiGIS 2012, Redondo Beach, CA

6. Shortcoming of Existing Approaches Spatio-temporal (where and when) prediction models are sequential rule based / trajectory pattern based methods Temporal and periodic regularities at different scale need different models Individual models are expensive and difficult to combine  Instead: Dynamically weighted ensemble of Inhomogeneous Continuous-Time Markov (ICTM) models to capture the temporal-, periodic- and sequential regularities in movements to predict when and where the object will move next. MobiGIS 2012, Redondo Beach, CA

7. Outline Motivation Related work Problem definition Inhomogeneous Continuous-Time Markov (ICTM) model for temporal and spatial mobility prediction Empirical evaluation Conclusions and future work MobiGIS 2012, Redondo Beach, CA

8. Problem Definition Given: moving object trajectory: • Ordered sequence of timestamped Euclidean locations Def: staytimein region R: Def: A set of mutually exclusive regions is prevalent and maximally discriminant (pmd-regions) ifthe total area of the regions in is minimal and Given the current region and the trajectory history upto time t predict: • Departure time t+s* as: • Next region as: MobiGIS 2012, Redondo Beach, CA

9. Outline Motivation Related work Problem definition Inhomogeneous Continuous-Time Markov (ICTM) model for temporal and spatial mobility prediction Empirical evaluation Conclusions and future work MobiGIS 2012, Redondo Beach, CA

10. Method Overview Preprocessing Grid-based spatial aggregation of temporal mobility statistics Grid-based detection of pmd-regions Tracking the evolution of pmd-regions Conversion from grid-based to region-based trajectory • Grid-based staytime statistics: g • pmd-regions: reg • pmd-regionvisit and transition statistics: reg_vis_trans Prediction Individual ICTM model parameter estimation via temporal domain projection and sequential, spatial and temporal constraints Weighted ensemble of ICTM models for prediction Departure time and next region MobiGIS 2012, Redondo Beach, CA

11. Grid-based Detection of pmd-regions Greedy spatially contiguous region growing of ”dense” grid cells until the min_rp-requirement for the extracted pmd-regions is met Definition of dense grid cell: • Staytime in grid cells exhibit power law distribution • Head part of the distribution tends to be qualitatively different and have distinct semantic meaning •  Grid cells in the head of the distribution (above the mean) are ”dense” MobiGIS 2012, Redondo Beach, CA

12. Tracking the Evolution of pmd-regions Grid-based mobility statistics change over time  pmd-regions evolve: shift, grow, shrink, disappear, reappear or emerge Tracking method: • Detect current pmd-regions • Spatially intersect current pmd-regions with pmd-regions from the past • Assign the ID of the intersected old pmd-region to the current pmd-region and update the spatial information according to the current pmd-region • Assign a new unique ID to any remaining current pmd-region and store it’s spatial information MobiGIS 2012, Redondo Beach, CA

13. Conversion from Grid-based to Region-based Trajectory Grid-based trajectory stream • Filter noisy GPS readings via buffering: • Valid arrival: minimum staytime threshold (min_tst) • Valid departure: maximum interruption time threshold (max_tint) Region-based trajectory stream Store in DB reg_vis_trans: <reg_id, arr_time, dep_time, prv_reg, nxt_reg, date, day_of_week, isweekend> MobiGIS 2012, Redondo Beach, CA

14. Continuous-Time Markov (CTM) Process Markov property: If is independent of t then the transition probabilities are homogeneous, otherwise the transition probabilities are inhomogeneous ICTM model. MobiGIS 2012, Redondo Beach, CA

15. Applicability of the ICTM Model The holding times in a state of a CTM process must be memoryless  exponentially distributed Transition probabilities are: • Temporally inhomogeneous: pattern drift • Periodically inhomogeneous: daily, weekly, weekend-weekday patterns • Sequentially inhomogeneous: sequential patterns (daycace  work  daycare) MobiGIS 2012, Redondo Beach, CA

16. Prediction Using the ICTM Model State space S (i.e., set of pmd-regions) Transition rateqij: number of times the process transitions from state i to state j in the unit time interval Rate parameter: Transition probability: pij = qij / vi Probability that the process remains in state i during (t, t+s] is: Departure time / staytime prediction: Next region prediction: MobiGIS 2012, Redondo Beach, CA

17. Estimation of Temporally Inhomogeneous Transition Rates Given that the object has arrived at the current pmd-region R_c at time t_a on date d_a and that the previous pmd-regions visited by the object was R_p: MobiGIS 2012, Redondo Beach, CA

18. Estimation of Periodically Inhomogeneous Transition Rates Given that the object has arrived at the current pmd-region R_c at time t_a on date d_a and that the previous pmd-regions visited by the object was R_p: MobiGIS 2012, Redondo Beach, CA

19. Estimation of Sequentially Inhomogeneous Transition Rates Given that the object has arrived at the current pmd-region R_c at time t_a on date d_a and that the previous pmd-regions visited by the object was R_p: MobiGIS 2012, Redondo Beach, CA

20. Weighted Ensemble of ICTM Models Given ICTM models M1,…,Mdthat capture different aspects of inhomogeneity PrM(i(s)|i): probability according to model M that the process remains in state i during the next s time units PrM(j|i): probability according model M that the process will transition from the current state i to the next state j Prediction using a weighted ensemble of models: • Departure time / staytime prediction: • Next region prediction: MobiGIS 2012, Redondo Beach, CA

21. Model Weights in the Ensemble Transitions rates of an ICTM model are estimated on the basis of a query condition QC and an evidence set EQC Importance of a model M with query condition QC over a finite-domain dimension D and evidence set EQC should be: • directly proportional to the relative size of the evidence set, |EQC|/|E0|, and • inversely proportional to the relative expected domain selectivity of the query condition, SD(QC)/SD(0), where SD(.) returns the size of its argument w.r.t. D MobiGIS 2012, Redondo Beach, CA

22. Outline Motivation Related work Problem definition Inhomogeneous Continuous-Time Markov (ICTM) Model for temporal and spatial mobility prediction Empirical evaluation Conclusions and future work MobiGIS 2012, Redondo Beach, CA

23. Empirical Evaluation Test environments: • 64-bit Windows 7 on Intel core i7 2630 QM with 8GB RAM • Android 2.3.7 on HTC G7 with 1GHz CPU and 512 MB RAM Data set: • Subset of the GeoLife: Trajectories of top 10 users with highest average sampling rate, longest continuous sampling period, and least amount of sampling gaps • 210,000 - 640,000 samples for 19 – 61 observation days Prediction performance measures: • Absolute Temporal Prediction Error (ATPE): lower the better [0, inf] (time units) • Relative Temporal Prediction Error (RTPE): lower the better [0, inf] • Overall Spatial Prediction Accuracy (OSPA): higher the better [0,1] • True Spatial Prediction Confidence (TSPC): higher the better [0,1] • False Spatial Prediction ”Confusion” (FSPC): lower the better [0,1] Baseline: rule-based prediction method with batch learning advantage MobiGIS 2012, Redondo Beach, CA

24. CPU and Battery Consumption Results CPU • Grid-based mobility statistics: 14% of CPU for sampling frequency of 4.7 seconds • pmd-region extraction and tracking: 4.8 seconds (executed infrequently) • Prediction: 1.4 seconds (executed 5-10 times a day) Battery: • Transient consumption is 47µAh/sec • On a 1300mAh battery application can run 7.68 hours With a sampling frequency of 1 minute (still yielding acceptable grid-based mobility statistics) the application can run 10-12 times longer than 7.68 hours. MobiGIS 2012, Redondo Beach, CA

25. Temporal Prediction Performance Results Individual ICTM models: Mtod, Mdow, and Mww Weighted ensemble ICTM models: Msta, Mdyn and Mbat Baseline: Mrule MobiGIS 2012, Redondo Beach, CA

26. Spatial Prediction Performance Results Individual ICTM models: Mtod, Mdow, and Mww Weighted ensemble ICTM models: Msta, Mdyn and Mbat Baseline: Mrule MobiGIS 2012, Redondo Beach, CA

27. Outline Motivation Related work Problem definition Inhomogeneous Continuous-Time Markov (ICTM) Model for temporal and spatial mobility prediction Empirical evaluation Conclusions and future work MobiGIS 2012, Redondo Beach, CA

28. Conclusion and Future Work Dynamically weighted ensemble of ICTM models, Mdyn, can simply and effectively capture the temporal-, periodic- and sequential- regularities in object movement In the long run perf(Mdyn)  perf(Mbat) > perf(Mrule) • Predict departure time within 45 minutes of actual departure time • Predict next region correctly in 67% of the cases Future work • Investigate other dynamical weighting schemes • How to perform prediction using the ICTM model fro a group of socially related individuals? MobiGIS 2012, Redondo Beach, CA

29. Thank you for your attention! Q/A? MobiGIS 2012, Redondo Beach, CA