Learning Location Correlation From GPS Trajectories

Yu Zheng

Microsoft Research Asia

March 16, 2010

Background

2

Locations are correlated in the space of human behaviorThese location might not belong to the same business categoriesThey would not be co-located

Cafe Cinema

Different categories

Jewel shop A

Jewel shop B

Jewel shop C

Far awayFar away

Far away

What We Do

Mine the correlation between locations from GPS trajectoriesThe relation between locations in the space of human behaviorEnable a location recommendation system

3

Challenges

The correlation between locations depends onSequence between locations being visitedThe travel experience (knowledge) of a user accessing these locations

4

A B C A C B CA

u1 u2 u3Trip1 Trip2 Trip3

B

1 20 1 20 1 20

A B C A C B CA

u1 u2 u3Trip1 Trip2 Trip3

B

1 20 1 20 1 20≠

e.g., One-way, accessibility

Cor(A, B)>Cor(A, C)>Cor(A,D)

Tourist

Local expert

A B C

1 20

D

3

A B C A C B CA

u1 u2 u3Trip1 Trip2 Trip3

B

1 20 1 20 1 20

A B C A C B CA

u1 u2 u3Trip1 Trip2 Trip3

B

1 20 1 20 1 20

CorExpert(A, B)>CorTourist(A, B)

Could be random access

Methodology

5

Modeling human location history

Inferring user experiences

Computing location correlation

Personalized location recommender

Solution – Step 1: Modeling human location history GPS logs P and GPS trajectory

Stay points S={s1, s2,…, sn}.Stands for a geo-region where a user has stayed for a whileCarry a semantic meaning beyond a raw GPS point

Location history: represented by a sequence of stay pointswith transition intervals

p4

p3

p5

p6

p7

A Stay Point S

p1

p2

Latitude, Longitude, Time

p1: Lat1, Lngt1, T1

p2: Lat2, Lngt2, T2

………...pn: Latn, Lngtn, Tn

𝐿𝑜𝑐𝐻= (𝑠1 ∆𝑡1ሱሮ 𝑠2 ∆𝑡2

ሱሮ ,…,∆𝑡𝑛−1ሱۛ ۛ ሮ 𝑠𝑛)

GPS Logs of User 1

GPS Logs of User 2

GPS Logs of User n

GPS Logs of User i

GPS Logs of User i+1

GPS Logs of User n-1

Stands for a stay point SStands for a stay point cluster cij

{C }High

Low

Shared Hierarchical Framework

c10

c20 c21

c30 c31 c32 c33 c34

1. Stay point detection

2. Hierarchical clustering

l1

G3

G1

G2

c30

c31

c32

c33

c34

c20

c21 l2

l3

3.Graph Building

Solution – 2. Infer a user’s experience

Mutual reinforcement relationshipA user with rich travel knowledge are more likely to visit more interesting locationsA interesting location would be accessed by many users with rich travel knowledge

A HITS-based inference modelUsers are hub nodesLocations are authority nodesTopic is the geo-region

8

9

Users: Hub nodes

Locations: Authority nodes

The HITS-based inference model

Solution – 3. Mining the location correlation

The correlation between locations can be represented by the sum of the experiences of the users taking this sequence

10

A B C A C B CA

u1 u2 u3Trip1 Trip2 Trip3

B

1 20 1 20 1 20

𝐶𝑜𝑟ሺ𝐴,𝐵ሻ= 𝑒1 𝐶𝑜𝑟ሺ𝐵,𝐶ሻ= 𝑒1

𝐶𝑜𝑟ሺ𝐴,𝐵ሻ= 𝛼∙𝑒𝑘𝑢𝑘∈𝑈′

Trip 1:

𝐶𝑜𝑟ሺ𝐴,𝐶ሻ= 12∙𝑒1 𝐶𝑜𝑟ሺ𝐴,𝐶ሻ= 𝑒2 𝐶𝑜𝑟ሺ𝐶,𝐵ሻ= 𝑒2 𝐶𝑜𝑟ሺ𝐴,𝐵ሻ= 12∙𝑒2 𝐶𝑜𝑟ሺ𝐵,𝐴ሻ= 𝑒3,𝐶𝑜𝑟ሺ𝐴,𝐶ሻ= 𝑒3,𝐶𝑜𝑟ሺ𝐵,𝐶ሻ= 12∙𝑒3 𝐶𝑜𝑟ሺ𝐵,𝐴ሻ= 𝑒3,𝐶𝑜𝑟ሺ𝐴,𝐶ሻ= 𝑒3,𝐶𝑜𝑟ሺ𝐵,𝐶ሻ= 12∙𝑒3 𝐶𝑜𝑟ሺ𝐵,𝐴ሻ= 𝑒3,𝐶𝑜𝑟ሺ𝐴,𝐶ሻ= 𝑒3,𝐶𝑜𝑟ሺ𝐵,𝐶ሻ= 12∙𝑒3

Trip 2:Trip 3:

𝐶𝑜𝑟ሺ𝐴,𝐵ሻ= 𝑒1 + 12∙𝑒2

𝐶𝑜𝑟ሺ𝐴,𝐶ሻ= 12∙𝑒1 + 𝑒2 + 𝑒3

Personalized Recommendation

Integrate the location correlation into a CF modelUser-location matrixSlope-One: an item-based CF model

11

𝑃൫𝑟𝑝𝑗൯= σ (𝑑𝑒𝑣𝑗,𝑖+𝑟𝑝𝑖 )∙|𝑆𝑗,𝑖(𝒳)|𝑖∈𝑆൫𝑅𝑝൯∧𝑖≠𝑗σ |𝑆𝑗,𝑖(𝒳)|𝑖∈𝑆൫𝑅𝑝൯∧𝑖≠𝑗

𝑃൫𝑟𝑝𝑗൯= σ (𝑑𝑒𝑣𝑗,𝑖 + 𝑟𝑝𝑖) ∙𝑐𝑗𝑖𝑖∈𝑆൫𝑅𝑝൯∧𝑖≠𝑗σ 𝑐𝑗𝑖𝑖∈𝑆൫𝑅𝑝൯∧𝑖≠𝑗

𝑀=𝑙0 𝑙1 𝑙2 𝑙3 𝑙4𝑢0𝑢1𝑢2𝑢3

൦

1 1 0 0 01 1 2 0 00 0 1 0 20 0 0 1 1൪

Slope-One model

Our method

𝑐𝑗𝑖

Experimental Settings

60 Devices and 136 usersFrom May 2007 ~ present

12

16%

45%

30%

9%

age<=22 22<age<=25

26<=age<29 age>=30

18%14%

10%58%

Microsoft emplyeesEmployees of other companies Government staffColleage students

• A large-scale GPS dataset (by Feb. 18, 2009)– 10+ million GPS points– 260+ million kilometers– 36 cities in China and a few city in the USA, Korea and Japan

Results

OursThe Pearson Correlation-

Based CF modelThe Weighted Slope

One Algorithm

NDCG@5 0.840 0.862 0.762

NDCG@10 0.922 0.938 0.891

MAP 0.798 0.804 0.665

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• Effectiveness• Perform a user study-based evaluation• Metric: NDCG & MAP• More effective than the slop-one-based method • Same performance with the Pearson correlation-based CF

Results

• Efficiency– Faster than the Pearson-based one– Almost have the same efficiency as the slop one

15

05

10152025303540

The Pearson Correlation-Based

Model

The Weighted Slope One Algorithm

Ours (Experience + Sequentiality)

Ours (Sequentiality)

Com

puti

ng T

imes

Per

Per

dict

ion (E+04)

Methods

Computing Complexity

Conclusion

The correlation between locations in the space of human behaviorSequence propertyUser experience

Conduct a personalized location recommender based on the correlationThe recommender is

Efficient than the Pearson correlation-based method and Effective than the slop one based approach

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Thanks!

yuzheng@microsoft.com

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