Modelling heterogeneous location habits in human populations for location

prediction under data sparsity

James McInerney1, Jiangchuan Zheng2, Alex Rogers1, Nick Jennings1

1. University of Southampton, United Kingdom2. Hong Kong University of Science and Technology, China

jem1c10@ecs.soton.ac.uk

UbiCompZurich, Switzerland

11th September 2013

2

Applications of Mobility Models

3

Applications of GroupMobility Models

Across domains:

– Exploration (e.g. visual summary of many individuals' behaviour; answer “what if?” by modifying parameters)

– Inference (e.g. find out who is similar to whom; step towards semantic labelling)

– Prediction (e.g. alleviate data sparsity in individual prediction; prediction conditioned on other people's locations)

4

Existing Group Mobility Work

Limited by assuming:

– Knowledge of the social network e.g., De Domenico et al. (2012), Sadilek et al. (2012)

– Prior semantic labelling e.g., Eagle & Pentland (2009)

5

Existing Group Mobility Work

Limited by assuming:

– Knowledge of the social network e.g., De Domenico et al. (2012), Sadilek et al. (2012)

– Prior semantic labelling e.g., Eagle & Pentland (2009)

Restrictive when considering large groups of possibly unconnected individuals

6

Existing Group Mobility Work

Limited by assuming:

– Knowledge of the social network e.g., De Domenico et al. (2012), Sadilek et al. (2012)

– Prior semantic labelling e.g., Eagle & Pentland (2009)

Restrictive when considering large groups of possibly unconnected individuals = populations

7

Our Individual Mobility Model

Idea: assign latent location habit to each observation

Location habit :=

Location +

Time of day +

Day of week

8

Our Individual Mobility Model

Idea: assign latent location habit to each observation

Location habit :=

Location +

Time of day +

Day of week

tn » N (µkµkµk)

dn » M(¯k¯k¯k)

x n » N (ÁkÁkÁk)

9

Periodic Location Behaviour

[Krumm & Brush, Pervasive (2011)]

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How Many Latent Habits?

Use a Dirichlet process

where Ni = ® for new habit

p(hn = ijh1::n¡1) /Ni

N + ®

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How Many Latent Habits?

Use a Dirichlet process

1 2 3

h1h3

h5

h2h4

Chinese restaurant process (CRP) interpretation:

where Ni = ® for new habit

p(hn = ijh1::n¡1) /Ni

N + ®

12

How Many Latent Habits?

Use a Dirichlet process

(where ® = 1)

1 2 3

h1h3

h5

h2h4

Chinese restaurant process (CRP) interpretation:

where Ni = ® for new habit

p(hn = ijh1::n¡1) /Ni

N + ®

p(h6jh1 = 1; h2 = 2; h3 = 1; h4 = 3; h5 = 1) =

µ1

2

1

6

1

6

1

6

¶

13

Generative ProcessFor each observation n: 1..N of a single individual:

1. Assign observation (e.g., h6 ) to a table (e.g., 3) using CRP

2. Draw spatial and temporal components of the observation

1 2 3

h1h3

h5

h2h4 h6

x 6 » N (Á3)

t6 » N (µ3)

d6 » M(¯3) Wednesday

2:31pm

(47:407877; 8:508089)

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Modelling Populations Requires Unified Model

– Strength in population exploration, inference, and prediction comes from shared parameters

– But too much sharing leads to inflexibility

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Modelling Populations Requires Unified Model

– Strength in population exploration, inference, and prediction comes from shared parameters

– But too much sharing leads to inflexibility

Implication: we want global pool of habits but individual mixture proportions and spatial parameters.

16

Hierarchical Dirichlet Process Expresses Topic Heterogeneity

– Globally shared set of topics (e.g., [car, drive, wheel, road] and [film, movie, actor, star, blockbuster]) but each document expresses topics to different extents

Article 1 Article 2

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Hierarchical Dirichlet Process Expresses Topic Heterogeneity

– Globally shared set of topics (e.g., [car, drive, wheel, road] and [film, movie, actor, star, blockbuster]) but each document expresses topics to different extents

Article 1 Article 2

18

Extension to Mobility Analysis

– Observing continuous locations and times instead of discrete words

– Shared locations is overly restrictive assumption

→ keep spatial parameters local to individuals

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LocHDP

Shaded nodes = known values

Square nodes = hyperparameters

Round nodes = random variables

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Simplifying Assumption of Habits

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Predictive Density

p(x¤jt¤; d¤;x1::Nx1::Nx1::N ; t1::N ; d1::Nd1::Nd1::N)

/Zp(x1:Nx1:Nx1:N ; t1:N ; d1:Nd1:Nd1:N jh1::Nh1::Nh1::N ; ´́́)p(´́́)dh1::Nh1::Nh1::Nd´́́

(Hyperparameters omitted)

22

Predictive Density

p(x¤jt¤; d¤;x1::Nx1::Nx1::N ; t1::N ; d1::Nd1::Nd1::N)

/Zp(x1:Nx1:Nx1:N ; t1:N ; d1:Nd1:Nd1:N jh1::Nh1::Nh1::N ; ´́́)p(´́́)dh1::Nh1::Nh1::Nd´́́

(Hyperparameters omitted)

Intractable, so use Gibbs sampling on hierarchical version of CRP, the Chinese restaurant franchise [Teh et al. 2006]

23

Nokia Dataset

– Nokia Lausanne dataset (38 individuals, 1 year)

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Applications

– Exploration (e.g. visual summary of many individuals' behaviour; answer “what if?” by modifying parameters)

– Inference (e.g. find out who is similar to whom; step towards semantic labelling)

– Prediction (e.g. alleviate data sparsity in individual prediction; prediction conditioned on other people's locations)

25

Experiment 1: Can LocHDP Help Overcome Data Sparsity?

Methodology:

– Simulate arrival of new user by truncating their observation history (real data)

– Gradually introduce longer history (independent variable)

– Examine predictive performance (dependent variable)

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Experiment 1: Can LocHDP Help Overcome Data Sparsity?

(Error bars indicate 95% confidence range)

27

Exploration Using LocHDPGPS (normalised) Day of Week Time of Day

Latitude

Longitude

Pr Pr

28

Experiment 1: Can LocHDP Help Overcome Data Sparsity?

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Experiment 2: How Many Auxiliary Users Needed?

(Error bars indicate 95% confidence range)

30

Applications

– Exploration (e.g. visual summary of many individuals' behaviour; answer “what if?” by modifying parameters)

– Inference (e.g. find out who is similar to whom; step towards semantic labelling)

– Prediction (e.g. alleviate data sparsity in individual prediction; prediction conditioned on other people's locations)

31

Exploration Using LocHDP

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Conclusions

– LocHDP unified model for location behaviour in populations that retains individual predictive/descriptive power

– Applied to help overcome data sparsity for individual prediction in ubiquitous systems

– Factor 2.4 benefit with < 2 weeks data for new users in Nokia dataset

– Maximum benefit achieved with pool of 10 established users

33

Future Work

– Test on many more users: Openpaths dataset (GPS), Orange Ivory Coast dataset (cell tower)

– Faster variational Bayes derivation for parameter inference

– Fuller exposition of capabilities of unified model, i.e., show what can be done further in exploration and inference

34

Future Work

– Test on many more users: Openpaths dataset (GPS), Orange Ivory Coast dataset (cell tower)

– Faster variational Bayes derivation for parameter inference

– Fuller exposition of capabilities of unified model, i.e., show what can be done further in exploration and inference

Thank you – Poster P42 on Thursday at 12:40pm

jem1c10@ecs.soton.ac.uk