when and where next: individual mobility prediction

When And Where Next: Individual Mobility Prediction

Gyözö Gidofalvi and Fang Dong

Geodesy and Geoinformatics

KTH – Royal Institute of Technology

Outline

Motivation Related work Problem definition Inhomogeneous Continuous-Time Markov (ICTM) model for temporal

and spatial mobility prediction Empirical evaluation Conclusions and future work

2012-11-06 MobiGIS 2012, Redondo Beach, CA 2

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


Outline




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: Application specific ROIs vs. density-based ROIs vs. grid-based ROIs

Prediction provision: Sequential spatial prediction (loc. of next ROI) vs. spatio-temporal prediction


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.


Outline




Problem Definition

Given: moving object trajectory: Ordered sequence of timestamped Euclidean locations

Def: staytime in region R:

Def: A set of mutually exclusive regions is

prevalent and maximally discriminant (pmd-regions) if the 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:


Outline




Method Overview


Preprocessing

Prediction

1. Grid-based spatial aggregation of temporal mobility statistics

2. Grid-based detection of pmd-regions3. Tracking the evolution of pmd-regions4. Conversion from grid-based to region-based

trajectory

• Grid-based staytime statistics: g

• pmd-regions: reg• pmd-region visit and

transition statistics: reg_vis_trans

1. Individual ICTM model parameter estimation via temporal domain projection and sequential, spatial and temporal constraints

2. Weighted ensemble of ICTM models for prediction

Departure time and next region

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”


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:1. Detect current pmd-regions

2. Spatially intersect current pmd-regions with pmd-regions from the past

3. 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

4. Assign a new unique ID to any remaining current pmd-region and store it’s spatial information


Conversion from Grid-based to Region-based Trajectory


Grid-based trajectory stream

Region-based trajectory stream

reg_vis_trans: <reg_id, arr_time, dep_time, prv_reg, nxt_reg, date, day_of_week, isweekend>

Filter noisy GPS readings via buffering:•Valid arrival: minimum staytime threshold (min_tst)•Valid departure: maximum interruption time threshold (max_tint)

Store in DB

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.


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)


Prediction Using the ICTM Model

State space S (i.e., set of pmd-regions) Transition rate qij : 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:


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:


Estimation of Periodically Inhomogeneous Transition Rates



Estimation of Sequentially Inhomogeneous Transition Rates



Weighted Ensemble of ICTM Models

Given ICTM models M1,…,Md that 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:


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


Outline

Motivation Related work Problem definition Inhomogeneous Continuous-Time Markov (ICTM) Model for temporal



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


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.


Temporal Prediction Performance Results

Individual ICTM models: Mtod, Mdow, and Mww

Weighted ensemble ICTM models: Msta, Mdyn and Mbat

Baseline: Mrule


Spatial Prediction Performance Results

Individual ICTM models: Mtod, Mdow, and Mww

Weighted ensemble ICTM models: Msta, Mdyn and Mbat

Baseline: Mrule


Outline

Motivation Related work Problem definition Inhomogeneous Continuous-Time Markov (ICTM) Model for temporal



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?


Thank you for your attention!

Q/A?


when and where next: individual mobility prediction

Documents

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spatiotemporal prediction2012

future work2012