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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

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when and where next individual mobility prediction

When And Where Next: Individual Mobility Prediction

GyözöGidofalvi and Fang Dong

Geodesy and Geoinformatics

KTH – Royal InstituteofTechnology

outline
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

motivation
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

outline1
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

related work
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

shortcoming of existing approaches
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

outline2
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

problem definition
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

outline3
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

method overview
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

grid based detection of pmd regions
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

tracking the evolution of pmd regions
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

conversion from grid based to region based trajectory
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:

nxt_reg, date, day_of_week, isweekend>

MobiGIS 2012, Redondo Beach, CA

continuous time markov ctm process
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

applicability of the 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)

MobiGIS 2012, Redondo Beach, CA

prediction using the ictm model
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

estimation of temporally inhomogeneous transition rates
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

estimation of periodically inhomogeneous transition rates
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

estimation of sequentially inhomogeneous transition rates
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

weighted ensemble of ictm models
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

model weights in the ensemble
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

outline4
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

empirical evaluation
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

cpu and battery consumption results
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

temporal prediction performance results
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

spatial prediction performance results
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

outline5
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

conclusion and future work
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

slide29
Thank you for your attention!

Q/A?

MobiGIS 2012, Redondo Beach, CA

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